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Kombinatorik & Graphentheorie » Graphentheorie » Streichholzgraphen 4-regulär und 4/n-regulär (n>4) und 2/5
Thema eröffnet 2016-02-17 22:35 von Slash
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Kein bestimmter Bereich Streichholzgraphen 4-regulär und 4/n-regulär (n>4) und 2/5
Slash
Aktiv Letzter Besuch: in der letzten Woche
Dabei seit: 23.03.2005
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Wohnort: Westerburg
  Beitrag No.1880, vom Themenstarter, eingetragen 2020-01-12

Ich habe, wie man auch dem Code entnehmen kann, den Graphen symmetrisch aufgebaut. Linkes unteres Viertel, an P13 und P19 gespiegelt, dann P37 eingesetzt. Wenn ich jetzt zuerst P35,P37 bzw. P17,P37 (Kante nicht gezeichnet!) auf 1 bringe und dann P18,P19 gibt es genau zwei Möglichkeiten von denen keine funktioniert. Sind die beiden Rauten an P37 groß wird der Graph "aufgebläht" mit 60 Grad Winkeln, sind die Rauten schmal verschwinden sie weil P17 und P18, sowie P35 und P36 zusammenfallen. 37 Knoten, 3×Grad 2, 3×Grad 3, 30×Grad 4, 1×Grad 5, 0? Überschneidungen 70 Kanten, minimal 0.99999999796318217449, maximal 1.00000000000000133227 einzustellende Kanten, Abstände und Winkel: |P35-P37|=0.99999999796318217449 |P18-P19|=0.99999999898158853373 $ %Eingabe war: % %4-regulärer Graph % % % % % % %P[1]=[199.99999996225333,-60.6264089832257]; %P[2]=[253.58572859643078,-91.56300388649035]; D=ab(1,2); A(2,1); L(3,1,2); L(4,3,2); L(5,4,2); %M(6,1,3,blue_angle,2,green_angle,2); %N(14,3,4); N(15,10,8); N(16,6,14); N(17,16,14); N(18,15,16); N(19,12,15); %A(18,19); %A(13,19,ab(13,19,[1,19],"gespiegelt")); %N(37,36,18); %RA(35,37); %RA(18,19); % % % %Ende der Eingabe. % Streichholzgraphen mit pgfplots, TikZ/pgf % v3.1a %\documentclass[margin=5mm, tikz]{standalone} %\usetikzlibrary{angles, quotes, babel} \usetikzlibrary{spy}%<- Neu \tikzset{SpyStyle/.style={ spy using outlines={rectangle, magnification=3, width=7.5cm, height=3cm, connect spies} }}%<- Neu %\usepackage{pgfplots} %\usepgfplotslibrary{patchplots} %\pgfplotsset{compat=1.13} % Eingaben =========================== \def\DefaultTextposition{south} % south west % etc. \def\AusnahmeTextposition{north} \def\AusnahmeListe{8,29} % Möglichst eingeben: \xdef\BeliebigesVorhandenesKoordinatenpaar{{3.46413352268023189140,3.99999999745406631391}} % 0,0 \colorlet{Kantenfarbe}{gray} \colorlet{Punktfarbe}{red} \def\Beschriftung{\punktnummer} % \punktnummer oder {} leer \pgfplotsset{ x=12mm, y=12mm, % Maßstab % width=20cm, height=5cm, % oder Bildmaße } \tikzset{font=\scriptsize} % Schrift Punktnummern und Winkel % =========================== %Unterprogramm, das Mehrfachplatzierung (je nach Pfadanzahl) % von Punktbezeichnungen verhindert ======= \xdef\LstPN{0} \newif\ifDupe \pgfplotsset{avoid dupes/.code={\Dupefalse \xdef\anker{\DefaultTextposition} % Default \foreach \X in \LstPN {\pgfmathtruncatemacro{\itest}{ifthenelse(\X==\punktnummer,1,0)} \ifnum\itest=1 \global\Dupetrue \breakforeach \fi} \ifDupe % auskommentieren: \typeout{\punktnummer\space ist\space ein\space Duplikat!}% \xdef\punktnummer{} %löscht mehrfache Nummern %\pgfkeysalso{/tikz/opacity=1} % macht mehrfache Nummern unsichtbar \else \xdef\LstPN{\LstPN,\punktnummer} \typeout{\punktnummer\space ist\space neu\space mit\space urprgl.\space Anker=\anker} \foreach \X in \LstExcept {\ifnum\X=\punktnummer %\pgfkeysalso{/tikz/anchor=-90} \xdef\anker{\AusnahmeTextposition} \fi} \typeout{\punktnummer\space ist\space neu\space mit\space Anker=\anker} \fi}} % ============ \begin{document} \xdef\LstExcept{\AusnahmeListe} % Für Zeichnung der Winkel \pgfdeclarelayer{bg} % declare background layer \pgfsetlayers{bg,main} % set the order of the layers (main is the standard % Aliaswerte für Aliasplot (Winkelplot) \pgfmathsetmacro{\xAlias}{\BeliebigesVorhandenesKoordinatenpaar[0]} \pgfmathsetmacro{\yAlias}{\BeliebigesVorhandenesKoordinatenpaar[1]} %\xAlias, \yAlias \begin{tikzpicture}[SpyStyle] % Punkte und Kanten ======================== \begin{axis}[hide axis, colormap={kantenfarbe}{color=(Kantenfarbe) color=(Kantenfarbe)}, thick, % Kanten ] \addplot+[mark size=1.125pt, mark options={Punktfarbe}, table/row sep=newline, patch, % Plot-Typ patch type=polygon, vertex count=2, % damit nur Kanten, keine Flächen, gezeichnet werden % % Angabe der Verbindungskanten ===================== patch table with point meta={ Startpkt Endpkt colordata \\ 1 1 \\ 2 1 \\ 3 1 \\ 3 2 \\ 4 3 \\ 4 2 \\ 5 4 \\ 5 2 \\ 6 1 \\ 7 1 \\ 7 6 \\ 8 7 \\ 8 6 \\ 9 7 \\ 9 8 \\ 10 9 \\ 11 9 \\ 11 10 \\ 12 11 \\ 12 10 \\ 13 11 \\ 13 12 \\ 13 30 \\ 13 31 \\ 14 3 \\ 14 4 \\ 15 10 \\ 15 8 \\ 16 6 \\ 16 14 \\ 17 16 \\ 17 14 \\ 18 15 \\ 18 16 \\ 19 12 \\ 19 15 \\ 19 31 \\ 19 33 \\ 20 20 \\ 21 20 \\ 22 20 \\ 22 21 \\ 23 21 \\ 23 22 \\ 24 21 \\ 24 23 \\ 25 20 \\ 26 20 \\ 26 25 \\ 27 25 \\ 27 26 \\ 28 26 \\ 28 27 \\ 29 28 \\ 30 28 \\ 30 29 \\ 31 29 \\ 31 30 \\ 32 22 \\ 32 23 \\ 33 27 \\ 33 29 \\ 34 25 \\ 34 32 \\ 35 32 \\ 35 34 \\ 35 37 \\ 36 33 \\ 36 34 \\ 36 19 \\ 37 36 \\ 37 18 \\ }, % % Beschriftung visualization depends on={value \thisrowno{0} \as \punktnummer}, every node near coord/.append style={ /pgfplots/avoid dupes,% Methode für Mehrfachplatzierung anwenden }, nodes near coords={\Beschriftung}, nodes near coords style={ anchor=\anker, text=black, %font=\scriptsize, name=p-\punktnummer, % Punkte bennennen path picture={% Jedem Punkt als Koordinate zuordnen: \coordinate[] (P\punktnummer) at (p-\punktnummer.\anker);} }, ] % Koordinatentabelle table[header=true, x index=1, y index=2, row sep=\\] { Nr x y \\ 0 0 0 \\% 0 Aliaspunkt 1 1.73206676133524650751 0.99997236471520989376 \\ 2 2.59810014259226695899 0.49998618235760483586 \\ 3 2.59808418742664182233 1.49998618223032109675 \\ 4 3.46411756868366227380 0.99999999987271626090 \\ 5 3.46413352384928696637 0.00000000000000000000 \\ 6 1.73208271532836000084 1.99997236458794502845 \\ 7 0.86604933465757927280 1.49998618121490534527 \\ 8 0.86606528865069276613 2.49998618108764025791 \\ 9 0.00003190797991197527 1.99999999771460124087 \\ 10 0.86604933465915800994 2.50001381421156265716 \\ 11 0.00001595398995598764 2.99999999758733615352 \\ 12 0.86603338066920210192 3.50001381408429734776 \\ 13 0.00000000000000000000 3.99999999746007173229 \\ 14 3.46410161351803624896 1.99999999974543274384 \\ 15 1.73208271533009372511 2.99999999758433411046 \\ 16 2.59808418625251968948 2.50001381522698107318 \\ 17 3.46411756633548373330 2.99999999961818630823 \\ 18 2.59810014142134315662 3.50001381509969711203 \\ 19 1.73206676134013726198 3.99999999745706880105 \\ 20 1.73206676134564752090 7.00002763019892881857 \\ 21 2.59810014260440258482 7.50001381255353027910 \\ 22 2.59808418743530999961 6.50001381268081424025 \\ 23 3.46411756869406239900 6.99999999503541747714 \\ 24 3.46413352386315542830 7.99999999490813351599 \\ 25 1.73208271533529378772 6.00002763032619323980 \\ 26 0.86604933466624656191 6.50001381370223363376 \\ 27 0.86606528865589349486 5.50001381382949983134 \\ 28 0.00003190798684619460 5.99999999720554111349 \\ 29 0.86604933466435829459 5.49998618070557832027 \\ 30 0.00001595399342309730 4.99999999733280642289 \\ 31 0.86603338067093560415 4.49998618083284274149 \\ 32 3.46410161352496936971 5.99999999516270055011 \\ 33 1.73208271533356072958 4.99999999732980349165 \\ 34 2.59808418625771997412 5.49998617968415359769 \\ 35 3.46411756633895162594 4.99999999528994631959 \\ 36 2.59810014142307643681 4.49998617981143844702 \\ 37 3.46413352268023189140 3.99999999745406631391 \\ }; % =================================== % Zeichnung der Dreiecke ===================== \addplot[no marks, % Aliasplot nodes near coords={},% Aliasplot visualization depends on={value \thisrowno{0} \as \PunktI}, visualization depends on={value \thisrowno{1} \as \PunktII}, visualization depends on={value \thisrowno{2} \as \PunktIII}, nodes near coords style={anchor=center,%Letzer Feinschliff für Aliaswerte path picture={%\pgftransformreset % Winkel zeichnen \begin{pgfonlayer}{bg} % 'select the background layer' für die Winkel \fill[black!10] (p-\PunktI) -- (p-\PunktII) -- (p-\PunktIII) ; \end{pgfonlayer} }},% ] table[header=true, x expr =\xAlias, y expr=\yAlias]{% Hier möglichst vorhandene Koordinaten eintragen Punkt1 Punkt2 Punkt3 }; % Zeichnung der Winkel ===================== \addplot[no marks, % Aliasplot nodes near coords={},% Aliasplot visualization depends on={value \thisrowno{0} \as \PunktI}, visualization depends on={value \thisrowno{1} \as \Scheitel}, visualization depends on={value \thisrowno{2} \as \PunktII}, visualization depends on={value \thisrowno{3} \as \Winkelradius}, visualization depends on={value \thisrowno{4} \as \Winkelfarbe}, visualization depends on={value \thisrowno{5} \as \Winkelname}, visualization depends on={value \thisrowno{6} \as \WinkelExzentrizitaet}, nodes near coords style={anchor=center,%Letzer Feinschliff für Aliaswerte path picture={%\pgftransformreset % Winkel zeichnen \begin{pgfonlayer}{bg} % 'select the background layer' für die Winkel \draw pic [angle radius=\Winkelradius cm,% fill=\Winkelfarbe!40, draw=\Winkelfarbe,%<- Winkel färben / zeichnen %-latex, %<- Winkel mit Pfeil "$\Winkelname$", angle eccentricity =\WinkelExzentrizitaet, text=\Winkelfarbe% ] {angle = P\PunktI--P\Scheitel--P\PunktII}; \end{pgfonlayer} }},% ] table[header=true, x expr =\xAlias, y expr=\yAlias]{% Hier möglichst vorhandene Koordinaten eintragen Punkt1 Scheitel Punkt2 Winkelradius[cm] Winkelfarbe Winkelname WinkelExz 3 1 6 0.5 Blue {} 1.5 \\ 8 9 10 0.5 Green {} 1.5 \\ }; \end{axis} % Annotationen %\node[above=3mm, align=center, font=\tiny] at (P11) {Wichtiger \\ Punkt}; %\draw[purple, very thick] (P8) -- (P10) node[near start, below, align=center, font=\tiny]{Wichtige \\ Kante}; %\begin{pgfonlayer}{bg} %\fill[yellow] (P12) -- (P13) -- (P14) -- cycle; %\end{pgfonlayer} %\foreach \n in \AusnahmeListe %\draw[cyan] (P\n) circle (3pt) %\if\n4 node[anchor=north west, font=\tiny, align=left]{Default-\\position \\ ge{\"a}ndert} \else\fi ; %\spy [red] on (P5) in node at (2.5,-1.25); %einzustellende Kanten, Abstände und Winkel: \draw[green,very thick] (P35) -- (P37); \draw[green,very thick] (P18) -- (P19); %nicht passende Kanten: \end{tikzpicture} \end{document} $ 37 Knoten, 3×Grad 2, 3×Grad 3, 30×Grad 4, 1×Grad 5, 8? Überschneidungen 70 Kanten, minimal 0.99999999999999888978, maximal 1.00000000000000288658 einzustellende Kanten, Abstände und Winkel: |P35-P37|=1.00000000000000088818 |P18-P19|=1.00000000000000288658 $ %Eingabe war: % %4-regulärer Graph % % % % % % %P[1]=[192.03544850833785,-114.13476613030267]; %P[2]=[269.0322607989641,-118.31712787460212]; D=ab(1,2); A(2,1); L(3,1,2); L(4,3,2); L(5,4,2); %M(6,1,3,blue_angle,2,green_angle,2); %N(14,3,4); N(15,10,8); N(16,6,14); N(17,16,14); N(18,15,16); N(19,12,15); %A(18,19); %A(13,19,ab(13,19,[1,19],"gespiegelt")); %N(37,36,18); %RA(35,37); %RA(18,19); % % % %Ende der Eingabe. % Streichholzgraphen mit pgfplots, TikZ/pgf % v3.1a %\documentclass[margin=5mm, tikz]{standalone} %\usetikzlibrary{angles, quotes, babel} \usetikzlibrary{spy}%<- Neu \tikzset{SpyStyle/.style={ spy using outlines={rectangle, magnification=3, width=7.5cm, height=3cm, connect spies} }}%<- Neu %\usepackage{pgfplots} %\usepgfplotslibrary{patchplots} %\pgfplotsset{compat=1.13} % Eingaben =========================== \def\DefaultTextposition{south} % south west % etc. \def\AusnahmeTextposition{north} \def\AusnahmeListe{8,16,18,29,33,35} % Möglichst eingeben: \xdef\BeliebigesVorhandenesKoordinatenpaar{{3.58096098925905748089,3.20968054257941037832}} % 0,0 \colorlet{Kantenfarbe}{gray} \colorlet{Punktfarbe}{red} \def\Beschriftung{\punktnummer} % \punktnummer oder {} leer \pgfplotsset{ x=12mm, y=12mm, % Maßstab % width=20cm, height=5cm, % oder Bildmaße } \tikzset{font=\scriptsize} % Schrift Punktnummern und Winkel % =========================== %Unterprogramm, das Mehrfachplatzierung (je nach Pfadanzahl) % von Punktbezeichnungen verhindert ======= \xdef\LstPN{0} \newif\ifDupe \pgfplotsset{avoid dupes/.code={\Dupefalse \xdef\anker{\DefaultTextposition} % Default \foreach \X in \LstPN {\pgfmathtruncatemacro{\itest}{ifthenelse(\X==\punktnummer,1,0)} \ifnum\itest=1 \global\Dupetrue \breakforeach \fi} \ifDupe % auskommentieren: \typeout{\punktnummer\space ist\space ein\space Duplikat!}% \xdef\punktnummer{} %löscht mehrfache Nummern %\pgfkeysalso{/tikz/opacity=1} % macht mehrfache Nummern unsichtbar \else \xdef\LstPN{\LstPN,\punktnummer} \typeout{\punktnummer\space ist\space neu\space mit\space urprgl.\space Anker=\anker} \foreach \X in \LstExcept {\ifnum\X=\punktnummer %\pgfkeysalso{/tikz/anchor=-90} \xdef\anker{\AusnahmeTextposition} \fi} \typeout{\punktnummer\space ist\space neu\space mit\space Anker=\anker} \fi}} % ============ \begin{document} \xdef\LstExcept{\AusnahmeListe} % Für Zeichnung der Winkel \pgfdeclarelayer{bg} % declare background layer \pgfsetlayers{bg,main} % set the order of the layers (main is the standard % Aliaswerte für Aliasplot (Winkelplot) \pgfmathsetmacro{\xAlias}{\BeliebigesVorhandenesKoordinatenpaar[0]} \pgfmathsetmacro{\yAlias}{\BeliebigesVorhandenesKoordinatenpaar[1]} %\xAlias, \yAlias \begin{tikzpicture}[SpyStyle] % Punkte und Kanten ======================== \begin{axis}[hide axis, colormap={kantenfarbe}{color=(Kantenfarbe) color=(Kantenfarbe)}, thick, % Kanten ] \addplot+[mark size=1.125pt, mark options={Punktfarbe}, table/row sep=newline, patch, % Plot-Typ patch type=polygon, vertex count=2, % damit nur Kanten, keine Flächen, gezeichnet werden % % Angabe der Verbindungskanten ===================== patch table with point meta={ Startpkt Endpkt colordata \\ 1 1 \\ 2 1 \\ 3 1 \\ 3 2 \\ 4 3 \\ 4 2 \\ 5 4 \\ 5 2 \\ 6 1 \\ 7 1 \\ 7 6 \\ 8 7 \\ 8 6 \\ 9 7 \\ 9 8 \\ 10 9 \\ 11 9 \\ 11 10 \\ 12 11 \\ 12 10 \\ 13 11 \\ 13 12 \\ 13 30 \\ 13 31 \\ 14 3 \\ 14 4 \\ 15 10 \\ 15 8 \\ 16 6 \\ 16 14 \\ 17 16 \\ 17 14 \\ 18 15 \\ 18 16 \\ 19 12 \\ 19 15 \\ 19 31 \\ 19 33 \\ 20 20 \\ 21 20 \\ 22 20 \\ 22 21 \\ 23 21 \\ 23 22 \\ 24 21 \\ 24 23 \\ 25 20 \\ 26 20 \\ 26 25 \\ 27 25 \\ 27 26 \\ 28 26 \\ 28 27 \\ 29 28 \\ 30 28 \\ 30 29 \\ 31 29 \\ 31 30 \\ 32 22 \\ 32 23 \\ 33 27 \\ 33 29 \\ 34 25 \\ 34 32 \\ 35 32 \\ 35 34 \\ 35 37 \\ 36 33 \\ 36 34 \\ 36 19 \\ 37 36 \\ 37 18 \\ }, % % Beschriftung visualization depends on={value \thisrowno{0} \as \punktnummer}, every node near coord/.append style={ /pgfplots/avoid dupes,% Methode für Mehrfachplatzierung anwenden }, nodes near coords={\Beschriftung}, nodes near coords style={ anchor=\anker, text=black, %font=\scriptsize, name=p-\punktnummer, % Punkte bennennen path picture={% Jedem Punkt als Koordinate zuordnen: \coordinate[] (P\punktnummer) at (p-\punktnummer.\anker);} }, ] % Koordinatentabelle table[header=true, x index=1, y index=2, row sep=\\] { Nr x y \\ 0 0 0 \\% 0 Aliaspunkt 1 1.79048049462953273725 0.10847735592002018257 \\ 2 2.78900849414339191412 0.05423867796001000108 \\ 3 2.33671656736751387484 0.94610863090907304507 \\ 4 3.33524456688137371785 0.89186995294906323828 \\ 5 3.78753649365725175713 0.00000000000000000000 \\ 6 1.85221375055123615994 1.10657003954880295282 \\ 7 0.95697350323647412118 0.66098626562093287795 \\ 8 1.01870675915817776591 1.65907894924971555106 \\ 9 0.12346651184341590757 1.21349517532184547619 \\ 10 0.95697350323647234482 1.76600408502276184919 \\ 11 0.06173325592170791215 2.21158785895062770521 \\ 12 0.89524024731476437022 2.76409676865154452230 \\ 13 0.00000000000000000000 3.20968054257941037832 \\ 14 2.88295264010549567857 1.78373990589812603247 \\ 15 1.85221375055123660403 2.21158785895062770521 \\ 16 1.93532274310601715150 2.10311050303060698141 \\ 17 2.68572074194429122329 2.76409676865154674275 \\ 18 2.68572074194429477600 2.76409676865154141367 \\ 19 1.79048049462952874045 3.20968054257941037832 \\ 20 1.79048049462953295929 6.31088372923880136511 \\ 21 2.78900849414339369048 6.36512240719881017270 \\ 22 2.33671656736751431893 5.47325245424974760056 \\ 23 3.33524456688137460603 5.52749113220975818450 \\ 24 3.78753649365725175713 6.41936108515882164482 \\ 25 1.85221375055123615994 5.31279104561001869200 \\ 26 0.95697350323647456527 5.75837481953788810074 \\ 27 1.01870675915817821000 4.76028213590910542763 \\ 28 0.12346651184341544960 5.20586590983697572455 \\ 29 0.95697350323647234482 4.65335700013605890746 \\ 30 0.06173325592170772480 4.20777322620819305143 \\ 31 0.89524024731476437022 3.65526431650727623435 \\ 32 2.88295264010549656675 4.63562117926069561236 \\ 33 1.85221375055123727016 4.20777322620819305143 \\ 34 1.93532274310601715150 4.31625058212821333115 \\ 35 2.68572074194429122329 3.65526431650727490208 \\ 36 2.68572074194429477600 3.65526431650727934297 \\ 37 3.58096098925905748089 3.20968054257941037832 \\ 38 3.89 0 0 \\ }; % =================================== % Zeichnung der Dreiecke ===================== \addplot[no marks, % Aliasplot nodes near coords={},% Aliasplot visualization depends on={value \thisrowno{0} \as \PunktI}, visualization depends on={value \thisrowno{1} \as \PunktII}, visualization depends on={value \thisrowno{2} \as \PunktIII}, nodes near coords style={anchor=center,%Letzer Feinschliff für Aliaswerte path picture={%\pgftransformreset % Winkel zeichnen \begin{pgfonlayer}{bg} % 'select the background layer' für die Winkel \fill[black!10] (p-\PunktI) -- (p-\PunktII) -- (p-\PunktIII) ; \end{pgfonlayer} }},% ] table[header=true, x expr =\xAlias, y expr=\yAlias]{% Hier möglichst vorhandene Koordinaten eintragen Punkt1 Punkt2 Punkt3 }; % Zeichnung der Winkel ===================== \addplot[no marks, % Aliasplot nodes near coords={},% Aliasplot visualization depends on={value \thisrowno{0} \as \PunktI}, visualization depends on={value \thisrowno{1} \as \Scheitel}, visualization depends on={value \thisrowno{2} \as \PunktII}, visualization depends on={value \thisrowno{3} \as \Winkelradius}, visualization depends on={value \thisrowno{4} \as \Winkelfarbe}, visualization depends on={value \thisrowno{5} \as \Winkelname}, visualization depends on={value \thisrowno{6} \as \WinkelExzentrizitaet}, nodes near coords style={anchor=center,%Letzer Feinschliff für Aliaswerte path picture={%\pgftransformreset % Winkel zeichnen \begin{pgfonlayer}{bg} % 'select the background layer' für die Winkel \draw pic [angle radius=\Winkelradius cm,% fill=\Winkelfarbe!40, draw=\Winkelfarbe,%<- Winkel färben / zeichnen %-latex, %<- Winkel mit Pfeil "$\Winkelname$", angle eccentricity =\WinkelExzentrizitaet, text=\Winkelfarbe% ] {angle = P\PunktI--P\Scheitel--P\PunktII}; \end{pgfonlayer} }},% ] table[header=true, x expr =\xAlias, y expr=\yAlias]{% Hier möglichst vorhandene Koordinaten eintragen Punkt1 Scheitel Punkt2 Winkelradius[cm] Winkelfarbe Winkelname WinkelExz 3 1 6 0.5 Blue {} 1.5 \\ 8 9 10 0.5 Green {} 1.5 \\ }; \end{axis} % Annotationen %\node[above=3mm, align=center, font=\tiny] at (P11) {Wichtiger \\ Punkt}; %\draw[purple, very thick] (P8) -- (P10) node[near start, below, align=center, font=\tiny]{Wichtige \\ Kante}; %\begin{pgfonlayer}{bg} %\fill[yellow] (P12) -- (P13) -- (P14) -- cycle; %\end{pgfonlayer} %\foreach \n in \AusnahmeListe %\draw[cyan] (P\n) circle (3pt) %\if\n4 node[anchor=north west, font=\tiny, align=left]{Default-\\position \\ ge{\"a}ndert} \else\fi ; %\spy [red] on (P5) in node at (2.5,-1.25); %einzustellende Kanten, Abstände und Winkel: \draw[green,very thick] (P35) -- (P37); \draw[green,very thick] (P18) -- (P19); %nicht passende Kanten: \end{tikzpicture} \end{document} $


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  Beitrag No.1881, eingetragen 2020-01-12

oh mann ist dass komplex im detail, also nochmal ausführlich meine herleitung dargestellt https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/35059_st-stossdaempfer.PNG ich hab eine konstruktion die immer in einem 60° winkel passt, aber elastisch mit nur einem einzigen winkel, ihre länge verändern kann wie ein stossdämpfer von ~3,5 bis 3,99, passt dabei immer noch immer in 60°! diese konstruktion passe ich in der länge auf einen erweiterten kite an, welcher erstaunlicherweise (wiso eigentlich?) auch in einen 60° winkel passt danach halbiere ich den stossdämpfer und setze also 60+30=90° zusammen und kann eine linie des kites umlegen,(die weisse), meine idee oder frage ist jetzt: "wird dies gebilde im 90° winkel beweglicher durch dieses umlegen, immerhin wird der kite ja damit aufgebrochen?" die konstruktion ist soweit absolut stringent und hat mit der grünen länge und vier mal gespiegelt grad 4/6, hat also soweit ab anfang nur vier zu lange strecken (die grünen 1.07er)... noch ohne irgendetwas hinzuziehen slash ich bewundere deine inzwischen erlernten hinzieh fähigkeiten sehr, aber diesmal meinte ich wohl schon meinen aufbau, also im detail irgend wie etwas anderes als du draus gemacht hast https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/35059_st-stossdaempfer2.PNG also kann man, wenn man erstmal die grünen falschen längen weglässt, den ganzen graphen über den kite-rest bewegen oder nicht ? ( z.B. über den winkel bei 6) änderung: die vier blauen waren nur für die geometrische konstruktion gedacht, und sollen für die beweglichkeitsfrage entfernt werden, ich will ja keinen 4/5/6er graphen untersuchen


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StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
Mitteilungen: 4165
Wohnort: Raun
  Beitrag No.1882, eingetragen 2020-01-12

Die beiden untersten (und obersten) blauen Linien sind im letzten Graph gegenüber #1867 rechts hinzugekommen und führen zu vier Knoten von Grad 5. Zuerst der untere linke Teilgraph vom letzten Graph, er soll im 90° Winkel liegen und um das einzustellen werden alle beweglichen Winkel verbraucht. 21 Knoten, 2×Grad 2, 5×Grad 3, 13×Grad 4, 1×Grad 5, 0 Überschneidungen 38 Kanten, minimal 0.99999999999999966693, maximal 1.00000000001218536383 einzustellende Kanten, Abstände und Winkel: |P20-P21|=1.00000000001218536383 ∠(P19-P20,P5-P7)=89.99999999990558308127° ∠(P19-P9,P5-P7)=90.00000000007770495358° $ %Eingabe war: % %#1881 unten % % % % % %P[1]=[-18.11479523711481,-11.925524469941678]; P[2]=[31.542078892652935,-17.77316088651216]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); M(7,6,4,blauerWinkel); L(8,6,7); L(9,8,7); L(10,6,8); N(11,1,10); L(12,1,11); L(13,12,11); L(14,12,13); M(15,13,11,gruenerWinkel); N(16,14,15); L(17,14,16); L(18,17,16); L(19,17,18); N(20,18,15); N(21,15,9); RA(20,21); RK([5,7],[19,20,9],90); % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LimeGreen}{rgb}{0.20,0.80,0.20} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.85122958680809945875/0.23390545666281925552, 2/2.84436706940345462868/0.11695272833140960000, 3/2.44908236188267780520/1.03551138187521774014, 4/3.44221984447803297513/0.91855865354380805687, 5/3.83750455199880979862/0.00000000000000000000, 6/3.04693513695725615165/1.83711730708761633579, 7/3.83750455200284568136/2.44948974277889908180, 8/2.91188975859404752811/2.82795672181774193632, 9/3.70245917363963750191/3.44032915750902468233, 10/2.12132034354845799839/2.21558428612645963440, 11/1.98627496517827872857/1.22474487139463938945, 12/1.06066017176452787041/0.84627789236098616144, 13/1.19570555013470714023/1.83711730709280618434, 14/0.27009075672095617104/1.45865032805915295633, 15/1.98627496517598878256/2.44948974278965048157, 16/1.06066017176823335078/2.07102276374825722272, 17/0.13504537836047808552/2.44948974278965048157, 18/0.92561479340775498770/3.06186217847875497000, 19/0.00000000000000000000/3.44032915752014822885, 20/1.85122958681551041948/3.44032915752014822885, 21/2.77684438023188207012/3.06186217846763097938} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 6/293.28/397.76/0.4/Blue, 13/322.24/397.76/0.4/Green} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/3, 6/4, 7/6, 8/6, 8/7, 9/8, 9/7, 10/6, 10/8, 11/1, 11/10, 12/1, 12/11, 13/12, 13/11, 14/12, 14/13, 15/13, 16/14, 16/15, 17/14, 17/16, 18/17, 18/16, 19/17, 19/18, 20/18, 20/15, 20/21, 21/15, 21/9} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,21} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[LimeGreen,very thick] (p-20) -- (p-21); %\draw[Violet,very thick] (p-5) -- (p-7); %\draw[Violet,very thick] (p-5) -- (p-7); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 6/293.28/397.76/0.4/Blue, 13/322.24/397.76/0.4/Green} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/292, 2/263, 3/83, 4/83, 5/323, 6/308, 7/8, 8/188, 9/68, 10/188, 11/52, 12/292, 13/52, 14/172, 15/248, 16/8, 17/188, 18/8, 19/128, 20/128, 21/8} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Der Graph ist nicht beweglich, wenn die Punkte 19,20,9,7,5 im 90°-Winkel verbleiben sollen. Der Winkel ∠(P19-P9,P5-P7)=90° muss sogar extra bewiesen werden, weil er nicht separat einstellbar ist. Der Graph im Ganzen (Button "Kaleidoskop"): 74 Knoten, 8×Grad 3, 56×Grad 4, 4×Grad 5, 6×Grad 6, 0 Überschneidungen 152 Kanten, minimal 0.99999999999999777955, maximal 1.00000000002292543932 einzustellende Kanten, Abstände und Winkel: |P20-P21|=1.00000000001218536383 ∠(P19-P20,P5-P7)=89.99999999990558308127° ∠(P19-P9,P5-P7)=90.00000000007770495358° $ %Eingabe war: % %#1881 unten % % % % % %P[1]=[-18.11479523711481,-11.925524469941678]; P[2]=[31.542078892652935,-17.77316088651216]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); M(7,6,4,blauerWinkel); L(8,6,7); L(9,8,7); L(10,6,8); N(11,1,10); L(12,1,11); L(13,12,11); L(14,12,13); M(15,13,11,gruenerWinkel); N(16,14,15); L(17,14,16); L(18,17,16); L(19,17,18); N(20,18,15); N(21,15,9); RA(20,21); RK([5,7],[19,20,9],90); % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LimeGreen}{rgb}{0.20,0.80,0.20} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.85122958680809945875/0.23390545666281925552, 2/2.84436706940345462868/0.11695272833140960000, 3/2.44908236188267780520/1.03551138187521774014, 4/3.44221984447803297513/0.91855865354380805687, 5/3.83750455199880979862/0.00000000000000000000, 6/3.04693513695725615165/1.83711730708761633579, 7/3.83750455200284568136/2.44948974277889908180, 8/2.91188975859404752811/2.82795672181774193632, 9/3.70245917363963750191/3.44032915750902468233, 10/2.12132034354845799839/2.21558428612645963440, 11/1.98627496517827872857/1.22474487139463938945, 12/1.06066017176452787041/0.84627789236098616144, 13/1.19570555013470714023/1.83711730709280618434, 14/0.27009075672095617104/1.45865032805915295633, 15/1.98627496517598878256/2.44948974278965048157, 16/1.06066017176823335078/2.07102276374825722272, 17/0.13504537836047808552/2.44948974278965048157, 18/0.92561479340775498770/3.06186217847875497000, 19/0.00000000000000000000/3.44032915752014822885, 20/1.85122958681551041948/3.44032915752014822885, 21/2.77684438023188207012/3.06186217846763097938, 22/1.85122958680809945875/6.64675285837747864548, 23/2.84436706940345596095/6.76370558670888666342, 24/2.44908236188267780520/5.84514693316507738530, 25/3.44221984447803341922/5.96209966149648629141, 26/3.83750455199880935453/6.88065831504029734589, 27/3.04693513695725615165/5.04354100795268056601, 28/3.83750455200284568136/4.43116857226139604364, 29/2.91188975859404752811/4.05270159322255452139, 30/2.12132034354845799839/4.66507402891383726740, 31/1.98627496517827917266/5.65591344364565529190, 32/1.06066017176452809245/6.03438042267930985219, 33/1.19570555013470669614/5.04354100794749005132, 34/0.27009075672095617104/5.42200798698114372343, 35/1.98627496517598900461/4.43116857225064553205, 36/1.06066017176823335078/4.80963555129203879090, 37/0.13504537836047808552/4.43116857225064553205, 38/0.92561479340775498770/3.81879613656154148771, 39/2.77684438023188207012/3.81879613657266459015, 40/5.82377951719029063327/6.64675285838402452043, 41/4.83064203459455043799/6.76370558671216048907, 42/5.22592674211835372944/5.84514693316965505687, 43/4.23278925952261353416/5.96209966149779280187, 44/4.62807396704641771379/5.04354100795528825785, 45/4.76311934541289172529/4.05270159322560896697, 46/3.97254993036931969286/3.44032915753171719686, 47/5.55368876045646331363/4.66507402891949496393, 48/5.68873413882337697345/5.65591344365175974218, 49/6.61434893223588193933/6.03438042268846075444, 50/6.47930355386896827952/5.04354100795619864073, 51/7.40491834728146969269/5.42200798699290320570, 52/5.68873413882970258015/4.43116857225674820597, 53/6.61434893223621056535/4.80963555130119058134, 54/7.53996372564521344373/4.43116857226285176807, 55/6.74939431059995431639/3.81879613657114003189, 56/7.67500910400895808294/3.44032915753279544546, 57/5.82377951719344633119/3.44032915752669499199, 58/4.89816472377582723396/3.81879613657616401312, 59/5.82377951721142217423/0.23390545666936704561, 60/4.83064203461645380600/0.11695272833468434159, 61/5.22592674213420149698/1.03551138187979541172, 62/4.23278925953923401693/0.91855865354511323506, 63/4.62807396705698526063/1.83711730709022447172, 64/4.76311934541692760803/2.82795672182079371737, 65/5.55368876046453596729/2.21558428613211688685, 66/5.68873413883797862667/1.22474487140074161928, 67/6.61434893225297670938/0.84627789237013906209, 68/6.47930355387953316182/1.83711730710151388557, 69/7.40491834729453213271/1.45865032807091044020, 70/5.68873413883623513243/2.44948974279575271140, 71/6.61434893224523623445/2.07102276375741034542, 72/7.53996372565174510783/2.44948974280185272079, 73/6.74939431060245009775/3.06186217848835173783, 74/4.89816472377832390350/3.06186217847112995827} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 6/293.28/397.76/0.4/Blue, 13/322.24/397.76/0.4/Green} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[LimeGreen,very thick] (p-20) -- (p-21); %\draw[Violet,very thick] (p-5) -- (p-7); %\draw[Violet,very thick] (p-5) -- (p-7); %Kanten als \draw[line width=0] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 5/62, 5/60, 6/3, 6/4, 7/6, 7/63, 7/64, 7/46, 8/6, 8/7, 9/8, 9/7, 9/29, 9/28, 9/39, 10/6, 10/8, 11/1, 11/10, 12/1, 12/11, 13/12, 13/11, 14/12, 14/13, 15/13, 16/14, 16/15, 17/14, 17/16, 18/17, 18/16, 19/17, 19/18, 19/37, 19/38, 20/18, 20/15, 20/21, 20/35, 20/38, 20/39, 21/15, 21/9, 23/22, 24/22, 24/23, 25/23, 25/24, 26/23, 26/25, 26/41, 26/43, 27/24, 27/25, 28/27, 28/44, 29/27, 29/28, 30/27, 30/29, 31/22, 31/30, 32/22, 32/31, 33/31, 33/32, 34/32, 34/33, 35/33, 36/34, 36/35, 37/34, 37/36, 38/36, 38/37, 39/35, 41/40, 42/40, 42/41, 43/41, 43/42, 44/42, 44/43, 45/44, 45/28, 46/28, 46/45, 46/64, 46/74, 47/44, 47/45, 48/40, 48/47, 49/40, 49/48, 50/48, 50/49, 51/49, 51/50, 52/50, 53/51, 53/52, 54/51, 54/53, 55/53, 55/54, 56/54, 56/55, 56/72, 56/73, 57/52, 57/55, 57/58, 57/70, 57/73, 57/74, 58/46, 58/52, 60/59, 61/59, 61/60, 62/60, 62/61, 63/61, 63/62, 64/63, 65/63, 65/64, 66/59, 66/65, 67/59, 67/66, 68/66, 68/67, 69/67, 69/68, 70/68, 71/69, 71/70, 72/69, 72/71, 73/71, 73/72, 74/70} \draw[line width=0] (p-\i) -- (p-\j); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 6/293.28/397.76/0.4/Blue, 13/322.24/397.76/0.4/Green} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/292, 2/263, 3/83, 4/83, 5/217, 6/308, 7/172, 8/188, 9/292, 10/188, 11/52, 12/292, 13/52, 14/172, 15/248, 16/8, 17/188, 18/8, 19/128, 20/128, 21/8, 22/68, 23/97, 24/157, 25/277, 26/143, 27/112, 28/188, 29/292, 30/172, 31/308, 32/68, 33/308, 34/112, 35/112, 36/352, 37/112, 38/352, 39/352, 40/112, 41/23, 42/323, 43/143, 44/68, 45/8, 46/112, 47/8, 48/172, 49/352, 50/232, 51/68, 52/68, 53/188, 54/8, 55/248, 56/308, 57/308, 58/188, 59/337, 60/337, 61/97, 62/217, 63/97, 64/112, 65/352, 66/188, 67/8, 68/68, 69/8, 70/292, 71/172, 72/352, 73/172, 74/172} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $


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StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
Mitteilungen: 4165
Wohnort: Raun
  Beitrag No.1883, eingetragen 2020-01-12

\quoteon(2020-01-12 16:36 - haribo in Beitrag No. 1881) diese konstruktion passe ich in der länge auf einen erweiterten kite an, welcher erstaunlicherweise (wiso eigentlich?) auch in einen 60° winkel passt \quoteoff Das scheint gar keine so einfache Geometrieaufgabe zu sein. Ich muss passen. Wieso ist ∠(P11-P14,P5-P13)=60°? $ %Eingabe war: % %#1803 % % % % %P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); Q(7,1,6,ab(1,6,[1,6]),ab(1,2,3)); M(13,12,6,blauerWinkel); L(14,12,13); RK([5,13],[11,14],360/6); A(6,13); % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.71352549156242095485/0.00000000000000000000, 2/2.71352549156242117689/0.00000000000000000000, 3/2.21352549156242117689/0.86602540378443859659, 4/3.21352549156242117689/0.86602540378443859659, 5/3.71352549156242117689/0.00000000000000000000, 6/2.71352549156242117689/1.73205080756887719318, 7/1.75000000000000000000/1.99966737489869483824, 8/0.87500000000000000000/1.51554445662276737750, 9/1.73176274578121058845/0.99983368744934741912, 10/0.85676274578121025538/0.51571076917342051349, 11/0.00000000000000000000/1.03142153834684013880, 12/2.46352549156242117689/2.70029664412073167057, 13/3.42705098312484190970/2.43268007679091402551, 14/3.17705098312484190970/3.40092591334276805881} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %Punkte als \fill[red] (p-1) circle (1.125pt) %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %\draw[Violet,very thick] (p-5) -- (p-13); %Kanten als \draw[line width=0] (p-1) -- (p-2); \foreach \i/\j in { 1/9, 1/10, 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/3, 6/4, 6/7, 6/13, 8/7, 9/7, 9/8, 10/8, 10/9, 11/8, 11/10, 12/7, 12/6, 13/12, 14/12, 14/13} \draw[line width=0] (p-\i) -- (p-\j); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/299, 2/330, 3/150, 4/330, 5/330, 6/254, 7/194, 8/59, 9/359, 10/179, 11/179, 12/74, 13/314, 14/74} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Im Moment kann ich es nur mit dem GAP-Programm nachrechnen, dass es exakt stimmt: \sourceon GAP gap> W60:=[[1/2,-1/2*Sqrt(3)],[1/2*Sqrt(3),1/2]]; #60°-Rotationsmatrix gap> Wbl:=[[1/4,-1/4*Sqrt(15)],[1/4*Sqrt(15),1/4]]*W60^-1; #spitzer Winkel im Dreieck mit Seitenlängen 1,2,2 ("acos(1/4)_Graph") gap> P[1]:=[0,0];; gap> P[2]:=[1,0];; gap> P[3]:=P[1]+W60*(P[2]-P[1]);; gap> P[4]:=P[3]+W60*(P[2]-P[3]);; gap> P[5]:=P[2]-(P[1]-P[2]);; gap> P[6]:=P[3]-(P[1]-P[3]);; gap> P[7]:=P[6]+(W60*Wbl)^-1*(P[3]-P[6]);; gap> P[8]:=P[7]+(W60*W60*Wbl)^-1*(P[6]-P[7]);; gap> P[9]:=P[7]+W60*(P[8]-P[7]);; gap> P[10]:=P[1]+W60*(P[9]-P[1]);; gap> P[11]:=P[8]-(P[7]-P[8]);; gap> P[12]:=P[7]+W60*(P[6]-P[7]);; gap> P[13]:=P[12]+W60*(P[6]-P[12]);; gap> P[14]:=P[12]-(P[7]-P[12]);; gap> Sqrt(((P[13]-P[5])*(P[14]-P[11]))*((P[13]-P[5])*(P[14]-P[11]))/((P[13]-P[5])*(P[13]-P[5]))/((P[14]-P[11])*(P[14]-P[11]))); 1/2 \sourceoff Ergebnis 1/2 für den Kosinus des Winkels, also 60°.


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haribo
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 25.10.2012
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  Beitrag No.1884, eingetragen 2020-01-13

@stefan, ja die blauen vier sollten nach konstruktion wieder entfernt werden, mein fehler gestern, sorry (hab es in dem obigen beitragsbild geändert) dann ist der erweiterte und geöffnete kite ausreichend beweglich um auch bei anderen inneren winkeln in ein 60° winkel zu passen, (konstruieren kann ich das auch mal wieder nur mit itterationsvorgängen...) damit kann man also weitere 6-fach rotationssymetrische graphen bauen z.B. diesen hier https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/35059_st-4-3er.png aber was dann nicht mehr geht, also wenn man den 60°stossdämpfer daneben legen würde wie in #1881, ist die weisse umgelegte linie offenbar stabilisiert also diese weisse umgelegte linie den graphen aus #1881, bzw macht ihn unbeweglich was mich, neben dem überhaupts 60° winkel für den erweiterten kite zusätzlich irritiert ist folgendes: die 6 60° sektoren in #1881 haben gar keine gemeinsame spitze, sie überschneiden sich innen klar geht das, aber ich hatte das bisher nicht auf dem radar für die winkeltheorie... immer wieder neues also haribo


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Slash
Aktiv Letzter Besuch: in der letzten Woche
Dabei seit: 23.03.2005
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Wohnort: Westerburg
  Beitrag No.1885, vom Themenstarter, eingetragen 2020-01-15

Hier ist mein Rechenweg für den Winkel Alpha. https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/8038_r_tsell_sungsweg.png Beweis: Der Reihe nach bestimmen wir die folgenden Winkel. $\cos{\delta}=\frac{0,5}{2}=\frac{1}{4}\Rightarrow\delta=\arccos{\frac{1}{4}}$ ${\epsilon}=\frac{360-2\cdot 60-\delta}{2}=120-\frac{\delta}{2}$ $\omega=180-90-\epsilon=90-\epsilon$ $\gamma=360-3\cdot 60-\delta=180-\delta$ $x^2=2^2+1^2-2\cdot 2\cdot 1\cdot\cos{\gamma}\Rightarrow x=\sqrt{5-4\cdot\cos{\gamma}}$ $\sin{\beta}=\frac{2}{x}\cdot\sin{\gamma}\Rightarrow\beta=\arcsin{(\frac{2}{x}\cdot\sin{\gamma})}$ $\kappa=180-2\cdot 60-\beta=60-\beta$ $\lambda=180-90-\kappa=90-\kappa$ $\sigma=180-60-\omega-\lambda=120-\omega-\lambda$ $\alpha=180-90-\sigma=90-\sigma$ Wir setzen alle bekannten Größen in die letzte Gleichung ein: $\alpha=-30+\frac{\arccos{\frac{1}{4}}}{2}+\arcsin{\Big(\frac{2}{\sqrt{5-4\cdot\cos{(180-\arccos{\frac{1}{4}})}}}\cdot\sin{(180-\arccos{\frac{1}{4}})}\Big)}$ Es gilt: $\cos{(180-\arccos{\frac{1}{4}})}=-\frac{1}{4}}$ $\alpha=-30+\frac{\arccos{\frac{1}{4}}}{2}+\arcsin{\Big(\frac{2}{\sqrt{6}}\cdot\sin{(180-\arccos{\frac{1}{4}})}\Big)}=60$


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haribo
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 25.10.2012
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  Beitrag No.1886, eingetragen 2020-01-16

erklärungsversuch... https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/35059_kite-winkel-3.png -aus symetriegründen liegt 6-9 parallel zu 11-14 -rotiert man das gesamte rotebild 3 mal um M dann liegt die blaue konstruktion 120° verdreht zur roten (dito die gelbe), -folglich würde 11-14 11´-14´ im 60° winkel schneiden 6´-9´ liegt wiederum parallel zu 11´-14´ also auch im 60°winkel zu 11-14 - wenn man zeigen kann das sowohl 6´als auch 9´auf der geraden 5-13 liegen hat man es geschafft... -6´ist trivial weil es bei der rotation auf 5 zu liegen kommt -die strecken 7-6 und 6-13 haben ohne frage einen schnittwinkel von 120° zueinander, -beim drehen, um auch 120°, hin zum blauen konstrukt wird also automatisch die strecke 6´-7´ parallel zu 6-13 -damit gibt es ein parallelogramm (grün)6/13/7´/6´(bzw 5) -die diagonalen jedes parallelogramms halbieren sich gegenseitig - 9´liegt (wegen blau) zwangsweise auf der halben strecke 6-7´, damit liegt 9´also auch exakt auf der hälfte der diagonalen 5-13 und somit auch auf der schwarzen winkellinie... ergebnis 60° q.e.d.


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StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
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Wohnort: Raun
  Beitrag No.1887, eingetragen 2020-01-18

Toll!! Zwei perfekte Beweise! So soll das sein. Auch bei der Fehlersuche muss ich passen, nichts dergleichen zu sehen :-D Da bleibt für mich jetzt nur noch übrig, etwas zur Beweglichkeit zu schreiben. \quoteon(2020-01-13 13:04 - haribo in Beitrag No. 1884) @stefan, ja die blauen vier sollten nach konstruktion wieder entfernt werden, mein fehler gestern, sorry (hab es in dem obigen beitragsbild geändert) \quoteoff Das ändere ich auch, mit einem dritten beweglichen Winkel in P12 anstelle der Kante P6-P13. 74 Knoten, 8×Grad 3, 62×Grad 4, 4×Grad 6, 0 Überschneidungen 148 Kanten, minimal 0.99999999999999544809, maximal 1.00000000000000266454 einzustellende Kanten, Abstände und Winkel: |P21-P14|=1.00000000000000066613 ∠(P18-P20,P5-P13)=90.00000000000001421085° ∠(P18-P14,P5-P13)=90.00000000000001421085° $ %Eingabe war: % %Anfang für einen neuen, noch unbenannten Streichholzgraph % % % % % % %P[1]=[-18.114795237025238,-11.925524469987494]; P[2]=[31.54207889274424,-17.773160886543337]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); M(7,1,3,blauerWinkel,2); N(11,7,6); L(12,11,6); M(13,12,6,gruenerWinkel); L(14,12,13); M(15,10,9,orangerWinkel,2); N(19,15,9); N(20,17,19); L(21,20,19); RA(21,14); % %RK([5,13],[18,20,14],360/4,true); % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LimeGreen}{rgb}{0.20,0.80,0.20} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.85/0.23, 2/2.84/0.12, 3/2.45/1.04, 4/3.44/0.92, 5/3.84/0.00, 6/3.05/1.84, 7/1.99/1.22, 8/1.06/0.85, 9/1.20/1.84, 10/0.27/1.46, 11/2.12/2.22, 12/2.91/2.83, 13/3.84/2.45, 14/3.70/3.44, 15/1.06/2.07, 16/0.14/2.45, 17/0.93/3.06, 18/0.00/3.44, 19/1.99/2.45, 20/1.85/3.44, 21/2.78/3.06, 22/1.85/6.65, 23/2.84/6.76, 24/2.45/5.85, 25/3.44/5.96, 26/3.84/6.88, 27/3.05/5.04, 28/1.99/5.66, 29/1.06/6.03, 30/1.20/5.04, 31/0.27/5.42, 32/2.12/4.67, 33/2.91/4.05, 34/3.84/4.43, 35/1.06/4.81, 36/0.14/4.43, 37/0.93/3.82, 38/1.99/4.43, 39/2.78/3.82, 40/5.82/6.65, 41/4.83/6.76, 42/5.23/5.85, 43/4.23/5.96, 44/4.63/5.04, 45/5.69/5.66, 46/6.61/6.03, 47/6.48/5.04, 48/7.40/5.42, 49/5.55/4.67, 50/4.76/4.05, 51/3.97/3.44, 52/6.61/4.81, 53/7.54/4.43, 54/6.75/3.82, 55/7.68/3.44, 56/5.69/4.43, 57/5.82/3.44, 58/4.90/3.82, 59/5.82/0.23, 60/4.83/0.12, 61/5.23/1.04, 62/4.23/0.92, 63/4.63/1.84, 64/5.69/1.22, 65/6.61/0.85, 66/6.48/1.84, 67/7.40/1.46, 68/5.55/2.22, 69/4.76/2.83, 70/6.61/2.07, 71/7.54/2.45, 72/6.75/3.06, 73/5.69/2.45, 74/4.90/3.06} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/53.28/82.24/0.4/Blue, 12/277.76/337.76/0.4/Green, 10/22.24/37.76/0.4/Orange} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 5/62, 5/60, 6/3, 6/4, 7/1, 8/1, 8/7, 9/8, 9/7, 10/8, 10/9, 11/7, 11/6, 12/11, 12/6, 13/12, 13/69, 13/51, 14/12, 14/13, 14/33, 14/34, 14/39, 15/10, 16/10, 16/15, 17/16, 17/15, 18/16, 18/17, 18/36, 18/37, 19/15, 19/9, 20/17, 20/19, 20/37, 20/38, 21/20, 21/19, 21/14, 23/22, 24/22, 24/23, 25/23, 25/24, 26/23, 26/25, 26/41, 26/43, 27/24, 27/25, 28/22, 29/22, 29/28, 30/28, 30/29, 31/29, 31/30, 32/27, 32/28, 33/27, 33/32, 34/33, 34/50, 35/31, 36/31, 36/35, 37/35, 37/36, 38/30, 38/35, 39/38, 39/20, 41/40, 42/40, 42/41, 43/41, 43/42, 44/42, 44/43, 45/40, 46/40, 46/45, 47/45, 47/46, 48/46, 48/47, 49/44, 49/45, 50/44, 50/49, 51/50, 51/34, 51/69, 51/74, 52/48, 53/48, 53/52, 54/52, 54/53, 55/53, 55/54, 55/71, 55/72, 56/47, 56/52, 57/54, 57/56, 57/72, 57/73, 58/51, 58/56, 58/57, 60/59, 61/59, 61/60, 62/60, 62/61, 63/61, 63/62, 64/59, 65/59, 65/64, 66/64, 66/65, 67/65, 67/66, 68/63, 68/64, 69/63, 69/68, 70/67, 71/67, 71/70, 72/70, 72/71, 73/66, 73/70, 74/73, 74/57} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,74} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[LimeGreen,very thick] (p-21) -- (p-14); %\draw[Violet,very thick] (p-5) -- (p-13); %\draw[Violet,very thick] (p-5) -- (p-13); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/53.28/82.24/0.4/Blue, 12/277.76/337.76/0.4/Green, 10/22.24/37.76/0.4/Orange} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/292, 2/323, 3/143, 4/23, 5/217, 6/308, 7/52, 8/172, 9/52, 10/172, 11/188, 12/68, 13/308, 14/292, 15/308, 16/128, 17/68, 18/232, 19/248, 20/128, 21/8, 22/68, 23/97, 24/157, 25/277, 26/37, 27/277, 28/8, 29/68, 30/248, 31/188, 32/172, 33/292, 34/52, 35/52, 36/232, 37/292, 38/112, 39/352, 40/112, 41/143, 42/323, 43/143, 44/128, 45/172, 46/112, 47/292, 48/352, 49/8, 50/8, 51/112, 52/188, 53/308, 54/188, 55/308, 56/68, 57/308, 58/188, 59/248, 60/337, 61/37, 62/217, 63/97, 64/188, 65/308, 66/68, 67/8, 68/352, 69/112, 70/232, 71/352, 72/172, 73/292, 74/172} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Dieser dritte Winkel muss jetzt mit verwendet werden, um die dritte Bedingung ∠(P18-P14,P5-P13)=90° einzustellen. So gesehen ändert sich an der Beweglichkeit vermutlich nichts und \quoteon(2020-01-13 13:04 - haribo in Beitrag No. 1884) offenbar stabilisiert also diese weisse umgelegte linie den graphen aus #1881, bzw macht ihn unbeweglich \quoteoff . Das extra GAP-Programm (Button "acos(1/4)", weil mit exakten Punktkoordinaten rechnen möglich) gibt ebenfalls als Ergebnis Beweglichkeit=0, also unbeweglich aus: GAP \showon \sourceon GAP W60:=[[1/2,-1/2*Sqrt(3)],[1/2*Sqrt(3),1/2]]; Wbl:=[[1/4,-1/4*Sqrt(15)],[1/4*Sqrt(15),1/4]]*W60^-1; #acos(1/4)_Graph P:=[]; P[1]:=[0,0]; P[2]:=[1,0]; P[3]:=P[1]+W60*(P[2]-P[1]);; P[4]:=P[3]+W60*(P[2]-P[3]);; P[5]:=P[2]-(P[1]-P[2]);; P[6]:=P[3]-(P[1]-P[3]);; P[7]:=P[1]+W60*Wbl^-2*(P[3]-P[1]);; P[8]:=P[1]+W60*(P[7]-P[1]);; P[9]:=P[8]+W60*(P[7]-P[8]);; P[10]:=P[8]-(P[1]-P[8]);; P[11]:=P[7]-(P[1]-P[7]);; P[12]:=P[11]+W60*(P[6]-P[11]);; P[13]:=P[12]+W60*(P[6]-P[12]);; P[14]:=P[12]-(P[11]-P[12]);; P[15]:=P[10]+Wbl*(P[9]-P[10]);; P[16]:=P[10]+W60*(P[15]-P[10]);; P[17]:=P[16]+W60*(P[15]-P[16]);; P[18]:=P[16]-(P[10]-P[16]);; P[19]:=P[9]+W60*Wbl*(P[7]-P[9]);; P[20]:=P[19]+W60^-2*(P[9]-P[19]);; P[21]:=P[19]-(P[9]-P[19]);; P[33]:=P[14]+W60^-1*(P[21]-P[14]);; P[34]:=P[33]+W60*(P[14]-P[33]);; P[36]:=P[18]+W60^3*Wbl^-1*(P[16]-P[18]);; P[37]:=P[20]-(P[21]-P[20]);; P[38]:=P[20]+(W60*Wbl)^-1*(P[37]-P[20]);; P[39]:=P[20]-(P[17]-P[20]);; P[50]:=P[34]+W60*Wbl*(P[14]-P[34]);; P[51]:=P[50]+W60*(P[34]-P[50]);; P[58]:=P[51]+Wbl^-1*(P[50]-P[51]);; P[62]:=P[5]+Wbl^-3*(P[4]-P[5]);; P[63]:=P[62]-(P[5]-P[62]);; P[68]:=P[63]+W60*W60*Wbl*(P[62]-P[63]);; P[69]:=P[51]+W60*(P[13]-P[51]);; P[74]:=P[51]+W60^-1*(P[50]-P[51]);; P[27]:=P[33]+W60*(P[34]-P[33]);; P[30]:=P[38]-(P[39]-P[38]);; P[31]:=P[36]-(P[18]-P[36]);; P[32]:=P[33]-(P[14]-P[33]);; P[35]:=P[31]+W60*(P[36]-P[31]);; P[44]:=P[50]+W60^-1*(P[34]-P[50]);; P[49]:=P[50]-(P[51]-P[50]);; P[56]:=P[58]+(W60^3*Wbl^-1)^-1*(P[51]-P[58]);; P[57]:=P[56]+W60*(P[58]-P[56]);; P[60]:=P[62]+W60*(P[5]-P[62]);; P[61]:=P[62]+W60*(P[60]-P[62]);; P[64]:=P[68]+W60*Wbl*(P[63]-P[68]);; P[65]:=P[64]+W60^-2*(P[68]-P[64]);; P[66]:=P[64]+W60*(P[65]-P[64]);; P[67]:=P[66]+W60*(P[65]-P[66]);; P[70]:=P[67]+Wbl^-1*(P[66]-P[67]);; P[71]:=P[70]+W60*(P[67]-P[70]);; P[72]:=P[57]-(P[58]-P[57]);; P[73]:=P[57]+W60*(P[74]-P[57]);; P[24]:=P[27]+(W60*Wbl)^-1*(P[32]-P[27]);; P[25]:=P[24]+W60*(P[27]-P[24]);; P[26]:=P[25]-(P[27]-P[25]);; P[28]:=P[30]+W60*Wbl*(P[38]-P[30]);; P[29]:=P[30]+W60*(P[28]-P[30]);; P[42]:=P[44]+W60*Wbl*(P[49]-P[44]);; P[43]:=P[44]+W60*(P[42]-P[44]);; P[45]:=P[49]+(W60*Wbl)^-1*(P[44]-P[49]);; P[46]:=P[45]+W60^2*(P[49]-P[45]);; P[47]:=P[56]-(P[58]-P[56]);; P[48]:=P[46]+W60*(P[47]-P[46]);; P[52]:=P[48]+Wbl*(P[47]-P[48]);; P[53]:=P[48]+W60*(P[52]-P[48]);; P[54]:=P[57]-(P[74]-P[57]);; P[55]:=P[53]-(P[48]-P[53]);; P[59]:=P[61]-(P[63]-P[61]);; P[22]:=P[24]-(P[27]-P[24]);; P[23]:=P[22]+W60*(P[24]-P[22]);; P[40]:=P[42]-(P[44]-P[42]);; P[41]:=P[26]+W60*(P[43]-P[26]);; Kante:=[ [1,2], [1,3], [2,3], [3,4], [2,4], [4,5], [2,5], [5,62],[5,60],[3,6], [4,6], [1,7], [1,8], [7,8], [8,9], [7,9], [8,10], [9,10], [7,11], [6,11], [11,12], [6,12], [12,13], [13,69],[13,51],[12,14], [13,14], [14,33],[14,34],[14,39],[10,15], [10,16], [15,16], [16,17], [15,17], [16,18], [17,18], [18,36],[18,37],[15,19], [9,19], [17,20], [19,20], [20,37],[20,38],[20,21], [19,21], [14,21], [22,23], [22,24], [23,24], [23,25], [24,25], [23,26], [25,26], [26,41],[26,43],[24,27], [25,27], [22,28], [22,29], [28,29], [28,30], [29,30], [29,31], [30,31], [27,32], [28,32], [27,33], [32,33], [33,34], [34,50],[31,35], [31,36], [35,36], [35,37], [36,37], [30,38], [35,38], [38,39], [20,39], [40,41], [40,42], [41,42], [41,43], [42,43], [42,44], [43,44], [40,45], [40,46], [45,46], [45,47], [46,47], [46,48], [47,48], [44,49], [45,49], [44,50], [49,50], [50,51], [34,51], [51,69],[51,74],[48,52], [48,53], [52,53], [52,54], [53,54], [53,55], [54,55], [55,71],[55,72],[47,56], [52,56], [54,57], [56,57], [57,72],[57,73],[51,58], [56,58], [57,58], [59,60], [59,61], [60,61], [60,62], [61,62], [61,63], [62,63], [59,64], [59,65], [64,65], [64,66], [65,66], [65,67], [66,67], [63,68], [64,68], [63,69], [68,69], [67,70], [67,71], [70,71], [70,72], [71,72], [66,73], [70,73], [73,74], [57,74], ];; Size(Kante); RESTKANTEN:=[[21,14],[5,13],[5,13],];; for K in Kante do Print(" ",(P[K[1]]-P[K[2]])^2); od; PUNKTEZAHL:=Size(P); KOORDINATENZAHL:=2*PUNKTEZAHL; KANTENZAHL:=Size(Kante); n:=Maximum(KOORDINATENZAHL,KANTENZAHL); A:=NullMat(n,n);; for i in [1..KANTENZAHL] do A[2*Kante[i][1]-1][i]:=P[Kante[i][2]][1]-P[Kante[i][1]][1]; A[2*Kante[i][1] ][i]:=P[Kante[i][2]][2]-P[Kante[i][1]][2]; A[2*Kante[i][2]-1][i]:=P[Kante[i][1]][1]-P[Kante[i][2]][1]; A[2*Kante[i][2] ][i]:=P[Kante[i][1]][2]-P[Kante[i][2]][2]; od; Nenner:=Lcm(List(Flat(A),i->DenominatorCyc(i))); A:=Nenner*A;;P:=Nenner*P;; AlterNenner:=1; RankA:=Rank(A); Print("gerechnet_mit_Button=\"",gerechnet_mit_Button,"\";"); Print("Beweglichkeit=",KOORDINATENZAHL-RankA-3); Print("Einsetzkanten=",KANTENZAHL-RankA); \sourceoff \showoff Um beim Zurechtziehen des Graphen Beweglichkeit festzustellen, sollte die Eingabe des Graphen besser so erfolgen, dass keine Beschränkung der Beweglichkeit durch nachträgliches Umlegen von Kanten oder durch einschränkende Symmetriebedingungen erfolgt. Mühsam, eine solche Eingabe des gesamten Graphen von Hand zu machen. Mit zum Beispiel Button neue Eingabe "wenig Winkel" geht das auch automatisch: 74 Knoten, 8×Grad 3, 62×Grad 4, 4×Grad 6, 0 Überschneidungen 148 Kanten, minimal 0.99999949693408940465, maximal 1.00000024068354642637 einzustellende Kanten, Abstände und Winkel: |P20-P38|=1.00000000000000044409 |P14-P21|=1.00000000000000022204 |P35-P38|=1.00000000000000088818 |P28-P32|=0.99999999999999156231 |P57-P72|=1.00000024068354642637 |P51-P58|=1.00000000000055733196 |P66-P73|=0.99999981613629274069 |P70-P73|=0.99999949693408940465 $ %Eingabe war: % %Anfang für einen neuen, noch unbenannten Streichholzgraph % % % % % % % % %P[1]=[-18.114795237025238,-11.925524469987494]; P[2]=[31.54207889274424,-17.773160886543337]; D=ab(1,2); A(1,2); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); M(60,5,2,blauerWinkel); L(62,5,60); M(59,60,5,-174.9999999999999); L(95,60,59); Q(61,62,60,D,ab(95,60,59,"gedreht")); L(63,62,61); M(7,1,2,gruenerWinkel); L(8,1,7); L(9,8,7); L(10,8,9); M(96,6,3,-70.52248781407008); L(12,96,6); Q(11,7,6,D,ab(96,6,12,"gedreht")); M(13,12,6,orangerWinkel); L(14,12,13); M(51,13,12,-70.52248781406995); L(97,51,13); M(68,63,61,80.52248781407002); L(98,63,68); Q(69,13,63,ab(97,13,51,"gedreht"),ab(98,63,68,"gedreht")); M(33,14,12,-70.52248781407002); L(99,33,14); M(100,51,13,-159.47751218593012); L(50,100,51); Q(34,14,51,ab(99,14,33,"gedreht"),ab(100,51,50,"gedreht")); M(101,59,60,-83.95502437185985); L(65,101,59); L(66,101,65); L(67,66,65); Q(64,68,59,D,ab(101,59,65,66,67,"gedreht")); M(39,14,12,vierterWinkel); M(15,10,8,fuenfterWinkel); L(16,10,15); L(17,16,15); L(18,16,17); N(19,15,9); M(102,19,9,-115); L(21,102,19); Q(20,17,19,D,ab(102,19,21,"gedreht")); M(38,20,17,-114.99999999999997); L(103,38,20); A(39,20,ab(103,20,38,"gedreht")); A(14,21); M(36,18,16,169.47751218592992); L(104,36,18); M(31,36,18,185); L(105,31,36); Q(35,36,104,ab(105,36,31,"gedreht"),D); Q(37,18,20,ab(104,18,31,35,36,"gedreht"),D); A(35,38); M(29,31,35,80.52248781407005); M(22,29,31,-174.99999999999983); L(28,22,29); L(107,28,29); Q(106,29,31,ab(107,29,22,28,"gedreht"),D); Q(30,31,38,ab(106,31,22,28,29,"gedreht"),D); M(23,22,28,93.95502437185986); L(24,23,22); L(25,23,24); L(26,23,25); L(108,25,24); M(109,33,14,125.00000000000007); L(32,33,109); Q(27,22,33,ab(108,22,23,24,25,26,"gedreht"),ab(109,33,32,"gedreht")); A(28,32); M(41,26,23,171.56746344221023); L(43,41,26); M(40,41,26,-175); L(111,40,41); Q(42,41,43,ab(111,41,40,"gedreht"),D); L(110,42,43); M(112,50,34,-55.000000000000014); L(49,112,50); Q(44,26,50,ab(110,26,40,41,42,43,"gedreht"),ab(112,50,49,"gedreht")); M(113,40,41,93.95502437185985); L(46,40,113); L(47,46,113); L(48,46,47); Q(45,40,49,ab(113,40,46,47,48,"gedreht"),D); M(52,48,46,80.52248781407002); L(53,48,52); L(54,53,52); L(114,53,54); M(70,67,65,-70.52248781406996); L(71,70,67); M(115,71,67,185); L(116,71,115); Q(72,70,71,D,ab(116,71,115,"gedreht")); Q(55,48,67,ab(114,48,52,53,54,"gedreht"),ab(115,67,70,71,72,"gedreht")); N(56,52,47); M(117,56,47,-115.00000000000007); L(58,117,56); Q(57,54,56,D,ab(117,56,58,"gedreht")); A(57,72); A(51,58); M(73,57,54,-115.00000000000017); L(118,73,57); Q(74,57,51,ab(118,57,73,"gedreht"),D); A(66,73); A(70,73); %R(20,38); // oder R(20,39); %R(14,21); %R(35,38); %R(28,32); %R(57,72); %R(51,58); %R(66,73); %R(70,73); % % % % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LimeGreen}{rgb}{0.20,0.80,0.20} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.85122958682191685043/0.23390545666223369614, 2/2.84436706941730665932/0.11695272833111682032, 3/2.44908236189625894141/1.03551138187480851194, 4/3.44221984449164830622/0.91855865354369159448, 5/3.83750455201269646821/0.00000000000000000000, 6/3.04693513697060103240/1.83711730708738341100, 7/1.98627496519077961779/1.22474487139158849658, 8/1.06066017177982185871/0.84627789235802808321, 9/1.19570555014868484811/1.83711730708738274487, 10/0.27009075673772686699/1.45865032805382210945, 11/2.12132034355964282923/2.21558428612094360233, 12/2.91188975860173737686/2.82795672181673829471, 13/3.83750455201269513594/2.44948974278317788134, 14/3.70245917364383192449/3.44032915751253298708, 15/1.06066017177982141462/2.07102276374961702388, 16/0.13504537836886357227/2.44948974278317699316, 17/0.92561479341095820317/3.06186217847897168554, 18/0.00000000000000000000/3.44032915751253209891, 19/1.98627496519077939574/2.44948974278317788134, 20/1.85122958682191596225/3.44032915751253254300, 21/2.77684438023287416542/3.06186217847897212962, 22/1.85122958682191640634/6.64675285836282991880, 23/2.84436706941730621523/6.76370558669395105511, 24/2.44908236189626160595/5.84514693315025724019, 25/3.44221984449165052666/5.96209966148137837649, 26/3.83750455201269513594/6.88065831502506952688, 27/3.04693513697060724965/5.04354100793768544975, 28/1.98627496519077872961/5.65591344363347392488, 29/1.06066017177982030439/6.03438042266703611460, 30/1.19570555014868329380/5.04354100793768100885, 31/0.27009075673772575676/5.42200798697124053405, 32/2.12132034355964771422/4.66507402890412858909, 33/2.91188975860174004140/4.05270159320833123218, 34/3.83750455201269957684/4.43116857224188720465, 35/1.06066017177981986030/4.80963555127544761802, 36/0.13504537836886273960/4.43116857224188631648, 37/0.92561479341095764806/3.81879613654609340045, 38/1.98627496519077872961/4.43116857224188809283, 39/2.77684438023287416542/3.81879613654609340045, 40/5.82377951720347208919/6.64675285836280504981, 41/4.83064203460808272439/6.76370558669393684426, 42/5.22592674212911756371/5.84514693315024125297, 43/4.23278925953372908708/5.96209966148137215924, 44/4.62807396705476392640/5.04354100793767479161, 45/5.68873434919859555237/5.65591341496214194962, 46/6.61434906225764063237/6.03438059051191277860, 47/6.47930389425276498372/5.04354114711125145476, 48/7.40491860731180828736/5.42200832266102228374, 49/5.55368876046573411998/4.66507402890414279995, 50/4.76311934542365733591/4.05270159320832323857, 51/3.97254993038155967966/3.44032915751253209891, 52/6.61434877154106359853/4.80963643012396246945, 53/7.53996330492708466409/4.43116881514933691477, 54/6.74939346915633997526/3.81879692261227710048, 55/7.67500800254235926445/3.44032930763765065763, 56/5.68873405848201496582/4.43116925457419963408, 57/5.82377875609729134254/3.44032974706251515329, 58/4.89816422271127116517/3.81879736203714070797, 59/5.82377951720347564191/0.23390545666222936627, 60/4.83064203460808627710/0.11695272833111461375, 61/5.22592674212913532727/1.03551138187480540331, 62/4.23278925953374507429/0.91855865354369103937, 63/4.62807396705479590082/1.83711730708738141260, 64/5.68873413883461331864/1.22474487139159138316, 65/6.61434893224557018954/0.84627789235802985957, 66/6.47930355387670786627/1.83711730708738452122, 67/7.40491834728766651352/1.45865032805382321968, 68/5.55368876046575188354/2.21558428612094626686, 69/4.76311934542365378320/2.82795672181673696244, 70/6.61434859186873058690/2.07102232432475252821, 71/7.53996317491501244490/2.44948981784573716070, 72/6.74939341949607651827/3.06186181411666646923, 73/5.68873468957494310416/2.44949015353735344291, 74/4.89816446376787961725/3.06186154253864328822} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 5/173.28/366.72/0.4/Blue, 1/353.28/442.24/0.4/Green, 12/277.76/337.76/0.4/Orange, 14/217.76/517.76/0.4/Violet, 10/322.24/397.76/0.4/Teal} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/3, 6/4, 7/1, 8/1, 8/7, 9/8, 9/7, 10/8, 10/9, 11/7, 11/6, 12/11, 12/6, 13/12, 14/12, 14/13, 14/21, 15/10, 16/10, 16/15, 17/16, 17/15, 18/16, 18/17, 19/15, 19/9, 20/17, 20/19, 21/20, 21/19, 22/29, 23/22, 24/23, 24/22, 25/23, 25/24, 26/23, 26/25, 27/24, 27/25, 27/33, 28/22, 28/29, 28/32, 29/31, 30/28, 30/29, 30/31, 30/38, 31/36, 32/33, 32/27, 33/14, 34/14, 34/33, 34/51, 35/31, 35/36, 35/37, 35/38, 36/18, 37/18, 37/36, 37/20, 38/20, 39/14, 39/20, 39/38, 40/41, 41/26, 42/40, 42/41, 42/43, 43/41, 43/26, 44/42, 44/43, 44/50, 45/40, 45/49, 46/40, 46/45, 47/46, 47/45, 48/46, 48/47, 49/44, 49/50, 50/34, 50/51, 51/13, 51/58, 52/48, 53/48, 53/52, 54/53, 54/52, 55/53, 55/54, 55/71, 56/52, 56/47, 57/54, 57/56, 57/72, 58/57, 58/56, 59/60, 60/5, 61/62, 61/59, 61/60, 62/5, 62/60, 63/62, 63/61, 64/68, 64/59, 65/64, 65/59, 66/64, 66/65, 66/73, 67/66, 67/65, 68/63, 69/13, 69/51, 69/63, 69/68, 70/67, 70/73, 71/70, 71/67, 72/70, 72/71, 72/55, 73/57, 74/57, 74/73, 74/51} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,74} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[LimeGreen,very thick] (p-20) -- (p-38); \draw[LimeGreen,very thick] (p-14) -- (p-21); \draw[LimeGreen,very thick] (p-35) -- (p-38); \draw[LimeGreen,very thick] (p-28) -- (p-32); \draw[LimeGreen,very thick] (p-57) -- (p-72); \draw[LimeGreen,very thick] (p-51) -- (p-58); \draw[LimeGreen,very thick] (p-66) -- (p-73); \draw[LimeGreen,very thick] (p-70) -- (p-73); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 5/173.28/366.72/0.4/Blue, 1/353.28/442.24/0.4/Green, 12/277.76/337.76/0.4/Orange, 14/217.76/517.76/0.4/Violet, 10/322.24/397.76/0.4/Teal} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/292, 2/323, 3/143, 4/23, 5/217, 6/308, 7/52, 8/172, 9/52, 10/172, 11/188, 12/68, 13/308, 14/68, 15/308, 16/128, 17/68, 18/232, 19/248, 20/128, 21/8, 22/68, 23/157, 24/277, 25/37, 26/143, 27/52, 28/308, 29/128, 30/308, 31/112, 32/172, 33/292, 34/52, 35/52, 36/232, 37/352, 38/112, 39/352, 40/23, 41/143, 42/323, 43/203, 44/263, 45/172, 46/112, 47/232, 48/68, 49/8, 50/248, 51/248, 52/188, 53/8, 54/188, 55/52, 56/68, 57/52, 58/188, 59/248, 60/277, 61/337, 62/157, 63/232, 64/128, 65/308, 66/128, 67/8, 68/352, 69/352, 70/232, 71/52, 72/112, 73/292, 74/172} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Es entsteht ein Graph mit 5 beweglichen Winkeln und 8 Einsetzkanten. Das sind Kanten, die am Ende passend in den Graph eingesetzt werden. 5 von diesen Kanten kann man mit den beweglichen Winkeln einstellen, die übrigen 3 müssen passen. Üblicherweise ist dann der Graph schon starr. Nur in Ausnahmefällen liegt eine Beweglichkeit vor und die macht sich eventuell bemerkbar, wenn man den Graph mit geringfügig geänderten beweglichen Winkeln erneut zurechtzieht. Dann kann es passieren, dass der Graph nicht wieder in die gleiche Position zurückgezogen wird sondern in eine andere mögliche Position entlang der Bewegungsbahn. Das Variieren der Winkel geht allerdings nur in einem kleinen Bereich, beispielsweise um 0,001°, ansonsten entstehen an anderer Stelle Überschneidungen öder ähnliches. Das ist eine ziemliche Fummelei. Obiger Graph wird immer wieder in die gleiche Position zurechtgezogen, also kein Anzeichen für eine Beweglichkeit. Ich suche nochmal ein anderes Beispiel für einen beweglichen Graph heraus, in einem neuen Beitrag, dann ist das noch deutlicher zu sehen. Wirklich exakte Ergebnisse sind nur das GAP-Programm mit Button "acos(1/4)" oder entsprechende geometrische Überlegungen.


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  Beitrag No.1888, vom Themenstarter, eingetragen 2020-01-18

Dieser Graph ist ein extremes Beispiel für einen starren Graphen mit falschen Kanten was die Genauigkeit (6 richtige Nachkommastellen) angeht, oder?


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  Beitrag No.1889, eingetragen 2020-01-18

Der Graph wäre exakt gezeichnet richtig. Er ist ein Beispiel dafür, dass sich die ursprüngliche Rechengenauigkeit von etwa 14 Nachkommastellen durch langatmige Eingabe ohne Ausnutzung von Symmetrieen auf 6 Nachkommastellen verschlechtern kann, wobei ich jetzt nicht nachgeschaut habe, aus welchem konkreten Grund die Ungenauigkeit entsteht. Für die Feststellung der Beweglichkeit mittels Zurechtziehen muss man aber diese ungenaue Eingabe in Kauf nehmen und irgendwie damit zurechtkommen. Ist nicht einfach alles. Das GAP-Programm sagt jedenfalls auch für den ungenauen Graph, dass alle Kantenlängen exakt Eins sind, weil es aus der ungenauen Eingabe versucht, die exakte Eingabe zu rekonstruieren, also ein 30.000001° Winkel wird als exakt 30° angenommen. Hier der Ausschnitt aus der GAP-Berechnung für den ungenaueren Graph: GAP \showon \sourceon GAP gap> P:=[]; gap> P[1]:=[0,0]; gap> P[2]:=[1,0]; gap> P[3]:=P[1]+W60*(P[2]-P[1]);; gap> P[4]:=P[3]+W60*(P[2]-P[3]);; gap> P[5]:=P[2]-(P[1]-P[2]);; gap> P[6]:=P[3]-(P[1]-P[3]);; gap> P[7]:=P[1]+W60*Wbl^-2*(P[3]-P[1]);; gap> P[8]:=P[1]+W60*(P[7]-P[1]);; gap> P[9]:=P[8]+W60*(P[7]-P[8]);; gap> P[10]:=P[8]-(P[1]-P[8]);; gap> P[11]:=P[7]-(P[1]-P[7]);; gap> P[12]:=P[11]+W60*(P[6]-P[11]);; gap> P[13]:=P[12]+W60*(P[6]-P[12]);; gap> P[14]:=P[12]-(P[11]-P[12]);; gap> P[15]:=P[10]+Wbl*(P[9]-P[10]);; gap> P[16]:=P[10]+W60*(P[15]-P[10]);; gap> P[17]:=P[16]+W60*(P[15]-P[16]);; gap> P[18]:=P[16]-(P[10]-P[16]);; gap> P[19]:=P[9]+W60*Wbl*(P[7]-P[9]);; gap> P[20]:=P[19]+W60^-2*(P[9]-P[19]);; gap> P[21]:=P[19]-(P[9]-P[19]);; gap> P[33]:=P[14]+W60^-1*(P[21]-P[14]);; gap> P[34]:=P[33]+W60*(P[14]-P[33]);; gap> P[36]:=P[18]+W60^3*Wbl^-1*(P[16]-P[18]);; gap> P[37]:=P[20]-(P[21]-P[20]);; gap> P[38]:=P[20]+(W60*Wbl)^-1*(P[37]-P[20]);; gap> P[39]:=P[20]-(P[17]-P[20]);; gap> P[50]:=P[34]+W60*Wbl*(P[14]-P[34]);; gap> P[51]:=P[50]+W60*(P[34]-P[50]);; gap> P[58]:=P[51]+Wbl^-1*(P[50]-P[51]);; gap> P[62]:=P[5]+Wbl^-3*(P[4]-P[5]);; gap> P[63]:=P[62]-(P[5]-P[62]);; gap> P[68]:=P[63]+W60*W60*Wbl*(P[62]-P[63]);; gap> P[69]:=P[51]+W60*(P[13]-P[51]);; gap> P[74]:=P[51]+W60^-1*(P[50]-P[51]);; gap> P[27]:=P[33]+W60*(P[34]-P[33]);; gap> P[30]:=P[38]-(P[39]-P[38]);; gap> P[31]:=P[36]-(P[18]-P[36]);; gap> P[32]:=P[33]-(P[14]-P[33]);; gap> P[35]:=P[31]+W60*(P[36]-P[31]);; gap> P[44]:=P[50]+W60^-1*(P[34]-P[50]);; gap> P[49]:=P[50]-(P[51]-P[50]);; gap> P[56]:=P[58]+(W60^3*Wbl^-1)^-1*(P[51]-P[58]);; gap> P[57]:=P[56]+W60*(P[58]-P[56]);; gap> P[60]:=P[62]+W60*(P[5]-P[62]);; gap> P[61]:=P[62]+W60*(P[60]-P[62]);; gap> P[64]:=P[68]+W60*Wbl*(P[63]-P[68]);; gap> P[65]:=P[64]+W60^-2*(P[68]-P[64]);; gap> P[66]:=P[64]+W60*(P[65]-P[64]);; gap> P[67]:=P[66]+W60*(P[65]-P[66]);; gap> P[70]:=P[67]+Wbl^-1*(P[66]-P[67]);; gap> P[71]:=P[70]+W60*(P[67]-P[70]);; gap> P[72]:=P[57]-(P[58]-P[57]);; gap> P[73]:=P[57]+W60*(P[74]-P[57]);; gap> P[24]:=P[27]+(W60*Wbl)^-1*(P[32]-P[27]);; gap> P[25]:=P[24]+W60*(P[27]-P[24]);; gap> P[26]:=P[25]-(P[27]-P[25]);; gap> P[28]:=P[32]+W60*Wbl*(P[27]-P[32]);; gap> P[29]:=P[31]+W60*(P[30]-P[31]);; gap> P[42]:=P[44]+W60*Wbl*(P[49]-P[44]);; gap> P[43]:=P[44]+W60*(P[42]-P[44]);; gap> P[45]:=P[49]+(W60*Wbl)^-1*(P[44]-P[49]);; gap> P[46]:=P[45]+W60^2*(P[49]-P[45]);; gap> P[47]:=P[56]-(P[58]-P[56]);; gap> P[48]:=P[46]+W60*(P[47]-P[46]);; gap> P[52]:=P[48]+Wbl*(P[47]-P[48]);; gap> P[53]:=P[48]+W60*(P[52]-P[48]);; gap> P[54]:=P[57]-(P[74]-P[57]);; gap> P[55]:=P[53]-(P[48]-P[53]);; gap> P[59]:=P[60]-(P[5]-P[60]);; gap> P[22]:=P[29]-(P[31]-P[29]);; gap> P[23]:=P[22]+W60*(P[24]-P[22]);; gap> P[40]:=P[42]-(P[44]-P[42]);; gap> P[41]:=P[26]+W60*(P[43]-P[26]);; gap> Kante:=[ [1,2],[1,3], [2,3], [3,4], [2,4], [4,5], [2,5], [3,6], [4,6], [1,7], [1,8], [7,8], [8,9], [7,9], [8,10], [9,10], [7,11], [6,11], [11,12], [6,12], [12,13], [12,14], [13,14], [14,21],[10,15], [10,16], [15,16], [16,17], [15,17], [16,18], [17,18], [15,19], [9,19], [17,20], [19,20], [20,21], [19,21], [22,29],[22,23], [23,24], [22,24], [23,25], [24,25], [23,26], [25,26], [24,27], [25,27], [27,33],[22,28], [28,29],[28,32],[29,31],[28,30], [29,30], [30,31],[30,38],[31,36],[32,33],[27,32], [14,33], [14,34], [33,34], [34,51],[31,35], [35,36],[35,37],[35,38],[18,36], [18,37], [36,37], [20,37], [20,38], [14,39], [20,39], [38,39], [40,41],[26,41], [40,42], [41,42], [42,43],[41,43], [26,43], [42,44], [43,44], [44,50],[40,45], [45,49],[40,46], [45,46], [46,47], [45,47], [46,48], [47,48], [44,49], [49,50],[34,50], [50,51],[13,51], [51,58],[48,52], [48,53], [52,53], [53,54], [52,54], [53,55], [54,55], [55,71],[52,56], [47,56], [54,57], [56,57], [57,72],[57,58], [56,58], [59,60],[5,60], [61,62],[59,61], [60,61], [5,62], [60,62], [62,63], [61,63], [64,68],[59,64], [64,65], [59,65], [64,66], [65,66], [66,73],[66,67], [65,67], [63,68], [13,69], [51,69], [63,69], [68,69], [67,70], [70,73],[70,71], [67,71], [70,72], [71,72], [55,72], [57,73], [57,74], [73,74], [51,74], ];; gap> Size(Kante); gap> RESTKANTEN:=[[20,38],[14,21],[35,38],[28,32],[57,72],[51,58],[66,73],[70,73],];; 148 gap> gap> for K in Kante do Print(" ",(P[K[1]]-P[K[2]])^2); od; gap> 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \sourceoff \showoff Die vielen Einsen am Ende sind alle Kantenlängen exakt 1.


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  Beitrag No.1890, vom Themenstarter, eingetragen 2020-01-18

Nach Feinjustieren des letzten Graphen werden auch 11 richtige Nachkommastellen angezeigt, also 0 oder 9. P11,P21 ist jetzt auch wie bei haribo 1.07046626931915200842.


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StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
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Wohnort: Raun
  Beitrag No.1891, eingetragen 2020-01-18

Dafür ändert sich beim Feinjustieren der vierte Winkel von vorher exakt -60°=300° auf 300.0000000000152°, also dadurch wird die Ungenauigkeit mehr auf die Winkel verlagert. Diese werden beim Feinjustieren so variiert, dass möglichst das gewünschte Ergebnis herauskommt. Wird mit möglichst exakten Winkeln losgerechnet, stimmen die Kantenlängen nicht so gut und wird so gerechnet, dass die genauesten Kantenlängen herauskommen, stimmen die Winkel nicht so gut. Irgendwo dazwischen geht Genauigkeit verloren.


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Wohnort: Raun
  Beitrag No.1892, eingetragen 2020-01-19

Den #467-2 habe ich ohne die beiden Kanten P22-P78 und P12-P77 eingegeben und erhalte nach Button neue Eingabe "wenig Winkel" folgenden Graph 88 Knoten, 4×Grad 3, 80×Grad 4, 2×Grad 5, 2×Grad 7, 0 Überschneidungen 178 Kanten, minimal 0.99999999999998800959, maximal 1.00000000000000910383 einzustellende Kanten, Abstände und Winkel: |P42-P80|=1.00000000000000555112 |P75-P83|=0.99999999999999711342 |P86-P87|=1.00000000000000421885 |P85-P87|=0.99999999999999833467 |P55-P87|=1.00000000000000421885 |P60-P61|=1.00000000000000177636 |P65-P66|=1.00000000000000643929 |P65-P85|=0.99999999999998800959 $ %Eingabe war: % %#1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78); % % % % % % %P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(1,2); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,2,blauerWinkel); L(9,1,6); L(10,9,6); L(11,9,10); N(7,6,3); M(109,7,3,95.00000000000001); L(73,7,109); Q(8,7,4,ab(109,7,73,"gedreht"),D); M(110,8,4,35.000000000000014); L(37,8,110); M(111,5,2,-85.00000000000001); L(38,111,5); Q(36,8,5,ab(110,8,37,"gedreht"),ab(111,5,38,"gedreht")); M(112,37,8,154.99999999999997); L(43,37,112); M(113,38,5,-144.99999999999994); L(44,113,38); Q(40,37,38,ab(112,37,43,"gedreht"),ab(113,38,44,"gedreht")); M(114,44,38,-85.00000000000017); M(71,114,44,125.00000000000043); M(69,71,114,125.00000000000016); L(116,69,71); Q(115,71,114,ab(116,71,69,"gedreht"),D); Q(72,114,44,ab(115,114,69,71,"gedreht"),D); Q(46,43,44,D,ab(114,44,69,71,72,"gedreht")); M(117,8,4,125.00000000000001); L(75,8,117); Q(74,8,43,ab(117,8,75,"gedreht"),D); M(118,73,7,-144.99999999999994); L(77,73,118); Q(76,73,75,ab(118,73,77,"gedreht"),D); M(12,10,6,gruenerWinkel); M(119,11,9,95.00000000000006); L(14,11,119); L(15,14,119); L(16,14,15); Q(13,11,12,ab(119,11,14,15,16,"gedreht"),D); N(17,15,12); M(120,16,14,94.99999999999991); L(19,16,120); L(20,19,120); L(21,19,20); Q(18,16,17,ab(120,16,19,20,21,"gedreht"),D); N(22,20,17); M(121,21,19,95.00000000000006); L(24,21,121); L(25,24,121); L(26,24,25); Q(23,21,22,ab(121,21,24,25,26,"gedreht"),D); M(27,25,23,orangerWinkel); M(122,26,24,95.00000000000001); L(29,26,122); L(30,29,122); L(31,29,30); Q(28,26,27,ab(122,26,29,30,31,"gedreht"),D); N(32,30,27); M(123,31,29,95.00000000000009); L(34,31,123); M(124,32,27,-114.99999999999997); L(35,124,32); Q(33,31,32,ab(123,31,34,"gedreht"),ab(124,32,35,"gedreht")); M(125,34,31,154.99999999999991); L(41,34,125); M(126,35,32,-144.99999999999986); L(42,126,35); Q(39,34,35,ab(125,34,41,"gedreht"),ab(126,35,42,"gedreht")); M(127,41,34,95.00000000000006); L(47,41,127); L(48,47,127); L(49,47,48); Q(45,41,42,ab(127,41,47,48,49,"gedreht"),D); M(128,42,35,-174.99999999999991); L(88,128,42); Q(50,48,42,D,ab(128,42,88,"gedreht")); M(129,49,47,95.00000000000014); L(52,49,129); L(53,52,129); L(54,52,53); Q(51,49,50,ab(129,49,52,53,54,"gedreht"),D); N(78,27,77); N(79,78,76); N(80,32,79); M(130,42,35,34.999999999999915); L(81,42,130); A(80,42,ab(130,42,81,"gedreht")); M(131,81,42,155.0000000000003); M(83,131,81,-115.0000000000004); L(132,131,83); Q(86,81,131,D,ab(132,131,83,"gedreht")); Q(82,81,79,ab(131,81,83,86,"gedreht"),D); A(75,83); M(87,86,81,-84.99999999999967); L(133,86,87); A(88,86,ab(133,86,87,"gedreht")); N(84,83,74); M(134,84,74,155.00000000000026); L(85,84,134); Q(70,84,71,ab(134,84,85,"gedreht"),D); A(85,87); M(67,69,71,-85.00000000000058); M(64,67,69,185); L(66,67,64); L(136,67,66); Q(135,69,67,D,ab(136,67,64,66,"gedreht")); Q(68,70,69,D,ab(135,69,64,66,67,"gedreht")); M(56,54,52,94.99999999999955); L(57,54,56); L(58,57,56); L(137,57,58); M(62,64,66,-84.99999999999945); M(138,62,64,185); L(61,62,138); L(139,62,61); Q(63,64,62,D,ab(139,62,138,61,"gedreht")); Q(59,54,64,ab(137,54,56,57,58,"gedreht"),ab(138,64,61,62,63,"gedreht")); N(55,56,53); A(55,87); N(60,58,55); A(60,61); N(65,63,60); A(65,66); A(65,85); %R(42,80); // oder R(42,81); %R(75,83); %R(86,87); // oder R(86,88); %R(85,87); %R(55,87); %R(60,61); %R(65,66); %R(65,85); % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LimeGreen}{rgb}{0.20,0.80,0.20} \definecolor{Orange}{rgb}{1.00,0.64,0.00} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/3.23/1.87, 8/4.23/1.87, 9/1.87/0.50, 10/1.87/1.50, 11/1.00/1.00, 12/2.37/2.37, 13/1.50/1.87, 14/0.50/1.87, 15/1.00/2.73, 16/0.00/2.73, 17/1.87/3.23, 18/0.87/3.23, 19/0.00/3.73, 20/0.87/4.23, 21/0.00/4.73, 22/1.87/4.23, 23/1.00/4.73, 24/0.50/5.60, 25/1.50/5.60, 26/1.00/6.46, 27/2.37/5.10, 28/1.87/5.96, 29/1.87/6.96, 30/2.73/6.46, 31/2.73/7.46, 32/3.23/5.60, 33/3.23/6.60, 34/3.73/7.46, 35/4.10/6.10, 36/4.73/1.00, 37/5.23/1.87, 38/5.60/0.50, 39/4.60/6.96, 40/6.10/1.37, 41/4.60/7.96, 42/5.10/6.10, 43/6.10/2.37, 44/6.60/0.50, 45/5.10/7.10, 46/6.60/1.50, 47/5.60/7.96, 48/6.10/7.10, 49/6.60/7.96, 50/6.10/6.10, 51/6.60/6.96, 52/7.46/7.46, 53/7.46/6.46, 54/8.33/6.96, 55/6.96/5.60, 56/7.83/6.10, 57/8.83/6.10, 58/8.33/5.23, 59/9.33/5.23, 60/7.46/4.73, 61/8.46/4.73, 62/9.33/4.23, 63/8.46/3.73, 64/9.33/3.23, 65/7.46/3.73, 66/8.33/3.23, 67/8.83/2.37, 68/7.83/2.37, 69/8.33/1.50, 70/6.96/2.87, 71/7.46/2.00, 72/7.46/1.00, 73/3.73/2.73, 74/5.10/2.37, 75/4.23/2.87, 76/3.73/3.73, 77/2.87/3.23, 78/2.87/4.23, 79/3.73/4.73, 80/4.23/5.60, 81/5.10/5.10, 82/4.60/4.23, 83/5.10/3.37, 84/5.96/2.87, 85/6.46/3.73, 86/5.60/4.23, 87/6.46/4.73, 88/5.60/5.23} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/0.00/90.00/0.4/Blue, 10/330.00/420.00/0.4/Green, 25/240.00/330.00/0.4/Orange} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 7/6, 7/3, 8/7, 8/4, 9/1, 9/6, 10/9, 10/6, 11/9, 11/10, 12/10, 13/11, 13/12, 14/11, 14/13, 15/14, 15/13, 16/14, 16/15, 17/15, 17/12, 18/16, 18/17, 19/16, 19/18, 20/19, 20/18, 21/19, 21/20, 22/20, 22/17, 23/21, 23/22, 24/21, 24/23, 25/24, 25/23, 26/24, 26/25, 27/25, 28/26, 28/27, 29/26, 29/28, 30/29, 30/28, 31/29, 31/30, 32/30, 32/27, 33/31, 33/32, 34/31, 34/33, 35/33, 35/32, 36/8, 36/5, 37/8, 37/36, 38/36, 38/5, 39/34, 39/35, 40/37, 40/38, 41/34, 41/39, 42/39, 42/35, 43/37, 43/40, 44/40, 44/38, 45/41, 45/42, 46/43, 46/44, 47/41, 47/45, 48/47, 48/45, 49/47, 49/48, 50/48, 50/42, 51/49, 51/50, 52/49, 52/51, 53/52, 53/51, 54/52, 54/53, 55/56, 55/53, 55/87, 56/54, 57/54, 57/56, 58/57, 58/56, 59/57, 59/58, 59/62, 60/58, 60/55, 60/61, 61/62, 61/59, 62/64, 63/64, 63/61, 63/62, 64/67, 65/63, 65/60, 65/66, 65/85, 66/67, 66/64, 67/69, 68/70, 68/66, 68/67, 68/69, 69/71, 70/84, 70/71, 71/46, 72/69, 72/71, 72/46, 72/44, 73/7, 73/8, 74/8, 74/43, 75/8, 75/74, 75/83, 76/73, 76/75, 77/73, 77/76, 78/27, 78/77, 79/78, 79/76, 80/32, 80/79, 80/42, 81/42, 81/80, 82/81, 82/79, 83/82, 84/83, 84/74, 85/84, 85/70, 85/87, 86/81, 86/83, 86/82, 87/86, 88/50, 88/42, 88/86, 88/87} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,88} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[LimeGreen,very thick] (p-42) -- (p-80); \draw[LimeGreen,very thick] (p-75) -- (p-83); \draw[LimeGreen,very thick] (p-86) -- (p-87); \draw[LimeGreen,very thick] (p-85) -- (p-87); \draw[LimeGreen,very thick] (p-55) -- (p-87); \draw[LimeGreen,very thick] (p-60) -- (p-61); \draw[LimeGreen,very thick] (p-65) -- (p-66); \draw[LimeGreen,very thick] (p-65) -- (p-85); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/0.00/90.00/0.4/Blue, 10/330.00/420.00/0.4/Green, 25/240.00/330.00/0.4/Orange} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/210, 2/330, 3/150, 4/30, 5/330, 6/60, 7/210, 8/330, 9/180, 10/60, 11/180, 12/348, 13/330, 14/270, 15/30, 16/150, 17/318, 18/360, 19/240, 20/360, 21/120, 22/48, 23/330, 24/150, 25/330, 26/90, 27/167, 28/300, 29/60, 30/360, 31/60, 32/240, 33/270, 34/30, 35/360, 36/270, 37/180, 38/360, 39/90, 40/90, 41/150, 42/60, 43/60, 44/330, 45/210, 46/120, 47/30, 48/330, 49/30, 50/30, 51/180, 52/360, 53/300, 54/90, 55/93, 56/150, 57/90, 58/270, 59/330, 60/137, 61/180, 62/360, 63/240, 64/300, 65/318, 66/90, 67/270, 68/150, 69/360, 70/330, 71/120, 72/360, 73/300, 74/360, 75/120, 76/60, 77/180, 78/257, 79/123, 80/180, 81/90, 82/210, 83/270, 84/210, 85/90, 86/240, 87/360, 88/120} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Er enthält 3 bewegliche Winkel und 8 einzustellende Kanten, noch kein Zeichen für Beweglichkeit (es müssten weniger einzustellende Kanten als Winkel sein). Auch der Versuch, die Winkel zu verändern, ist erfolglos (Graph mit Kursor wie Text markieren, ins Streichholzprogramm großes Eingabefenster kopieren, Button "neu zeichnen", dann mit Button "-0.01" den blauen Winkel ändern oder auch andere Winkel anklicken und ändern, dann entstehen nicht passende Kanten). Wenn ich aber den blauen Winkel um -0.01° verändere und dann den Graph mit Button Feinjustieren(3) wieder zurechtziehe, so wird nicht mehr der Ausgangswert 90° erreicht: blauerWinkel = 89.99483124096407 gruenerWinkel = 90.00516875903601 orangerWinkel = 89.99483124096504 ein Zeichen für Beweglichkeit des Graphen. Das Ergebnis lässt auch vermuten, das gruenerWinkel=180°-blauerWinkel und orangerWinkel=blauerWinkel ist. Das übernehme ich in die Eingabe und wenn man jetzt den blauen Winkel verändert (Animationsknopf "Start_blauerWinkel" links vom Graph im Streichholzprogramm), so bleiben diesmal alle Kantenlängen erhalten, der Graph ist beweglich. $ %Eingabe war: % %#1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78); % % % % % % %P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(1,2); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,2,blauerWinkel); L(9,1,6); L(10,9,6); L(11,9,10); N(7,6,3); M(109,7,3,95.00000000000001); L(73,7,109); Q(8,7,4,ab(109,7,73,"gedreht"),D); M(110,8,4,35.000000000000014); L(37,8,110); M(111,5,2,-85.00000000000001); L(38,111,5); Q(36,8,5,ab(110,8,37,"gedreht"),ab(111,5,38,"gedreht")); M(112,37,8,154.99999999999997); L(43,37,112); M(113,38,5,-144.99999999999994); L(44,113,38); Q(40,37,38,ab(112,37,43,"gedreht"),ab(113,38,44,"gedreht")); M(114,44,38,-85.00000000000017); M(71,114,44,125.00000000000043); M(69,71,114,125.00000000000016); L(116,69,71); Q(115,71,114,ab(116,71,69,"gedreht"),D); Q(72,114,44,ab(115,114,69,71,"gedreht"),D); Q(46,43,44,D,ab(114,44,69,71,72,"gedreht")); M(117,8,4,125.00000000000001); L(75,8,117); Q(74,8,43,ab(117,8,75,"gedreht"),D); M(118,73,7,-144.99999999999994); L(77,73,118); Q(76,73,75,ab(118,73,77,"gedreht"),D); M(12,10,6,180-blauerWinkel); M(119,11,9,95.00000000000006); L(14,11,119); L(15,14,119); L(16,14,15); Q(13,11,12,ab(119,11,14,15,16,"gedreht"),D); N(17,15,12); M(120,16,14,94.99999999999991); L(19,16,120); L(20,19,120); L(21,19,20); Q(18,16,17,ab(120,16,19,20,21,"gedreht"),D); N(22,20,17); M(121,21,19,95.00000000000006); L(24,21,121); L(25,24,121); L(26,24,25); Q(23,21,22,ab(121,21,24,25,26,"gedreht"),D); M(27,25,23,blauerWinkel); M(122,26,24,95.00000000000001); L(29,26,122); L(30,29,122); L(31,29,30); Q(28,26,27,ab(122,26,29,30,31,"gedreht"),D); N(32,30,27); M(123,31,29,95.00000000000009); L(34,31,123); M(124,32,27,-114.99999999999997); L(35,124,32); Q(33,31,32,ab(123,31,34,"gedreht"),ab(124,32,35,"gedreht")); M(125,34,31,154.99999999999991); L(41,34,125); M(126,35,32,-144.99999999999986); L(42,126,35); Q(39,34,35,ab(125,34,41,"gedreht"),ab(126,35,42,"gedreht")); M(127,41,34,95.00000000000006); L(47,41,127); L(48,47,127); L(49,47,48); Q(45,41,42,ab(127,41,47,48,49,"gedreht"),D); M(128,42,35,-174.99999999999991); L(88,128,42); Q(50,48,42,D,ab(128,42,88,"gedreht")); M(129,49,47,95.00000000000014); L(52,49,129); L(53,52,129); L(54,52,53); Q(51,49,50,ab(129,49,52,53,54,"gedreht"),D); N(78,27,77); N(79,78,76); N(80,32,79); M(130,42,35,34.999999999999915); L(81,42,130); A(80,42,ab(130,42,81,"gedreht")); M(131,81,42,155.0000000000003); M(83,131,81,-115.0000000000004); L(132,131,83); Q(86,81,131,D,ab(132,131,83,"gedreht")); Q(82,81,79,ab(131,81,83,86,"gedreht"),D); A(75,83); M(87,86,81,-84.99999999999967); L(133,86,87); A(88,86,ab(133,86,87,"gedreht")); N(84,83,74); M(134,84,74,155.00000000000026); L(85,84,134); Q(70,84,71,ab(134,84,85,"gedreht"),D); A(85,87); M(67,69,71,-85.00000000000058); M(64,67,69,185); L(66,67,64); L(136,67,66); Q(135,69,67,D,ab(136,67,64,66,"gedreht")); Q(68,70,69,D,ab(135,69,64,66,67,"gedreht")); M(56,54,52,94.99999999999955); L(57,54,56); L(58,57,56); L(137,57,58); M(62,64,66,-84.99999999999945); M(138,62,64,185); L(61,62,138); L(139,62,61); Q(63,64,62,D,ab(139,62,138,61,"gedreht")); Q(59,54,64,ab(137,54,56,57,58,"gedreht"),ab(138,64,61,62,63,"gedreht")); N(55,56,53); A(55,87); N(60,58,55); A(60,61); N(65,63,60); A(65,66); A(65,85); %R(42,80); // oder R(42,81); %R(75,83); %R(86,87); // oder R(86,88); %R(85,87); %R(55,87); %R(60,61); %R(65,66); %R(65,85); % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{LimeGreen}{rgb}{0.20,0.80,0.20} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/3.23/1.87, 8/4.23/1.87, 9/1.87/0.50, 10/1.87/1.50, 11/1.00/1.00, 12/2.37/2.37, 13/1.50/1.87, 14/0.50/1.87, 15/1.00/2.73, 16/0.00/2.73, 17/1.87/3.23, 18/0.87/3.23, 19/0.00/3.73, 20/0.87/4.23, 21/0.00/4.73, 22/1.87/4.23, 23/1.00/4.73, 24/0.50/5.60, 25/1.50/5.60, 26/1.00/6.46, 27/2.37/5.10, 28/1.87/5.96, 29/1.87/6.96, 30/2.73/6.46, 31/2.73/7.46, 32/3.23/5.60, 33/3.23/6.60, 34/3.73/7.46, 35/4.10/6.10, 36/4.73/1.00, 37/5.23/1.87, 38/5.60/0.50, 39/4.60/6.96, 40/6.10/1.37, 41/4.60/7.96, 42/5.10/6.10, 43/6.10/2.37, 44/6.60/0.50, 45/5.10/7.10, 46/6.60/1.50, 47/5.60/7.96, 48/6.10/7.10, 49/6.60/7.96, 50/6.10/6.10, 51/6.60/6.96, 52/7.46/7.46, 53/7.46/6.46, 54/8.33/6.96, 55/6.96/5.60, 56/7.83/6.10, 57/8.83/6.10, 58/8.33/5.23, 59/9.33/5.23, 60/7.46/4.73, 61/8.46/4.73, 62/9.33/4.23, 63/8.46/3.73, 64/9.33/3.23, 65/7.46/3.73, 66/8.33/3.23, 67/8.83/2.37, 68/7.83/2.37, 69/8.33/1.50, 70/6.96/2.87, 71/7.46/2.00, 72/7.46/1.00, 73/3.73/2.73, 74/5.10/2.37, 75/4.23/2.87, 76/3.73/3.73, 77/2.87/3.23, 78/2.87/4.23, 79/3.73/4.73, 80/4.23/5.60, 81/5.10/5.10, 82/4.60/4.23, 83/5.10/3.37, 84/5.96/2.87, 85/6.46/3.73, 86/5.60/4.23, 87/6.46/4.73, 88/5.60/5.23} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/0.00/90.00/0.4/Blue, 25/240.00/330.00/0.4/Blue} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 7/6, 7/3, 8/7, 8/4, 9/1, 9/6, 10/9, 10/6, 11/9, 11/10, 12/10, 13/11, 13/12, 14/11, 14/13, 15/14, 15/13, 16/14, 16/15, 17/15, 17/12, 18/16, 18/17, 19/16, 19/18, 20/19, 20/18, 21/19, 21/20, 22/20, 22/17, 23/21, 23/22, 24/21, 24/23, 25/24, 25/23, 26/24, 26/25, 27/25, 28/26, 28/27, 29/26, 29/28, 30/29, 30/28, 31/29, 31/30, 32/30, 32/27, 33/31, 33/32, 34/31, 34/33, 35/33, 35/32, 36/8, 36/5, 37/8, 37/36, 38/36, 38/5, 39/34, 39/35, 40/37, 40/38, 41/34, 41/39, 42/39, 42/35, 43/37, 43/40, 44/40, 44/38, 45/41, 45/42, 46/43, 46/44, 47/41, 47/45, 48/47, 48/45, 49/47, 49/48, 50/48, 50/42, 51/49, 51/50, 52/49, 52/51, 53/52, 53/51, 54/52, 54/53, 55/56, 55/53, 55/87, 56/54, 57/54, 57/56, 58/57, 58/56, 59/57, 59/58, 59/62, 60/58, 60/55, 60/61, 61/62, 61/59, 62/64, 63/64, 63/61, 63/62, 64/67, 65/63, 65/60, 65/66, 65/85, 66/67, 66/64, 67/69, 68/70, 68/66, 68/67, 68/69, 69/71, 70/84, 70/71, 71/46, 72/69, 72/71, 72/46, 72/44, 73/7, 73/8, 74/8, 74/43, 75/8, 75/74, 75/83, 76/73, 76/75, 77/73, 77/76, 78/27, 78/77, 79/78, 79/76, 80/32, 80/79, 80/42, 81/42, 81/80, 82/81, 82/79, 83/82, 84/83, 84/74, 85/84, 85/70, 85/87, 86/81, 86/83, 86/82, 87/86, 88/50, 88/42, 88/86, 88/87} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,88} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[LimeGreen,very thick] (p-42) -- (p-80); \draw[LimeGreen,very thick] (p-75) -- (p-83); \draw[LimeGreen,very thick] (p-86) -- (p-87); \draw[LimeGreen,very thick] (p-85) -- (p-87); \draw[LimeGreen,very thick] (p-55) -- (p-87); \draw[LimeGreen,very thick] (p-60) -- (p-61); \draw[LimeGreen,very thick] (p-65) -- (p-66); \draw[LimeGreen,very thick] (p-65) -- (p-85); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/0.00/90.00/0.4/Blue, 25/240.00/330.00/0.4/Blue} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/210, 2/330, 3/150, 4/30, 5/330, 6/60, 7/210, 8/330, 9/180, 10/60, 11/180, 12/348, 13/330, 14/270, 15/30, 16/150, 17/318, 18/360, 19/240, 20/360, 21/120, 22/48, 23/330, 24/150, 25/330, 26/180, 27/167, 28/300, 29/60, 30/300, 31/60, 32/240, 33/120, 34/30, 35/210, 36/270, 37/180, 38/360, 39/300, 40/90, 41/150, 42/60, 43/60, 44/330, 45/270, 46/120, 47/150, 48/330, 49/30, 50/30, 51/180, 52/360, 53/240, 54/90, 55/93, 56/210, 57/30, 58/210, 59/60, 60/137, 61/180, 62/60, 63/240, 64/30, 65/318, 66/150, 67/330, 68/150, 69/360, 70/330, 71/120, 72/360, 73/300, 74/360, 75/120, 76/60, 77/180, 78/257, 79/123, 80/180, 81/90, 82/150, 83/270, 84/210, 85/90, 86/240, 87/360, 88/120} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $


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haribo
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 25.10.2012
Mitteilungen: 3872
  Beitrag No.1893, eingetragen 2020-01-20

\quoteon(2020-01-18 15:41 - Slash in Beitrag No. 1890) P11,P21 ist jetzt auch wie bei haribo 1.07046626931915200842. \quoteoff ok, also soweit herzlichen dank für die aufwendigste untersucheng in der geschichte der 4/6er der graph aus #1881 ist also starr, dann kann man ja mal anfangen wieder kreativ zu werden... wenn man 9-19 herausnimmt wie beweglich verhält sich dann die strecke 15-11?, just playing around without target und ich würde immer gerne einen verstellwinkel bei 1-7-11 haben anstelle von 3-1-7... weil es ein winkel ist der in beide richtungen gedrückt werden kann auch die frage ob man eigentlich alle vier symetrisch zu 9-19 liegenden herausnehmen muss oder nur ein oder zwei für beweglichkeit schon reichen würden... sicherlich unter verlust der symetrien aber die sich ja immer nur der gedankeneinfachheit geschuldet weil niemand bisher den "360°" winkel denken kann, also den komplett unsymetrischen graphen [Die Antwort wurde nach Beitrag No.1891 begonnen.]


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StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
Mitteilungen: 4165
Wohnort: Raun
  Beitrag No.1894, eingetragen 2020-01-25

Die Punktnummern beziehe ich auf zuletzt #1887. Der richtige Ansatz ist vier Kanten entfernen, dann ist der Graph nach der Knotenabweichungsgleichung garantiert beweglich. 74 Knoten, 16×Grad 3, 54×Grad 4, 4×Grad 6, 0 Überschneidungen 144 Kanten, minimal 0.99999999999999544809, maximal 1.00000000000000266454 einzustellende Kanten, Abstände und Winkel: |P21-P14|=1.00000000000000066613 ∠(P18-P20,P5-P13)=90.00000000000001421085° ∠(P18-P14,P5-P13)=90.00000000000001421085° $ %Eingabe war: % %#1894-1 % % % % % % % %P[1]=[-18.114795237025238,-11.925524469987494]; P[2]=[31.54207889274424,-17.773160886543337]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); M(7,1,3,blauerWinkel,2); N(11,7,6); L(12,11,6); M(13,12,6,gruenerWinkel); L(14,12,13); M(15,10,9,orangerWinkel,2); M(19,15,10,vierterWinkel); N(20,17,19); L(21,20,19); RA(21,14); % %RK([5,13],[18,20,14],360/4,true); % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LimeGreen}{rgb}{0.20,0.80,0.20} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.85/0.23, 2/2.84/0.12, 3/2.45/1.04, 4/3.44/0.92, 5/3.84/0.00, 6/3.05/1.84, 7/1.99/1.22, 8/1.06/0.85, 9/1.20/1.84, 10/0.27/1.46, 11/2.12/2.22, 12/2.91/2.83, 13/3.84/2.45, 14/3.70/3.44, 15/1.06/2.07, 16/0.14/2.45, 17/0.93/3.06, 18/0.00/3.44, 19/1.99/2.45, 20/1.85/3.44, 21/2.78/3.06, 22/1.85/6.65, 23/2.84/6.76, 24/2.45/5.85, 25/3.44/5.96, 26/3.84/6.88, 27/3.05/5.04, 28/1.99/5.66, 29/1.06/6.03, 30/1.20/5.04, 31/0.27/5.42, 32/2.12/4.67, 33/2.91/4.05, 34/3.84/4.43, 35/1.06/4.81, 36/0.14/4.43, 37/0.93/3.82, 38/1.99/4.43, 39/2.78/3.82, 40/5.82/6.65, 41/4.83/6.76, 42/5.23/5.85, 43/4.23/5.96, 44/4.63/5.04, 45/5.69/5.66, 46/6.61/6.03, 47/6.48/5.04, 48/7.40/5.42, 49/5.55/4.67, 50/4.76/4.05, 51/3.97/3.44, 52/6.61/4.81, 53/7.54/4.43, 54/6.75/3.82, 55/7.68/3.44, 56/5.69/4.43, 57/5.82/3.44, 58/4.90/3.82, 59/5.82/0.23, 60/4.83/0.12, 61/5.23/1.04, 62/4.23/0.92, 63/4.63/1.84, 64/5.69/1.22, 65/6.61/0.85, 66/6.48/1.84, 67/7.40/1.46, 68/5.55/2.22, 69/4.76/2.83, 70/6.61/2.07, 71/7.54/2.45, 72/6.75/3.06, 73/5.69/2.45, 74/4.90/3.06} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/53.28/82.24/0.4/Blue, 12/277.76/337.76/0.4/Green, 10/22.24/37.76/0.4/Orange, 15/217.76/382.24/0.4/Violet} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 5/62, 5/60, 6/3, 6/4, 7/1, 8/1, 8/7, 9/8, 9/7, 10/8, 10/9, 11/7, 11/6, 12/11, 12/6, 13/12, 13/69, 13/51, 14/12, 14/13, 14/33, 14/34, 14/39, 15/10, 16/10, 16/15, 17/16, 17/15, 18/16, 18/17, 18/36, 18/37, 19/15, 20/17, 20/19, 20/37, 20/38, 21/20, 21/19, 21/14, 23/22, 24/22, 24/23, 25/23, 25/24, 26/23, 26/25, 26/41, 26/43, 27/24, 27/25, 28/22, 29/22, 29/28, 30/28, 30/29, 31/29, 31/30, 32/27, 32/28, 33/27, 33/32, 34/33, 34/50, 35/31, 36/31, 36/35, 37/35, 37/36, 38/35, 39/38, 39/20, 41/40, 42/40, 42/41, 43/41, 43/42, 44/42, 44/43, 45/40, 46/40, 46/45, 47/45, 47/46, 48/46, 48/47, 49/44, 49/45, 50/44, 50/49, 51/50, 51/34, 51/69, 51/74, 52/48, 53/48, 53/52, 54/52, 54/53, 55/53, 55/54, 55/71, 55/72, 56/52, 57/54, 57/56, 57/72, 57/73, 58/51, 58/56, 58/57, 60/59, 61/59, 61/60, 62/60, 62/61, 63/61, 63/62, 64/59, 65/59, 65/64, 66/64, 66/65, 67/65, 67/66, 68/63, 68/64, 69/63, 69/68, 70/67, 71/67, 71/70, 72/70, 72/71, 73/70, 74/73, 74/57} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,74} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[LimeGreen,very thick] (p-21) -- (p-14); %\draw[Violet,very thick] (p-5) -- (p-13); %\draw[Violet,very thick] (p-5) -- (p-13); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/53.28/82.24/0.4/Blue, 12/277.76/337.76/0.4/Green, 10/22.24/37.76/0.4/Orange, 15/217.76/382.24/0.4/Violet} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/292, 2/323, 3/143, 4/23, 5/217, 6/308, 7/52, 8/172, 9/52, 10/172, 11/188, 12/68, 13/308, 14/292, 15/308, 16/128, 17/68, 18/232, 19/248, 20/128, 21/8, 22/68, 23/97, 24/157, 25/277, 26/37, 27/277, 28/8, 29/68, 30/248, 31/188, 32/172, 33/292, 34/52, 35/52, 36/232, 37/292, 38/112, 39/352, 40/112, 41/143, 42/323, 43/143, 44/128, 45/172, 46/112, 47/292, 48/352, 49/8, 50/8, 51/112, 52/188, 53/308, 54/188, 55/308, 56/68, 57/308, 58/188, 59/248, 60/337, 61/37, 62/217, 63/97, 64/188, 65/308, 66/68, 67/8, 68/352, 69/112, 70/232, 71/352, 72/172, 73/292, 74/172} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Da kann ich den vierten Winkel (violett, in P15) beliebig in 1° Schritten verändern und anschließend die übrigen drei Winkel mit Button "Feinjustieren(3,3)" neu einstellen. In Richtung kleinerer vierter Winkel erhalte ich $ %Eingabe war: % %#1894-1 % % % % % % % %P[1]=[-18.170417966471057,-12.057944075335968]; P[2]=[31.48453077044413,-17.921907405228126]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); M(7,1,3,blauerWinkel,2); N(11,7,6); L(12,11,6); M(13,12,6,gruenerWinkel); L(14,12,13); M(15,10,9,orangerWinkel,2); M(19,15,10,vierterWinkel); N(20,17,19); L(21,20,19); RA(21,14); % %RK([5,13],[18,20,14],360/4,true); % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LimeGreen}{rgb}{0.20,0.80,0.20} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.23/0.23, 2/3.23/0.12, 3/2.83/1.04, 4/3.82/0.92, 5/4.22/0.00, 6/3.43/1.84, 7/2.54/1.19, 8/1.56/0.98, 9/1.87/1.93, 10/0.89/1.72, 11/2.49/2.19, 12/3.26/2.82, 13/4.22/2.53, 14/3.99/3.51, 15/1.44/2.55, 16/0.44/2.61, 17/1.00/3.44, 18/0.00/3.51, 19/2.44/2.61, 20/2.00/3.51, 21/2.99/3.44, 22/2.23/6.78, 23/3.23/6.90, 24/2.83/5.98, 25/3.82/6.10, 26/4.22/7.01, 27/3.43/5.18, 28/2.54/5.83, 29/1.56/6.04, 30/1.87/5.09, 31/0.89/5.30, 32/2.49/4.83, 33/3.26/4.19, 34/4.22/4.48, 35/1.44/4.47, 36/0.44/4.40, 37/1.00/3.57, 38/2.44/4.40, 39/2.99/3.57, 40/6.21/6.78, 41/5.21/6.90, 42/5.61/5.98, 43/4.61/6.10, 44/5.01/5.18, 45/5.90/5.83, 46/6.88/6.04, 47/6.57/5.09, 48/7.55/5.30, 49/5.95/4.83, 50/5.18/4.19, 51/4.45/3.51, 52/7.00/4.47, 53/7.99/4.40, 54/7.44/3.57, 55/8.44/3.51, 56/6.00/4.40, 57/6.44/3.51, 58/5.44/3.57, 59/6.21/0.23, 60/5.21/0.12, 61/5.61/1.04, 62/4.61/0.92, 63/5.01/1.84, 64/5.90/1.19, 65/6.88/0.98, 66/6.57/1.93, 67/7.55/1.72, 68/5.95/2.19, 69/5.18/2.82, 70/7.00/2.55, 71/7.99/2.61, 72/7.44/3.44, 73/6.00/2.61, 74/5.44/3.44} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/53.26/72.21/0.4/Blue, 12/279.62/343.14/0.4/Green, 10/12.21/56.41/0.4/Orange, 15/236.41/363.59/0.4/Violet} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 5/62, 5/60, 6/3, 6/4, 7/1, 8/1, 8/7, 9/8, 9/7, 10/8, 10/9, 11/7, 11/6, 12/11, 12/6, 13/12, 13/69, 13/51, 14/12, 14/13, 14/33, 14/34, 14/39, 15/10, 16/10, 16/15, 17/16, 17/15, 18/16, 18/17, 18/36, 18/37, 19/15, 20/17, 20/19, 20/37, 20/38, 21/20, 21/19, 21/14, 23/22, 24/22, 24/23, 25/23, 25/24, 26/23, 26/25, 26/41, 26/43, 27/24, 27/25, 28/22, 29/22, 29/28, 30/28, 30/29, 31/29, 31/30, 32/27, 32/28, 33/27, 33/32, 34/33, 34/50, 35/31, 36/31, 36/35, 37/35, 37/36, 38/35, 39/38, 39/20, 41/40, 42/40, 42/41, 43/41, 43/42, 44/42, 44/43, 45/40, 46/40, 46/45, 47/45, 47/46, 48/46, 48/47, 49/44, 49/45, 50/44, 50/49, 51/50, 51/34, 51/69, 51/74, 52/48, 53/48, 53/52, 54/52, 54/53, 55/53, 55/54, 55/71, 55/72, 56/52, 57/54, 57/56, 57/72, 57/73, 58/51, 58/56, 58/57, 60/59, 61/59, 61/60, 62/60, 62/61, 63/61, 63/62, 64/59, 65/59, 65/64, 66/64, 66/65, 67/65, 67/66, 68/63, 68/64, 69/63, 69/68, 70/67, 71/67, 71/70, 72/70, 72/71, 73/70, 74/73, 74/57} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,74} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[LimeGreen,very thick] (p-21) -- (p-14); %\draw[Violet,very thick] (p-5) -- (p-13); %\draw[Violet,very thick] (p-5) -- (p-13); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/53.26/72.21/0.4/Blue, 12/279.62/343.14/0.4/Green, 10/12.21/56.41/0.4/Orange, 15/236.41/363.59/0.4/Violet} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/203, 2/263, 3/143, 4/23, 5/323, 6/83, 7/342, 8/162, 9/42, 10/162, 11/190, 12/70, 13/313, 14/287, 15/26, 16/206, 17/26, 18/146, 19/266, 20/214, 21/26, 22/78, 23/97, 24/157, 25/277, 26/37, 27/277, 28/18, 29/138, 30/318, 31/94, 32/170, 33/290, 34/133, 35/334, 36/154, 37/274, 38/94, 39/334, 40/102, 41/83, 42/263, 43/263, 44/130, 45/222, 46/102, 47/282, 48/342, 49/10, 50/13, 51/107, 52/146, 53/326, 54/206, 55/326, 56/86, 57/326, 58/206, 59/337, 60/277, 61/37, 62/97, 63/97, 64/138, 65/318, 66/138, 67/274, 68/350, 69/110, 70/154, 71/334, 72/154, 73/274, 74/154} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ und in Richtung größerer vierter Winkel $ %Eingabe war: % %#1894-1 % % % % % % % %P[1]=[-18.11479523702524,-11.925524469987494]; P[2]=[31.542078892744236,-17.773160886543337]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); M(7,1,3,blauerWinkel,2); N(11,7,6); L(12,11,6); M(13,12,6,gruenerWinkel); L(14,12,13); M(15,10,9,orangerWinkel,2); M(19,15,10,vierterWinkel); N(20,17,19); L(21,20,19); RA(21,14); % %RK([5,13],[18,20,14],360/4,true); % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LimeGreen}{rgb}{0.20,0.80,0.20} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.61/0.23, 2/2.60/0.12, 3/2.20/1.04, 4/3.20/0.92, 5/3.59/0.00, 6/2.80/1.84, 7/1.72/1.23, 8/0.81/0.83, 9/0.925/1.827, 10/0.01/1.43, 11/1.88/2.22, 12/2.666/2.828, 13/3.59/2.44, 14/3.46/3.43, 15/0.898/1.884, 16/0.06/2.43, 17/0.95/2.88, 18/0.12/3.43, 19/1.73/2.43, 20/1.79/3.43, 21/2.626/2.885, 22/1.60/6.63, 23/2.59/6.75, 24/2.20/5.83, 25/3.19/5.95, 26/3.58/6.87, 27/2.80/5.03, 28/1.72/5.64, 29/0.80/6.03, 30/0.920/5.036, 31/0.00/5.43, 32/1.87/4.65, 33/2.664/4.039, 34/3.59/4.43, 35/0.894/4.978, 36/0.06/4.43, 37/0.95/3.98, 38/1.73/4.43, 39/2.624/3.982, 40/5.57/6.64, 41/4.58/6.75, 42/4.97/5.83, 43/3.98/5.95, 44/4.37/5.03, 45/5.45/5.64, 46/6.37/6.04, 47/6.250/5.043, 48/7.17/5.44, 49/5.30/4.65, 50/4.509/4.041, 51/3.71/3.43, 52/6.277/4.985, 53/7.11/4.44, 54/6.22/3.99, 55/7.06/3.44, 56/5.44/4.44, 57/5.39/3.44, 58/4.549/3.985, 59/5.58/0.24, 60/4.58/0.12, 61/4.98/1.04, 62/3.98/0.92, 63/4.38/1.84, 64/5.46/1.23, 65/6.38/0.84, 66/6.254/1.833, 67/7.17/1.44, 68/5.30/2.22, 69/4.510/2.830, 70/6.281/1.891, 71/7.12/2.44, 72/6.22/2.89, 73/5.44/2.44, 74/4.550/2.887} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/53.28/83.15/0.4/Blue, 12/277.78/337.34/0.4/Green, 10/23.15/26.78/0.4/Orange, 15/206.78/393.36/0.4/Violet} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 5/62, 5/60, 6/3, 6/4, 7/1, 8/1, 8/7, 9/8, 9/7, 10/8, 10/9, 11/7, 11/6, 12/11, 12/6, 13/12, 13/69, 13/51, 14/12, 14/13, 14/33, 14/34, 14/39, 15/10, 16/10, 16/15, 17/16, 17/15, 18/16, 18/17, 18/36, 18/37, 19/15, 20/17, 20/19, 20/37, 20/38, 21/20, 21/19, 21/14, 23/22, 24/22, 24/23, 25/23, 25/24, 26/23, 26/25, 26/41, 26/43, 27/24, 27/25, 28/22, 29/22, 29/28, 30/28, 30/29, 31/29, 31/30, 32/27, 32/28, 33/27, 33/32, 34/33, 34/50, 35/31, 36/31, 36/35, 37/35, 37/36, 38/35, 39/38, 39/20, 41/40, 42/40, 42/41, 43/41, 43/42, 44/42, 44/43, 45/40, 46/40, 46/45, 47/45, 47/46, 48/46, 48/47, 49/44, 49/45, 50/44, 50/49, 51/50, 51/34, 51/69, 51/74, 52/48, 53/48, 53/52, 54/52, 54/53, 55/53, 55/54, 55/71, 55/72, 56/52, 57/54, 57/56, 57/72, 57/73, 58/51, 58/56, 58/57, 60/59, 61/59, 61/60, 62/60, 62/61, 63/61, 63/62, 64/59, 65/59, 65/64, 66/64, 66/65, 67/65, 67/66, 68/63, 68/64, 69/63, 69/68, 70/67, 71/67, 71/70, 72/70, 72/71, 73/70, 74/73, 74/57} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,74} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[LimeGreen,very thick] (p-21) -- (p-14); %\draw[Violet,very thick] (p-5) -- (p-13); %\draw[Violet,very thick] (p-5) -- (p-13); %\draw[LimeGreen,very thick] (p-11) -- (p-21); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/53.28/83.15/0.4/Blue, 12/277.78/337.34/0.4/Green, 10/23.15/26.78/0.4/Orange, 15/206.78/393.36/0.4/Violet} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/293, 2/323, 3/143, 4/23, 5/217, 6/308, 7/53, 8/293, 9/53, 10/237, 11/188, 12/68, 13/233, 14/67, 15/297, 16/237, 17/57, 18/243, 19/237, 20/117, 21/357, 22/67, 23/97, 24/157, 25/277, 26/143, 27/277, 28/307, 29/67, 30/247, 31/123, 32/172, 33/292, 34/127, 35/63, 36/243, 37/303, 38/123, 39/3, 40/23, 41/23, 42/23, 43/203, 44/128, 45/233, 46/113, 47/293, 48/57, 49/8, 50/248, 51/247, 52/177, 53/357, 54/237, 55/297, 56/57, 57/63, 58/177, 59/247, 60/217, 61/337, 62/97, 63/97, 64/187, 65/247, 66/67, 67/7, 68/352, 69/353, 70/183, 71/3, 72/183, 73/303, 74/183} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ [Graph ins Streichholzprogramm großes Eingabefenster kopieren, Button "neu zeichnen", dann vierterWinkel anklicken, anschließend Button "-1" und Button "Feinjustieren(3,3)" abwechselnd wiederholen] Eine weitere einstellbare Kante habe ich keine gesehen. Der Versuch, Abstand P11-P21 auf 1 zu bringen, führt zu einem Graph mit vielen zusammenfallenden Knoten 12×Grad 3, 44×Grad 4, 10×Grad 6. \quoteon(2020-01-20 10:35 - haribo in Beitrag No. 1893) und ich würde immer gerne einen verstellwinkel bei 1-7-11 haben anstelle von 3-1-7... weil es ein winkel ist der in beide richtungen gedrückt werden kann \quoteoff Das ging nicht ohne die Punkte neu zu nummerieren, ich zeichne sie deshalb blau. 74 Knoten, 16×Grad 3, 54×Grad 4, 4×Grad 6, 0 Überschneidungen 144 Kanten, minimal 0.99999999999999633626, maximal 1.00000000000000444089 einzustellende Kanten, Abstände und Winkel: |P21-P14|=0.99999999999999988898 ∠(P18-P20,P12-P13)=90.00000000000000000000° ∠(P18-P14,P12-P13)=90.00000000000000000000° $ %Eingabe war: % %#1894-1 % % % % % % % %P[1]=[-18.114795237025238,-11.925524469987494]; P[2]=[-57.64326598912998,18.693097314802216]; D=ab(1,2); A(2,1,Bew(1)); L(3,2,1); L(4,2,3); L(5,2,4); M(6,3,1,blauerWinkel); Q(7,6,1,ab(1,2,3),ab(5,1,[2,4])); L(12,11,10); M(13,8,7,gruenerWinkel); L(14,8,13); M(15,5,4,orangerWinkel,2); M(19,15,5,vierterWinkel); N(20,17,19); L(21,20,19); RA(21,14); % %RK([12,13],[18,20,14],360/4,true); % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LimeGreen}{rgb}{0.20,0.80,0.20} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.85/0.23, 2/1.06/0.85, 3/1.99/1.22, 4/1.20/1.84, 5/0.27/1.46, 6/2.12/2.22, 7/3.05/1.84, 8/2.91/2.83, 9/2.45/1.04, 10/2.84/0.12, 11/3.44/0.92, 12/3.84/0.00, 13/3.84/2.45, 14/3.70/3.44, 15/1.06/2.07, 16/0.14/2.45, 17/0.93/3.06, 18/0.00/3.44, 19/1.99/2.45, 20/1.85/3.44, 21/2.78/3.06, 22/1.85/6.65, 23/1.06/6.03, 24/1.99/5.66, 25/1.20/5.04, 26/0.27/5.42, 27/2.12/4.67, 28/3.05/5.04, 29/2.91/4.05, 30/2.45/5.85, 31/2.84/6.76, 32/3.44/5.96, 33/3.84/6.88, 34/3.84/4.43, 35/1.06/4.81, 36/0.14/4.43, 37/0.93/3.82, 38/1.99/4.43, 39/2.78/3.82, 40/5.82/6.65, 41/6.61/6.03, 42/5.69/5.66, 43/6.48/5.04, 44/7.40/5.42, 45/5.55/4.67, 46/4.63/5.04, 47/4.76/4.05, 48/5.23/5.85, 49/4.83/6.76, 50/4.23/5.96, 51/3.97/3.44, 52/6.61/4.81, 53/7.54/4.43, 54/6.75/3.82, 55/7.68/3.44, 56/5.69/4.43, 57/5.82/3.44, 58/4.90/3.82, 59/5.82/0.23, 60/6.61/0.85, 61/5.69/1.22, 62/6.48/1.84, 63/7.40/1.46, 64/5.55/2.22, 65/4.63/1.84, 66/4.76/2.83, 67/5.23/1.04, 68/4.83/0.12, 69/4.23/0.92, 70/6.61/2.07, 71/7.54/2.45, 72/6.75/3.06, 73/5.69/2.45, 74/4.90/3.06} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 3/262.24/442.24/0.4/Blue, 8/277.76/337.76/0.4/Green, 5/22.24/37.76/0.4/Orange, 15/217.76/382.24/0.4/Violet} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/2, 3/1, 4/2, 4/3, 5/2, 5/4, 6/3, 6/7, 7/9, 7/11, 8/7, 8/6, 9/1, 10/1, 10/9, 11/9, 11/10, 12/11, 12/10, 12/69, 12/68, 13/8, 13/66, 13/51, 14/8, 14/13, 14/29, 14/34, 14/39, 15/5, 16/5, 16/15, 17/16, 17/15, 18/16, 18/17, 18/36, 18/37, 19/15, 20/17, 20/19, 20/37, 20/38, 21/20, 21/19, 21/14, 23/22, 24/22, 24/23, 25/23, 25/24, 26/23, 26/25, 27/24, 27/28, 28/30, 28/32, 29/27, 29/28, 30/22, 31/22, 31/30, 32/30, 32/31, 33/31, 33/32, 33/49, 33/50, 34/29, 34/47, 35/26, 36/26, 36/35, 37/35, 37/36, 38/35, 39/38, 39/20, 41/40, 42/40, 42/41, 43/41, 43/42, 44/41, 44/43, 45/42, 45/46, 46/48, 46/50, 47/45, 47/46, 48/40, 49/40, 49/48, 50/48, 50/49, 51/47, 51/34, 51/66, 51/74, 52/44, 53/44, 53/52, 54/52, 54/53, 55/53, 55/54, 55/71, 55/72, 56/52, 57/54, 57/56, 57/72, 57/73, 58/51, 58/56, 58/57, 60/59, 61/59, 61/60, 62/60, 62/61, 63/60, 63/62, 64/61, 64/65, 65/67, 65/69, 66/64, 66/65, 67/59, 68/59, 68/67, 69/67, 69/68, 70/63, 71/63, 71/70, 72/70, 72/71, 73/70, 74/73, 74/57} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,74} \fill[blue] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[LimeGreen,very thick] (p-21) -- (p-14); %\draw[Violet,very thick] (p-12) -- (p-13); %\draw[Violet,very thick] (p-12) -- (p-13); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 3/262.24/442.24/0.4/Blue, 8/277.76/337.76/0.4/Green, 5/22.24/37.76/0.4/Orange, 15/217.76/382.24/0.4/Violet} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/292, 2/232, 3/52, 4/52, 5/248, 6/188, 7/83, 8/68, 9/143, 10/323, 11/323, 12/217, 13/232, 14/292, 15/308, 16/188, 17/68, 18/128, 19/248, 20/128, 21/8, 22/68, 23/188, 24/8, 25/308, 26/112, 27/172, 28/52, 29/172, 30/157, 31/157, 32/337, 33/143, 34/128, 35/52, 36/172, 37/352, 38/112, 39/352, 40/23, 41/52, 42/232, 43/232, 44/68, 45/8, 46/263, 47/248, 48/23, 49/143, 50/203, 51/248, 52/128, 53/8, 54/188, 55/308, 56/68, 57/308, 58/188, 59/337, 60/308, 61/128, 62/68, 63/8, 64/352, 65/232, 66/352, 67/337, 68/217, 69/157, 70/232, 71/352, 72/172, 73/292, 74/172} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $


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StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
Mitteilungen: 4165
Wohnort: Raun
  Beitrag No.1895, eingetragen 2020-01-25

Wie in Beitrag No.1876 festgestellt, sollte vor der Suche nach Beweglichkeit eigentlich noch Button neue Eingabe "wenig Winkel" erfolgen, damit auch unsymmetrische Bewegungen gefunden werden können. Doch der funktioniert bei diesem Graph nicht wegen unbekanntem Fehler. Ich habe deshalb Button neue Eingabe "Rahmen zuerst" verwendet. Mit neun beweglichen Winkeln müssen acht Einsetzkanten eingestellt werden. Da kann ich den neunten Winkel beliebig in kleinen Schritten verändern und anschließend die acht Einsetzkanten mit den ersten acht Winkeln einstellen. Das ergibt aber ebenfalls wieder den symmetrischen Graph. 74 Knoten, 16×Grad 3, 54×Grad 4, 4×Grad 6, 0 Überschneidungen 144 Kanten, minimal 0.99999999999993893773, maximal 1.00000000000003885781 einzustellende Kanten, Abstände und Winkel: |P14-P12|=0.99999999999999955591 |P14-P13|=0.99999999999995181632 |P14-P33|=0.99999999999999800160 |P34-P14|=1.00000000000000466294 |P51-P13|=0.99999999999993893773 |P51-P50|=1.00000000000000088818 |P51-P34|=1.00000000000000799361 |P51-P69|=1.00000000000003885781 $ %Eingabe war: % %#1894-1 % % % % % % % % % % % % %P[5]=[81.1989530225137,-23.620797303099177]; P[2]=[31.54207889274424,-17.773160886543337]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(8,1,2,blauerWinkel); N(7,8,1); N(9,8,7); N(10,8,9); M(16,10,8,gruenerWinkel); N(15,16,10); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(31,36,35); M(30,31,36,vierterWinkel); N(29,31,30); N(28,29,30); N(22,29,28); M(24,22,29,fuenfterWinkel); N(23,22,24); N(25,23,24); N(26,23,25); M(43,26,23,sechsterWinkel); N(41,26,43); N(42,41,43); N(40,41,42); M(46,40,41,siebenterWinkel); N(45,46,40); N(47,46,45); N(48,46,47); M(53,48,46,achterWinkel); N(52,53,48); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(67,71,70); Q(59,67,5,2*D,2*D); A(59,67); A(59,5); H(60,5,59,2); A(60,5); L(62,5,60); H(65,67,59,2); A(65,67); L(66,65,67); A(65,59); L(64,59,65); A(64,66); A(60,59); L(61,60,59); A(62,61); N(6,3,4); N(11,7,6); N(20,37,17); N(27,25,24); N(32,27,28); N(38,35,20); N(44,42,43); N(49,45,44); N(57,72,54); N(63,62,61); N(68,63,64); N(73,70,57); N(19,20,15); N(56,57,52); N(12,11,6); N(21,20,19); N(33,27,32); N(39,38,20); N(50,49,44); N(58,57,56); N(69,63,68); N(74,73,57); N(13,69,12); N(14,39,21); N(34,33,50); N(51,74,58); %A(14,12); R(14,12,"green"); %A(14,13); R(14,13,"green"); %A(14,33); R(14,33,"green"); %A(34,14); R(34,14,"green"); %A(51,13); R(51,13,"green"); %A(51,50); R(51,50,"green"); %A(51,34); R(51,34,"green"); %A(51,69); R(51,69,"green"); % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LightBlue}{rgb}{0.68,0.84,0.90} \definecolor{LightCoral}{rgb}{0.94,0.50,0.50} \definecolor{LightCyan}{rgb}{0.88,1.00,1.00} \definecolor{Lime}{rgb}{0.00,1.00,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.22/0.23, 2/3.21/0.12, 3/2.82/1.04, 4/3.81/0.92, 5/4.21/0.00, 6/3.42/1.84, 7/2.52/1.19, 8/1.54/0.97, 9/1.83/1.92, 10/0.86/1.70, 11/2.48/2.19, 12/3.25/2.82, 13/4.21/2.53, 14/3.99/3.50, 15/1.43/2.52, 16/0.43/2.60, 17/1.00/3.43, 18/0.00/3.50, 19/2.42/2.60, 20/1.99/3.50, 21/2.99/3.42, 22/2.22/6.77, 23/3.22/6.89, 24/2.82/5.97, 25/3.81/6.09, 26/4.21/7.01, 27/3.42/5.17, 28/2.52/5.82, 29/1.54/6.04, 30/1.84/5.09, 31/0.86/5.31, 32/2.48/4.82, 33/3.25/4.18, 34/4.21/4.48, 35/1.43/4.49, 36/0.43/4.41, 37/1.00/3.58, 38/2.42/4.41, 39/2.99/3.58, 40/6.20/6.77, 41/5.20/6.89, 42/5.60/5.97, 43/4.61/6.09, 44/5.00/5.17, 45/5.90/5.82, 46/6.88/6.04, 47/6.58/5.08, 48/7.56/5.31, 49/5.94/4.82, 50/5.16/4.18, 51/4.43/3.50, 52/6.99/4.48, 53/7.99/4.40, 54/7.42/3.58, 55/8.42/3.50, 56/5.99/4.40, 57/6.42/3.50, 58/5.43/3.58, 59/6.19/0.23, 60/5.20/0.12, 61/5.60/1.03, 62/4.60/0.92, 63/5.00/1.84, 64/5.90/1.19, 65/6.88/0.96, 66/6.58/1.92, 67/7.56/1.70, 68/5.94/2.19, 69/5.16/2.82, 70/6.99/2.52, 71/7.99/2.60, 72/7.42/3.42, 73/5.99/2.60, 74/5.43/3.42} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/353.28/492.89/0.4/Blue, 10/312.89/475.47/0.4/Green, 18/295.47/364.47/0.4/Orange, 31/244.47/347.05/0.4/Violet, 22/227.05/306.66/0.4/Teal, 26/186.66/293.28/0.4/Lime, 40/173.28/312.89/0.4/LightBlue, 48/132.89/295.47/0.4/LightCoral, 55/115.47/184.47/0.4/LightCyan} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 1/3, 2/5, 3/2, 3/4, 4/2, 4/5, 6/3, 6/4, 7/8, 7/1, 8/1, 9/8, 9/7, 10/8, 10/9, 11/7, 11/6, 12/11, 12/6, 13/69, 13/12, 14/39, 14/21, 14/12, 14/13, 14/33, 15/16, 15/10, 16/10, 17/16, 17/15, 18/16, 18/17, 19/20, 19/15, 20/37, 20/17, 21/20, 21/19, 22/29, 22/28, 23/22, 23/24, 24/22, 25/23, 25/24, 26/23, 26/25, 27/25, 27/24, 28/29, 28/30, 29/31, 29/30, 30/31, 31/36, 31/35, 32/27, 32/28, 33/27, 33/32, 34/33, 34/50, 34/14, 35/36, 35/37, 36/18, 36/37, 37/18, 38/35, 38/20, 39/38, 39/20, 40/41, 40/42, 41/26, 41/43, 42/41, 42/43, 43/26, 44/42, 44/43, 45/46, 45/40, 46/40, 47/46, 47/45, 48/46, 48/47, 49/45, 49/44, 50/49, 50/44, 51/74, 51/58, 51/13, 51/50, 51/34, 51/69, 52/53, 52/48, 53/48, 54/53, 54/52, 55/53, 55/54, 56/57, 56/52, 57/72, 57/54, 58/57, 58/56, 60/5, 60/59, 61/60, 61/59, 62/5, 62/60, 62/61, 63/62, 63/61, 64/59, 64/65, 64/66, 65/67, 65/59, 66/65, 66/67, 67/71, 67/70, 68/63, 68/64, 69/63, 69/68, 70/71, 70/72, 71/55, 71/72, 72/55, 73/70, 73/57, 74/73, 74/57} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,74} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-14) -- (p-12); \draw[Green,very thick] (p-14) -- (p-13); \draw[Green,very thick] (p-14) -- (p-33); \draw[Green,very thick] (p-34) -- (p-14); \draw[Green,very thick] (p-51) -- (p-13); \draw[Green,very thick] (p-51) -- (p-50); \draw[Green,very thick] (p-51) -- (p-34); \draw[Green,very thick] (p-51) -- (p-69); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/353.28/492.89/0.4/Blue, 10/312.89/475.47/0.4/Green, 18/295.47/364.47/0.4/Orange, 31/244.47/347.05/0.4/Violet, 22/227.05/306.66/0.4/Teal, 26/186.66/293.28/0.4/Lime, 40/173.28/312.89/0.4/LightBlue, 48/132.89/295.47/0.4/LightCoral, 55/115.47/184.47/0.4/LightCyan} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/203, 2/323, 3/83, 4/23, 5/323, 6/83, 7/343, 8/223, 9/43, 10/265, 11/189, 12/193, 13/313, 14/287, 15/25, 16/265, 17/85, 18/145, 19/265, 20/214, 21/25, 22/77, 23/157, 24/157, 25/337, 26/143, 27/51, 28/17, 29/197, 30/257, 31/197, 32/171, 33/291, 34/47, 35/334, 36/154, 37/334, 38/94, 39/334, 40/103, 41/23, 42/263, 43/143, 44/129, 45/163, 46/43, 47/283, 48/343, 49/9, 50/249, 51/253, 52/145, 53/25, 54/205, 55/325, 56/85, 57/34, 58/205, 59/337, 60/277, 61/337, 62/217, 63/97, 64/137, 65/317, 66/77, 67/274, 68/351, 69/347, 70/154, 71/274, 72/94, 73/274, 74/154} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ [Graph ins Streichholzprogramm großes Eingabefenster kopieren, Button "neu zeichnen", dann neunterterWinkel anklicken, anschließend Button "+1" und Button "Feinjustieren(8,8)" abwechselnd wiederholen]


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haribo
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 25.10.2012
Mitteilungen: 3872
  Beitrag No.1896, eingetragen 2020-01-25

19/12 (bzw 19/8 beim umnummerierten). könnte man auf 1 einsetzen ( dito die vier symetrischen dazu)danach wieder eine der dabei entstandenen 5er Knoten eine Linie wieder löschen ... Dadurch ist es wieder beweglich also die nächste Möglichkeit suchen usw... In der Hoffnung irgendwann die dreier zu vierern umzuwandeln...


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StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
Mitteilungen: 4165
Wohnort: Raun
  Beitrag No.1897, eingetragen 2020-01-25

Das beste Ergebnis ist 4 Knoten mit Grad 3. Also 19-8 (nach neuer Nummerierung) einsetzen und dafür 8-14 entfernen. Weil dann geht Punkt 4 nur mit Punkt 6 zu verbinden und dann ist der Graph starr. 21-39 geht nicht mehr einzustellen. Wenn ich anstelle 8-14 der Reihe nach 8-13 oder 8-7 oder 8-6 entferne, immer muss 4-6 rein und der Graph wird starr, mit noch mehr Knoten von Grad 3 und dann sogar 2. 74 Knoten, 4×Grad 3, 68×Grad 4, 2×Grad 6, 0 Überschneidungen 148 Kanten, minimal 0.99999999999993904876, maximal 1.00000000000005773160 $ %Eingabe war: % %#1897-1 % % % % % % % % % % % % %P[12]=[81.19895302251368,-23.620797303099163]; P[10]=[31.54207889274421,-17.773160886543323]; D=ab(12,10); A(10,12); N(11,10,12); N(9,10,11); N(1,10,9); M(3,1,10,blauerWinkel); N(2,1,3); N(4,2,3); N(5,2,4); M(16,5,2,gruenerWinkel); N(15,16,5); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(26,36,35); M(25,26,36,vierterWinkel); N(23,26,25); N(24,23,25); N(22,23,24); M(31,22,23,fuenfterWinkel); N(30,31,22); N(32,31,30); N(33,31,32); M(50,33,31,sechsterWinkel); N(49,33,50); N(48,49,50); N(40,49,48); M(42,40,49,siebenterWinkel); N(41,40,42); N(43,41,42); N(44,41,43); M(53,44,41,achterWinkel); N(52,53,44); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(63,71,70); Q(59,63,12,2*D,2*D); A(59,63); A(59,12); H(68,12,59,2); A(68,12); L(69,12,68); H(60,63,59,2); A(60,63); L(62,60,63); A(60,59); L(61,59,60); A(61,62); A(68,59); L(67,68,59); A(69,67); N(7,9,11); N(20,37,17); N(28,32,30); N(38,35,20); N(46,48,50); N(57,72,54); N(65,69,67); N(73,70,57); N(6,3,7); N(19,20,15); N(27,28,24); N(45,42,46); N(56,57,52); N(64,65,61); N(8,19,6); N(21,20,19); N(29,28,38); N(39,38,20); N(47,56,46); N(58,57,56); N(66,65,73); N(74,73,57); N(13,66,8); N(14,39,21); N(34,29,47); N(51,74,58); %A(8,7); R(8,7,"green"); %A(29,27); R(29,27,"green"); %A(47,45); R(47,45,"green"); %A(66,64); R(66,64,"green"); %A(14,13); R(14,13,"green"); %A(34,14); R(34,14,"green"); %A(51,13); R(51,13,"green"); %A(51,34); R(51,34,"green"); RA(4,6); A(62,64); A(43,45); A(25,27); % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LightBlue}{rgb}{0.68,0.84,0.90} \definecolor{LightCoral}{rgb}{0.94,0.50,0.50} \definecolor{LightCyan}{rgb}{0.88,1.00,1.00} \definecolor{Lime}{rgb}{0.00,1.00,0.00} \definecolor{LimeGreen}{rgb}{0.20,0.80,0.20} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.85/0.23, 2/1.06/0.85, 3/1.99/1.22, 4/1.20/1.84, 5/0.27/1.46, 6/2.12/2.22, 7/3.05/1.84, 8/2.91/2.83, 9/2.45/1.04, 10/2.84/0.12, 11/3.44/0.92, 12/3.84/0.00, 13/3.84/2.45, 14/3.70/3.44, 15/1.06/2.07, 16/0.14/2.45, 17/0.93/3.06, 18/0.00/3.44, 19/1.99/2.45, 20/1.85/3.44, 21/2.78/3.06, 22/1.85/6.65, 23/1.06/6.03, 24/1.99/5.66, 25/1.20/5.04, 26/0.27/5.42, 27/2.12/4.67, 28/3.05/5.04, 29/2.91/4.05, 30/2.45/5.85, 31/2.84/6.76, 32/3.44/5.96, 33/3.84/6.88, 34/3.84/4.43, 35/1.06/4.81, 36/0.14/4.43, 37/0.93/3.82, 38/1.99/4.43, 39/2.78/3.82, 40/5.82/6.65, 41/6.61/6.03, 42/5.69/5.66, 43/6.48/5.04, 44/7.40/5.42, 45/5.55/4.67, 46/4.63/5.04, 47/4.76/4.05, 48/5.23/5.85, 49/4.83/6.76, 50/4.23/5.96, 51/3.97/3.44, 52/6.61/4.81, 53/7.54/4.43, 54/6.75/3.82, 55/7.68/3.44, 56/5.69/4.43, 57/5.82/3.44, 58/4.90/3.82, 59/5.82/0.23, 60/6.61/0.85, 61/5.69/1.22, 62/6.48/1.84, 63/7.40/1.46, 64/5.55/2.22, 65/4.63/1.84, 66/4.76/2.83, 67/5.23/1.04, 68/4.83/0.12, 69/4.23/0.92, 70/6.61/2.07, 71/7.54/2.45, 72/6.75/3.06, 73/5.69/2.45, 74/4.90/3.06} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/353.28/442.24/0.4/Blue, 5/322.24/457.76/0.4/Green, 18/277.76/382.24/0.4/Orange, 26/262.24/337.76/0.4/Violet, 22/217.76/366.72/0.4/Teal, 33/186.72/293.28/0.4/Lime, 40/173.28/262.24/0.4/LightBlue, 44/142.24/277.76/0.4/LightCoral, 55/97.76/202.24/0.4/LightCyan} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/10, 1/9, 2/1, 2/3, 3/1, 4/2, 4/3, 4/6, 5/2, 5/4, 6/3, 6/7, 7/9, 7/11, 8/19, 8/6, 8/7, 9/10, 9/11, 10/12, 11/10, 11/12, 13/66, 13/8, 14/39, 14/21, 14/13, 15/16, 15/5, 16/5, 17/16, 17/15, 18/16, 18/17, 19/20, 19/15, 20/37, 20/17, 21/20, 21/19, 22/23, 22/24, 23/26, 23/25, 24/23, 24/25, 25/26, 25/27, 26/36, 26/35, 27/28, 27/24, 28/32, 28/30, 29/28, 29/38, 29/27, 30/31, 30/22, 31/22, 32/31, 32/30, 33/31, 33/32, 34/29, 34/47, 34/14, 35/36, 35/37, 36/18, 36/37, 37/18, 38/35, 38/20, 39/38, 39/20, 40/49, 40/48, 41/40, 41/42, 42/40, 43/41, 43/42, 43/45, 44/41, 44/43, 45/42, 45/46, 46/48, 46/50, 47/56, 47/46, 47/45, 48/49, 48/50, 49/33, 49/50, 50/33, 51/74, 51/58, 51/13, 51/34, 52/53, 52/44, 53/44, 54/53, 54/52, 55/53, 55/54, 56/57, 56/52, 57/72, 57/54, 58/57, 58/56, 60/63, 60/59, 61/59, 61/60, 61/62, 62/60, 62/63, 62/64, 63/71, 63/70, 64/65, 64/61, 65/69, 65/67, 66/65, 66/73, 66/64, 67/68, 67/59, 68/12, 68/59, 69/12, 69/68, 69/67, 70/71, 70/72, 71/55, 71/72, 72/55, 73/70, 73/57, 74/73, 74/57} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,74} \fill[blue] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-8) -- (p-7); \draw[Green,very thick] (p-29) -- (p-27); \draw[Green,very thick] (p-47) -- (p-45); \draw[Green,very thick] (p-66) -- (p-64); \draw[Green,very thick] (p-14) -- (p-13); \draw[Green,very thick] (p-34) -- (p-14); \draw[Green,very thick] (p-51) -- (p-13); \draw[Green,very thick] (p-51) -- (p-34); \draw[LimeGreen,very thick] (p-4) -- (p-6); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/353.28/442.24/0.4/Blue, 5/322.24/457.76/0.4/Green, 18/277.76/382.24/0.4/Orange, 26/262.24/337.76/0.4/Violet, 22/217.76/366.72/0.4/Teal, 33/186.72/293.28/0.4/Lime, 40/173.28/262.24/0.4/LightBlue, 44/142.24/277.76/0.4/LightCoral, 55/97.76/202.24/0.4/LightCyan} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/292, 2/172, 3/52, 4/52, 5/248, 6/52, 7/308, 8/68, 9/83, 10/323, 11/23, 12/323, 13/235, 14/62, 15/308, 16/128, 17/68, 18/128, 19/248, 20/128, 21/8, 22/68, 23/128, 24/8, 25/308, 26/188, 27/308, 28/52, 29/292, 30/277, 31/97, 32/277, 33/143, 34/55, 35/52, 36/112, 37/292, 38/112, 39/352, 40/112, 41/352, 42/112, 43/292, 44/68, 45/8, 46/263, 47/248, 48/263, 49/83, 50/143, 51/123, 52/188, 53/8, 54/188, 55/52, 56/68, 57/52, 58/188, 59/337, 60/308, 61/248, 62/68, 63/292, 64/352, 65/97, 66/112, 67/37, 68/277, 69/97, 70/172, 71/292, 72/112, 73/292, 74/172} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ ohne 8-13: 74 Knoten, 2×Grad 2, 4×Grad 3, 64×Grad 4, 4×Grad 6, 0 Überschneidungen 148 Kanten, minimal 0.99999999999998623323, maximal 1.00000000000001487699 $ %Eingabe war: % %#1897-2 % % % % % % % % % % % % %P[12]=[81.19895302251368,-23.620797303099163]; P[10]=[31.54207889274421,-17.773160886543323]; D=ab(12,10); A(10,12); N(11,10,12); N(9,10,11); N(1,10,9); M(3,1,10,blauerWinkel); N(2,1,3); N(4,2,3); N(5,2,4); M(16,5,2,gruenerWinkel); N(15,16,5); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(26,36,35); M(25,26,36,vierterWinkel); N(23,26,25); N(24,23,25); N(22,23,24); M(31,22,23,fuenfterWinkel); N(30,31,22); N(32,31,30); N(33,31,32); M(50,33,31,sechsterWinkel); N(49,33,50); N(48,49,50); N(40,49,48); M(42,40,49,siebenterWinkel); N(41,40,42); N(43,41,42); N(44,41,43); M(53,44,41,achterWinkel); N(52,53,44); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(63,71,70); Q(59,63,12,2*D,2*D); A(59,63); A(59,12); H(68,12,59,2); A(68,12); L(69,12,68); H(60,63,59,2); A(60,63); L(62,60,63); A(60,59); L(61,59,60); A(61,62); A(68,59); L(67,68,59); A(69,67); N(7,9,11); N(20,37,17); N(28,32,30); N(38,35,20); N(46,48,50); N(57,72,54); N(65,69,67); N(73,70,57); N(6,3,7); N(19,20,15); N(27,28,24); N(45,42,46); N(56,57,52); N(64,65,61); N(8,19,6); N(21,20,19); N(29,28,38); N(39,38,20); N(47,56,46); N(58,57,56); N(66,65,73); N(74,73,57); N(14,39,21); N(51,74,58); N(13,51,14); N(34,14,51); %A(8,7); R(8,7,"green"); %A(29,27); R(29,27,"green"); %A(47,45); R(47,45,"green"); %A(66,64); R(66,64,"green"); %A(14,8); R(14,8,"green"); %A(14,29); R(14,29,"green"); %A(51,47); R(51,47,"green"); %A(51,66); R(51,66,"green"); RA(4,6); A(62,64); A(43,45); A(25,27); % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LightBlue}{rgb}{0.68,0.84,0.90} \definecolor{LightCoral}{rgb}{0.94,0.50,0.50} \definecolor{LightCyan}{rgb}{0.88,1.00,1.00} \definecolor{Lime}{rgb}{0.00,1.00,0.00} \definecolor{LimeGreen}{rgb}{0.20,0.80,0.20} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.85/0.23, 2/1.06/0.85, 3/1.99/1.22, 4/1.20/1.84, 5/0.27/1.46, 6/2.12/2.22, 7/3.05/1.84, 8/2.91/2.83, 9/2.45/1.04, 10/2.84/0.12, 11/3.44/0.92, 12/3.84/0.00, 13/3.84/2.45, 14/3.70/3.44, 15/1.06/2.07, 16/0.14/2.45, 17/0.93/3.06, 18/0.00/3.44, 19/1.99/2.45, 20/1.85/3.44, 21/2.78/3.06, 22/1.85/6.65, 23/1.06/6.03, 24/1.99/5.66, 25/1.20/5.04, 26/0.27/5.42, 27/2.12/4.67, 28/3.05/5.04, 29/2.91/4.05, 30/2.45/5.85, 31/2.84/6.76, 32/3.44/5.96, 33/3.84/6.88, 34/3.84/4.43, 35/1.06/4.81, 36/0.14/4.43, 37/0.93/3.82, 38/1.99/4.43, 39/2.78/3.82, 40/5.82/6.65, 41/6.61/6.03, 42/5.69/5.66, 43/6.48/5.04, 44/7.40/5.42, 45/5.55/4.67, 46/4.63/5.04, 47/4.76/4.05, 48/5.23/5.85, 49/4.83/6.76, 50/4.23/5.96, 51/3.97/3.44, 52/6.61/4.81, 53/7.54/4.43, 54/6.75/3.82, 55/7.68/3.44, 56/5.69/4.43, 57/5.82/3.44, 58/4.90/3.82, 59/5.82/0.23, 60/6.61/0.85, 61/5.69/1.22, 62/6.48/1.84, 63/7.40/1.46, 64/5.55/2.22, 65/4.63/1.84, 66/4.76/2.83, 67/5.23/1.04, 68/4.83/0.12, 69/4.23/0.92, 70/6.61/2.07, 71/7.54/2.45, 72/6.75/3.06, 73/5.69/2.45, 74/4.90/3.06} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/353.28/442.24/0.4/Blue, 5/322.24/457.76/0.4/Green, 18/277.76/382.24/0.4/Orange, 26/262.24/337.76/0.4/Violet, 22/217.76/366.72/0.4/Teal, 33/186.72/293.28/0.4/Lime, 40/173.28/262.24/0.4/LightBlue, 44/142.24/277.76/0.4/LightCoral, 55/97.76/202.24/0.4/LightCyan} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/10, 1/9, 2/1, 2/3, 3/1, 4/2, 4/3, 4/6, 5/2, 5/4, 6/3, 6/7, 7/9, 7/11, 8/19, 8/6, 8/7, 9/10, 9/11, 10/12, 11/10, 11/12, 13/51, 13/14, 14/39, 14/21, 14/8, 14/29, 15/16, 15/5, 16/5, 17/16, 17/15, 18/16, 18/17, 19/20, 19/15, 20/37, 20/17, 21/20, 21/19, 22/23, 22/24, 23/26, 23/25, 24/23, 24/25, 25/26, 25/27, 26/36, 26/35, 27/28, 27/24, 28/32, 28/30, 29/28, 29/38, 29/27, 30/31, 30/22, 31/22, 32/31, 32/30, 33/31, 33/32, 34/14, 34/51, 35/36, 35/37, 36/18, 36/37, 37/18, 38/35, 38/20, 39/38, 39/20, 40/49, 40/48, 41/40, 41/42, 42/40, 43/41, 43/42, 43/45, 44/41, 44/43, 45/42, 45/46, 46/48, 46/50, 47/56, 47/46, 47/45, 48/49, 48/50, 49/33, 49/50, 50/33, 51/74, 51/58, 51/47, 51/66, 52/53, 52/44, 53/44, 54/53, 54/52, 55/53, 55/54, 56/57, 56/52, 57/72, 57/54, 58/57, 58/56, 60/63, 60/59, 61/59, 61/60, 61/62, 62/60, 62/63, 62/64, 63/71, 63/70, 64/65, 64/61, 65/69, 65/67, 66/65, 66/73, 66/64, 67/68, 67/59, 68/12, 68/59, 69/12, 69/68, 69/67, 70/71, 70/72, 71/55, 71/72, 72/55, 73/70, 73/57, 74/73, 74/57} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,74} \fill[blue] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-8) -- (p-7); \draw[Green,very thick] (p-29) -- (p-27); \draw[Green,very thick] (p-47) -- (p-45); \draw[Green,very thick] (p-66) -- (p-64); \draw[Green,very thick] (p-14) -- (p-8); \draw[Green,very thick] (p-14) -- (p-29); \draw[Green,very thick] (p-51) -- (p-47); \draw[Green,very thick] (p-51) -- (p-66); \draw[LimeGreen,very thick] (p-4) -- (p-6); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/353.28/442.24/0.4/Blue, 5/322.24/457.76/0.4/Green, 18/277.76/382.24/0.4/Orange, 26/262.24/337.76/0.4/Violet, 22/217.76/366.72/0.4/Teal, 33/186.72/293.28/0.4/Lime, 40/173.28/262.24/0.4/LightBlue, 44/142.24/277.76/0.4/LightCoral, 55/97.76/202.24/0.4/LightCyan} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/292, 2/172, 3/52, 4/52, 5/172, 6/52, 7/308, 8/68, 9/83, 10/323, 11/23, 12/217, 13/93, 14/295, 15/308, 16/128, 17/68, 18/128, 19/248, 20/128, 21/8, 22/68, 23/188, 24/8, 25/188, 26/188, 27/308, 28/52, 29/292, 30/217, 31/157, 32/37, 33/37, 34/273, 35/352, 36/112, 37/292, 38/112, 39/352, 40/23, 41/352, 42/172, 43/352, 44/68, 45/232, 46/128, 47/248, 48/23, 49/23, 50/263, 51/115, 52/188, 53/68, 54/248, 55/308, 56/68, 57/308, 58/188, 59/248, 60/248, 61/128, 62/8, 63/292, 64/128, 65/232, 66/112, 67/37, 68/277, 69/217, 70/172, 71/352, 72/112, 73/292, 74/172} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ ohne 8-7: 74 Knoten, 8×Grad 3, 62×Grad 4, 4×Grad 6, 0 Überschneidungen 148 Kanten, minimal 0.99999999999995581312, maximal 1.00000000000017252866 $ %Eingabe war: % %#1894-3 % % % % % % % % % % % % %P[12]=[81.19895302251368,-23.620797303099163]; P[10]=[31.54207889274421,-17.773160886543323]; D=ab(12,10); A(10,12); N(11,10,12); N(9,10,11); N(1,10,9); M(3,1,10,blauerWinkel); N(2,1,3); N(4,2,3); N(5,2,4); M(16,5,2,gruenerWinkel); N(15,16,5); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(26,36,35); M(25,26,36,vierterWinkel); N(23,26,25); N(24,23,25); N(22,23,24); M(31,22,23,fuenfterWinkel); N(30,31,22); N(32,31,30); N(33,31,32); M(50,33,31,sechsterWinkel); N(49,33,50); N(48,49,50); N(40,49,48); M(42,40,49,siebenterWinkel); N(41,40,42); N(43,41,42); N(44,41,43); M(53,44,41,achterWinkel); N(52,53,44); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(63,71,70); Q(59,63,12,2*D,2*D); A(59,63); A(59,12); H(68,12,59,2); A(68,12); L(69,12,68); H(60,63,59,2); A(60,63); L(62,60,63); A(60,59); L(61,59,60); A(61,62); A(68,59); L(67,68,59); A(69,67); N(7,9,11); N(20,37,17); N(28,32,30); N(38,35,20); N(46,48,50); N(57,72,54); N(65,69,67); N(73,70,57); N(6,3,7); N(19,20,15); N(27,28,24); N(45,42,46); N(56,57,52); N(64,65,61); N(8,19,6); N(21,20,19); N(29,27,38); N(39,38,20); N(47,56,45); N(58,57,56); N(66,64,73); N(74,73,57); N(13,66,8); N(14,39,21); N(34,29,47); N(51,74,58); %A(14,8); R(14,8,"green"); %A(14,13); R(14,13,"green"); %A(14,29); R(14,29,"green"); %A(34,14); R(34,14,"green"); %A(51,13); R(51,13,"green"); %A(51,47); R(51,47,"green"); %A(51,34); R(51,34,"green"); %A(51,66); R(51,66,"green"); RA(4,6); A(62,64); A(43,45); A(25,27); % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LightBlue}{rgb}{0.68,0.84,0.90} \definecolor{LightCoral}{rgb}{0.94,0.50,0.50} \definecolor{LightCyan}{rgb}{0.88,1.00,1.00} \definecolor{Lime}{rgb}{0.00,1.00,0.00} \definecolor{LimeGreen}{rgb}{0.20,0.80,0.20} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.85/0.23, 2/1.06/0.85, 3/1.99/1.22, 4/1.20/1.84, 5/0.27/1.46, 6/2.12/2.22, 7/3.05/1.84, 8/2.91/2.83, 9/2.45/1.04, 10/2.84/0.12, 11/3.44/0.92, 12/3.84/0.00, 13/3.84/2.45, 14/3.70/3.44, 15/1.06/2.07, 16/0.14/2.45, 17/0.93/3.06, 18/0.00/3.44, 19/1.99/2.45, 20/1.85/3.44, 21/2.78/3.06, 22/1.85/6.65, 23/1.06/6.03, 24/1.99/5.66, 25/1.20/5.04, 26/0.27/5.42, 27/2.12/4.67, 28/3.05/5.04, 29/2.91/4.05, 30/2.45/5.85, 31/2.84/6.76, 32/3.44/5.96, 33/3.84/6.88, 34/3.84/4.43, 35/1.06/4.81, 36/0.14/4.43, 37/0.93/3.82, 38/1.99/4.43, 39/2.78/3.82, 40/5.82/6.65, 41/6.61/6.03, 42/5.69/5.66, 43/6.48/5.04, 44/7.40/5.42, 45/5.55/4.67, 46/4.63/5.04, 47/4.76/4.05, 48/5.23/5.85, 49/4.83/6.76, 50/4.23/5.96, 51/3.97/3.44, 52/6.61/4.81, 53/7.54/4.43, 54/6.75/3.82, 55/7.68/3.44, 56/5.69/4.43, 57/5.82/3.44, 58/4.90/3.82, 59/5.82/0.23, 60/6.61/0.85, 61/5.69/1.22, 62/6.48/1.84, 63/7.40/1.46, 64/5.55/2.22, 65/4.63/1.84, 66/4.76/2.83, 67/5.23/1.04, 68/4.83/0.12, 69/4.23/0.92, 70/6.61/2.07, 71/7.54/2.45, 72/6.75/3.06, 73/5.69/2.45, 74/4.90/3.06} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/353.28/442.24/0.4/Blue, 5/322.24/457.76/0.4/Green, 18/277.76/382.24/0.4/Orange, 26/262.24/337.76/0.4/Violet, 22/217.76/366.72/0.4/Teal, 33/186.72/293.28/0.4/Lime, 40/173.28/262.24/0.4/LightBlue, 44/142.24/277.76/0.4/LightCoral, 55/97.76/202.24/0.4/LightCyan} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/10, 1/9, 2/1, 2/3, 3/1, 4/2, 4/3, 4/6, 5/2, 5/4, 6/3, 6/7, 7/9, 7/11, 8/19, 8/6, 9/10, 9/11, 10/12, 11/10, 11/12, 13/66, 13/8, 14/39, 14/21, 14/8, 14/13, 14/29, 15/16, 15/5, 16/5, 17/16, 17/15, 18/16, 18/17, 19/20, 19/15, 20/37, 20/17, 21/20, 21/19, 22/23, 22/24, 23/26, 23/25, 24/23, 24/25, 25/26, 25/27, 26/36, 26/35, 27/28, 27/24, 28/32, 28/30, 29/27, 29/38, 30/31, 30/22, 31/22, 32/31, 32/30, 33/31, 33/32, 34/29, 34/47, 34/14, 35/36, 35/37, 36/18, 36/37, 37/18, 38/35, 38/20, 39/38, 39/20, 40/49, 40/48, 41/40, 41/42, 42/40, 43/41, 43/42, 43/45, 44/41, 44/43, 45/42, 45/46, 46/48, 46/50, 47/56, 47/45, 48/49, 48/50, 49/33, 49/50, 50/33, 51/74, 51/58, 51/13, 51/47, 51/34, 51/66, 52/53, 52/44, 53/44, 54/53, 54/52, 55/53, 55/54, 56/57, 56/52, 57/72, 57/54, 58/57, 58/56, 60/63, 60/59, 61/59, 61/60, 61/62, 62/60, 62/63, 62/64, 63/71, 63/70, 64/65, 64/61, 65/69, 65/67, 66/64, 66/73, 67/68, 67/59, 68/12, 68/59, 69/12, 69/68, 69/67, 70/71, 70/72, 71/55, 71/72, 72/55, 73/70, 73/57, 74/73, 74/57} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,74} \fill[blue] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-14) -- (p-8); \draw[Green,very thick] (p-14) -- (p-13); \draw[Green,very thick] (p-14) -- (p-29); \draw[Green,very thick] (p-34) -- (p-14); \draw[Green,very thick] (p-51) -- (p-13); \draw[Green,very thick] (p-51) -- (p-47); \draw[Green,very thick] (p-51) -- (p-34); \draw[Green,very thick] (p-51) -- (p-66); \draw[LimeGreen,very thick] (p-4) -- (p-6); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/353.28/442.24/0.4/Blue, 5/322.24/457.76/0.4/Green, 18/277.76/382.24/0.4/Orange, 26/262.24/337.76/0.4/Violet, 22/217.76/366.72/0.4/Teal, 33/186.72/293.28/0.4/Lime, 40/173.28/262.24/0.4/LightBlue, 44/142.24/277.76/0.4/LightCoral, 55/97.76/202.24/0.4/LightCyan} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/292, 2/172, 3/352, 4/172, 5/172, 6/52, 7/83, 8/188, 9/83, 10/323, 11/23, 12/217, 13/308, 14/68, 15/308, 16/188, 17/68, 18/128, 19/248, 20/232, 21/8, 22/68, 23/128, 24/68, 25/308, 26/112, 27/308, 28/277, 29/172, 30/277, 31/97, 32/277, 33/143, 34/128, 35/52, 36/172, 37/352, 38/112, 39/352, 40/23, 41/352, 42/112, 43/232, 44/68, 45/232, 46/263, 47/8, 48/23, 49/23, 50/263, 51/112, 52/128, 53/8, 54/188, 55/308, 56/68, 57/52, 58/188, 59/248, 60/8, 61/248, 62/68, 63/292, 64/128, 65/97, 66/352, 67/337, 68/277, 69/157, 70/172, 71/292, 72/112, 73/292, 74/172} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ ohne 8-6: 74 Knoten, 8×Grad 3, 62×Grad 4, 4×Grad 6, 0 Überschneidungen 148 Kanten, minimal 0.99999999999998567812, maximal 1.00000000000000222045 $ %Eingabe war: % %#1894-4 % % % % % % % % % % % % %P[12]=[31.198953022513678,-23.620797303099163]; P[10]=[-18.45792110725579,-17.773160886543323]; D=ab(12,10); A(10,12); N(11,10,12); N(9,10,11); N(1,10,9); M(3,1,10,blauerWinkel); N(2,1,3); N(4,2,3); N(5,2,4); M(16,5,2,gruenerWinkel); N(15,16,5); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(26,36,35); M(25,26,36,vierterWinkel); N(23,26,25); N(24,23,25); N(22,23,24); M(31,22,23,fuenfterWinkel); N(30,31,22); N(32,31,30); N(33,31,32); M(50,33,31,sechsterWinkel); N(49,33,50); N(48,49,50); N(40,49,48); M(42,40,49,siebenterWinkel); N(41,40,42); N(43,41,42); N(44,41,43); M(53,44,41,achterWinkel); N(52,53,44); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(63,71,70); Q(59,63,12,2*D,2*D); A(59,63); A(59,12); H(68,12,59,2); A(68,12); L(69,12,68); H(60,63,59,2); A(60,63); L(62,60,63); A(60,59); L(61,59,60); A(61,62); A(68,59); L(67,68,59); A(69,67); N(7,9,11); N(20,37,17); N(28,32,30); N(38,35,20); N(46,48,50); N(57,72,54); N(65,69,67); N(73,70,57); N(6,3,7); N(19,20,15); N(27,28,24); N(45,42,46); N(56,57,52); N(64,65,61); N(8,19,7); N(21,20,19); N(29,28,38); N(39,38,20); N(47,56,46); N(58,57,56); N(66,65,73); N(74,73,57); N(13,66,8); N(14,39,21); N(34,29,47); N(51,74,58); %A(14,8); R(14,8,"green"); %A(14,13); R(14,13,"green"); %A(14,29); R(14,29,"green"); %A(34,14); R(34,14,"green"); %A(51,13); R(51,13,"green"); %A(51,47); R(51,47,"green"); %A(51,34); R(51,34,"green"); %A(51,66); R(51,66,"green"); RA(4,6); A(62,64); A(43,45); A(25,27); % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LightBlue}{rgb}{0.68,0.84,0.90} \definecolor{LightCoral}{rgb}{0.94,0.50,0.50} \definecolor{LightCyan}{rgb}{0.88,1.00,1.00} \definecolor{Lime}{rgb}{0.00,1.00,0.00} \definecolor{LimeGreen}{rgb}{0.20,0.80,0.20} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.85/0.23, 2/1.06/0.85, 3/1.99/1.22, 4/1.20/1.84, 5/0.27/1.46, 6/2.12/2.22, 7/3.05/1.84, 8/2.91/2.83, 9/2.45/1.04, 10/2.84/0.12, 11/3.44/0.92, 12/3.84/0.00, 13/3.84/2.45, 14/3.70/3.44, 15/1.06/2.07, 16/0.14/2.45, 17/0.93/3.06, 18/0.00/3.44, 19/1.99/2.45, 20/1.85/3.44, 21/2.78/3.06, 22/1.85/6.65, 23/1.06/6.03, 24/1.99/5.66, 25/1.20/5.04, 26/0.27/5.42, 27/2.12/4.67, 28/3.05/5.04, 29/2.91/4.05, 30/2.45/5.85, 31/2.84/6.76, 32/3.44/5.96, 33/3.84/6.88, 34/3.84/4.43, 35/1.06/4.81, 36/0.14/4.43, 37/0.93/3.82, 38/1.99/4.43, 39/2.78/3.82, 40/5.82/6.65, 41/6.61/6.03, 42/5.69/5.66, 43/6.48/5.04, 44/7.40/5.42, 45/5.55/4.67, 46/4.63/5.04, 47/4.76/4.05, 48/5.23/5.85, 49/4.83/6.76, 50/4.23/5.96, 51/3.97/3.44, 52/6.61/4.81, 53/7.54/4.43, 54/6.75/3.82, 55/7.68/3.44, 56/5.69/4.43, 57/5.82/3.44, 58/4.90/3.82, 59/5.82/0.23, 60/6.61/0.85, 61/5.69/1.22, 62/6.48/1.84, 63/7.40/1.46, 64/5.55/2.22, 65/4.63/1.84, 66/4.76/2.83, 67/5.23/1.04, 68/4.83/0.12, 69/4.23/0.92, 70/6.61/2.07, 71/7.54/2.45, 72/6.75/3.06, 73/5.69/2.45, 74/4.90/3.06} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/353.28/442.24/0.4/Blue, 5/322.24/457.76/0.4/Green, 18/277.76/382.24/0.4/Orange, 26/262.24/337.76/0.4/Violet, 22/217.76/366.72/0.4/Teal, 33/186.72/293.28/0.4/Lime, 40/173.28/262.24/0.4/LightBlue, 44/142.24/277.76/0.4/LightCoral, 55/97.76/202.24/0.4/LightCyan} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/10, 1/9, 2/1, 2/3, 3/1, 4/2, 4/3, 4/6, 5/2, 5/4, 6/3, 6/7, 7/9, 7/11, 8/19, 8/7, 9/10, 9/11, 10/12, 11/10, 11/12, 13/66, 13/8, 14/39, 14/21, 14/8, 14/13, 14/29, 15/16, 15/5, 16/5, 17/16, 17/15, 18/16, 18/17, 19/20, 19/15, 20/37, 20/17, 21/20, 21/19, 22/23, 22/24, 23/26, 23/25, 24/23, 24/25, 25/26, 25/27, 26/36, 26/35, 27/28, 27/24, 28/32, 28/30, 29/28, 29/38, 30/31, 30/22, 31/22, 32/31, 32/30, 33/31, 33/32, 34/29, 34/47, 34/14, 35/36, 35/37, 36/18, 36/37, 37/18, 38/35, 38/20, 39/38, 39/20, 40/49, 40/48, 41/40, 41/42, 42/40, 43/41, 43/42, 43/45, 44/41, 44/43, 45/42, 45/46, 46/48, 46/50, 47/56, 47/46, 48/49, 48/50, 49/33, 49/50, 50/33, 51/74, 51/58, 51/13, 51/47, 51/34, 51/66, 52/53, 52/44, 53/44, 54/53, 54/52, 55/53, 55/54, 56/57, 56/52, 57/72, 57/54, 58/57, 58/56, 60/63, 60/59, 61/59, 61/60, 61/62, 62/60, 62/63, 62/64, 63/71, 63/70, 64/65, 64/61, 65/69, 65/67, 66/65, 66/73, 67/68, 67/59, 68/12, 68/59, 69/12, 69/68, 69/67, 70/71, 70/72, 71/55, 71/72, 72/55, 73/70, 73/57, 74/73, 74/57} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,74} \fill[blue] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-14) -- (p-8); \draw[Green,very thick] (p-14) -- (p-13); \draw[Green,very thick] (p-14) -- (p-29); \draw[Green,very thick] (p-34) -- (p-14); \draw[Green,very thick] (p-51) -- (p-13); \draw[Green,very thick] (p-51) -- (p-47); \draw[Green,very thick] (p-51) -- (p-34); \draw[Green,very thick] (p-51) -- (p-66); \draw[LimeGreen,very thick] (p-4) -- (p-6); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/353.28/442.24/0.4/Blue, 5/322.24/457.76/0.4/Green, 18/277.76/382.24/0.4/Orange, 26/262.24/337.76/0.4/Violet, 22/217.76/366.72/0.4/Teal, 33/186.72/293.28/0.4/Lime, 40/173.28/262.24/0.4/LightBlue, 44/142.24/277.76/0.4/LightCoral, 55/97.76/202.24/0.4/LightCyan} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/203, 2/292, 3/292, 4/52, 5/172, 6/52, 7/83, 8/188, 9/83, 10/323, 11/23, 12/217, 13/308, 14/292, 15/8, 16/128, 17/68, 18/232, 19/248, 20/128, 21/8, 22/68, 23/68, 24/68, 25/308, 26/112, 27/308, 28/277, 29/172, 30/157, 31/37, 32/337, 33/143, 34/52, 35/352, 36/172, 37/352, 38/112, 39/352, 40/112, 41/352, 42/112, 43/292, 44/352, 45/232, 46/263, 47/8, 48/323, 49/83, 50/143, 51/248, 52/128, 53/68, 54/248, 55/308, 56/68, 57/308, 58/188, 59/337, 60/8, 61/128, 62/8, 63/292, 64/128, 65/97, 66/352, 67/37, 68/277, 69/97, 70/172, 71/292, 72/112, 73/292, 74/172} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $


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StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
Mitteilungen: 4165
Wohnort: Raun
  Beitrag No.1898, eingetragen 2020-01-25

\quoteon(2020-01-19 08:44 - StefanVogel in Beitrag No. 1892) Wenn ich aber den blauen Winkel um -0.01° verändere und dann den Graph mit Button Feinjustieren(3) wieder zurechtziehe, so wird nicht mehr der Ausgangswert 90° erreicht: blauerWinkel = 89.99483124096407 gruenerWinkel = 90.00516875903601 orangerWinkel = 89.99483124096504 ein Zeichen für Beweglichkeit des Graphen. Das Ergebnis lässt auch vermuten, das gruenerWinkel=180°-blauerWinkel und orangerWinkel=blauerWinkel ist. \quoteoff Diese Abhhängigkeit ist auch aus der Matrix ablesbar, welche beim Feinjustieren verwendet wird (ist im Streichholzprogramm beschrieben): \sourceon -1.7453327028071897e-7,-3.7606695291181325e-7,-2.0153348168072682e-7 4.3633292889921904e-7, 3.3556678469270906e-7,-1.0076635215128249e-7 -1.308999086901963e-7 ,-2.3166669071983392e-7,-1.0076669032521579e-7 \sourceoff Die drei Spalten der Matrix sind nahezu linear abhängig. Erste Spalte minus zweite Spalte plus dritte Spalte ergibt Null. Das bedeutet wieder die gleiche Abhängigkeit für die Winkeländerung. Wenn blauerWinkel um 1' vergrößert wird und gruenerWinkel um 1' verkleinert und orangerWinkel um 1' vergrößert, bleiben die Kantenlängen unverändert. Der Graph ist beweglich. Das kann ohne Probieren gleich mit aus der Matrix herausgelesen werden und es stellt sich hier die berechtigte Frage, warum nicht gleich so. Das kann ich nur mit Ausreden versuchen zu beantworten. Bei Graphen mit nur einem beweglichen Winkel gibt es keinen solchen Zusammenhang. Symmetrische Eingabe des Graphen schränkt die Beweglichkeit ein und da funktioniert das nicht. Buttons für neue Eingabe ohne Symmetriebedingungen gab es anfangs nur solche, wo dann 10 oder 20 bewegliche Winkel entstehen mit entsprechend großer Matrix. Damit in javascript weiter rechnen ist nicht gerade verlockend. Deshalb hatte ich lieber das extra GAP-Programm verwendet. Doch inzwischen scheint Button neue Eingabe "wenig Winkel" (der aber auch nicht immer funktioniert) eine echte Alternative zu bieten, nur eine 3x3 Matrix statt 20*20 nach neuer Eingabe mit mehr Winkeln oder 100*100 im extra GAP-Programm. Das schreibe ich jetzt nochmal genau auf. Mit drei beweglichen Winkeln \(\alpha, \beta, \gamma\) werden drei Kantenlängen \(a, b, c\) eingestellt. Die Kantenlängen sind Funktionen der Winkel \(a = a(\alpha, \beta, \gamma)\), \(b = b(\alpha, \beta, \gamma)\), \(c = c(\alpha, \beta, \gamma)\). Wie die Funktionen ungefähr aussehen, siehe die Berechnung von x im Beweis von Slash. Meistens liegen dann noch mehr Knoten und Kanten dazwischen. Bei einem beweglichen Graph lassen sich die Winkel abhängig von einem Bahnparameter t (zum Beispiel Zeit t) verändern \(\alpha = \alpha(t)\), \(\beta = \beta(t)\), \(\gamma = \gamma(t)\), ohne dass sich dabei die Kantenlängen ändern \(\begin{pmatrix} a(\alpha(t), \beta(t), \gamma(t)) \\ b(\alpha(t), \beta(t), \gamma(t)) \\ c(\alpha(t), \beta(t), \gamma(t)) \\ \end{pmatrix} = \mathbb{const}\). Bei einer konstanten Funktion jedoch sind sämtliche Ableitungen Null. Für die erste Ableitung mit mehrdimensionaler Kettenregel ausgerechnet bedeutet das \(\displaystyle \begin{pmatrix} \dfrac{\partial{a}}{\partial{\alpha}} && \dfrac{\partial{a}}{\partial{\beta}} && \dfrac{\partial{a}}{\partial{\gamma}} \\ \dfrac{\partial{b}}{\partial{\alpha}} && \dfrac{\partial{b}}{\partial{\beta}} && \dfrac{\partial{b}}{\partial{\gamma}} \\ \dfrac{\partial{c}}{\partial{\alpha}} && \dfrac{\partial{c}}{\partial{\beta}} && \dfrac{\partial{c}}{\partial{\gamma}} \\ \end{pmatrix} \begin{pmatrix} \dfrac{\mathrm{d}\alpha}{\mathrm{d}t} \\ \dfrac{\mathrm{d}\beta}{\mathrm{d}t} \\ \dfrac{\mathrm{d}\gamma}{\mathrm{d}t} \\ \end{pmatrix} = 0\). Dafür gibt es nur von Null verschiedene Lösungen, wenn die Spalten der Matrix linear abhängig sind und die Linearfaktoren erscheinen dann nochmal in der Lösung. Gleiches gilt für die höheren Ableitungen. Die müssen gleich Null gesetzt ebenfalls alle diese Lösungen haben. An der Stelle löst sich auch das mit der falschen Beweglichkeit auf, Beitrag No.785/787. Der Graph ist nicht mehr statisch bestimmt, wenn die erste Ableitung Null ist, aber erst wirklich beweglich, wenn auch die höheren Ableitungen Null sind. Das herauszufinden hat das extra GAP-Programm nicht geschafft. Ob sich das konkret alles mit ausreichender Genauigkeit rechnen lässt, muss sich noch herausstellen. Die Matrix am Anfang des Beitrages ist eine Näherung für die Matrix in der ersten Ableitung, zusammengestellt aus der Änderung der Kantenlängen bei geringfügiger Variation der Winkel, und da ist ja die lineare Abhängigkeit ganz gut erkennbar. [Die Antwort wurde nach Beitrag No.1895 begonnen.]


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StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
Mitteilungen: 4165
Wohnort: Raun
  Beitrag No.1899, eingetragen 2020-01-26

Eine kleine Hürde noch: Aus Graph #1892-1 erhalte ich nach Button neue Eingabe "egal wie" folgende Eingabe 88 Knoten, 4×Grad 3, 80×Grad 4, 2×Grad 5, 2×Grad 7, 0 Überschneidungen 178 Kanten, minimal 0.99999999999960054176, maximal 1.00000000000029820590 einzustellende Kanten, Abstände und Winkel: |P50-P88|=1.00000000000005773160 |P80-P81|=0.99999999999997546407 |P47-P49|=0.99999999999993238742 |P33-P35|=0.99999999999984556798 |P29-P31|=1.00000000000003330669 |P14-P16|=0.99999999999960054176 |P15-P16|=0.99999999999966382447 |P15-P17|=1.00000000000029820590 $ %Eingabe war: % %Automatisch generierte Eingabe zu: #1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78); % % % % % % %P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(38,5,4,blauerWinkel); N(36,5,38); N(8,4,36); N(37,8,36); N(40,37,38); N(43,37,40); N(44,40,38); N(46,43,44); N(72,46,44); N(74,8,43); N(75,8,74); N(7,3,8); N(71,46,72); N(73,7,8); N(76,73,75); N(77,73,76); N(6,1,7); N(9,1,6); N(10,9,6); N(11,9,10); N(69,71,72); M(84,74,8,gruenerWinkel); N(70,84,71); N(83,75,84); N(85,84,70); N(68,70,69); N(67,68,69); N(66,68,67); N(64,66,67); N(65,85,66); N(63,65,64); N(62,63,64); N(61,63,62); N(59,61,62); N(60,65,61); N(58,60,59); N(57,58,59); N(56,58,57); N(54,56,57); N(55,60,56); N(87,85,55); N(53,55,54); N(86,83,87); N(88,86,87); N(52,53,54); N(82,83,86); N(51,53,52); N(79,76,82); N(81,82,86); N(42,81,88); N(49,51,52); N(50,51,42); N(78,77,79); N(80,79,42); N(48,50,49); N(45,42,48); N(47,45,48); N(41,45,47); N(39,42,41); N(34,39,41); N(35,42,39); N(32,80,35); N(33,32,34); N(27,78,32); N(31,33,34); N(30,32,31); N(28,27,30); N(29,28,30); N(26,28,29); N(25,27,26); N(24,25,26); N(23,25,24); N(21,23,24); M(22,23,25,orangerWinkel); N(20,22,21); N(19,20,21); N(18,20,19); N(16,18,19); N(17,22,18); N(12,17,10); N(13,11,12); N(14,11,13); N(15,14,13); %A(50,88); R(50,88,"green"); %A(80,81); R(80,81,"green"); %A(47,49); R(47,49,"green"); %A(33,35); R(33,35,"green"); %A(29,31); R(29,31,"green"); %A(14,16); R(14,16,"green"); %A(15,16); R(15,16,"green"); %A(15,17); R(15,17,"green"); % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/3.23/1.87, 8/4.23/1.87, 9/1.87/0.50, 10/1.87/1.50, 11/1.00/1.00, 12/2.37/2.37, 13/1.50/1.87, 14/0.50/1.87, 15/1.00/2.73, 16/0.00/2.73, 17/1.87/3.23, 18/0.87/3.23, 19/0.00/3.73, 20/0.87/4.23, 21/0.00/4.73, 22/1.87/4.23, 23/1.00/4.73, 24/0.50/5.60, 25/1.50/5.60, 26/1.00/6.46, 27/2.37/5.10, 28/1.87/5.96, 29/1.87/6.96, 30/2.73/6.46, 31/2.73/7.46, 32/3.23/5.60, 33/3.23/6.60, 34/3.73/7.46, 35/4.10/6.10, 36/4.73/1.00, 37/5.23/1.87, 38/5.60/0.50, 39/4.60/6.96, 40/6.10/1.37, 41/4.60/7.96, 42/5.10/6.10, 43/6.10/2.37, 44/6.60/0.50, 45/5.10/7.10, 46/6.60/1.50, 47/5.60/7.96, 48/6.10/7.10, 49/6.60/7.96, 50/6.10/6.10, 51/6.60/6.96, 52/7.46/7.46, 53/7.46/6.46, 54/8.33/6.96, 55/6.96/5.60, 56/7.83/6.10, 57/8.83/6.10, 58/8.33/5.23, 59/9.33/5.23, 60/7.46/4.73, 61/8.46/4.73, 62/9.33/4.23, 63/8.46/3.73, 64/9.33/3.23, 65/7.46/3.73, 66/8.33/3.23, 67/8.83/2.37, 68/7.83/2.37, 69/8.33/1.50, 70/6.96/2.87, 71/7.46/2.00, 72/7.46/1.00, 73/3.73/2.73, 74/5.10/2.37, 75/4.23/2.87, 76/3.73/3.73, 77/2.87/3.23, 78/2.87/4.23, 79/3.73/4.73, 80/4.23/5.60, 81/5.10/5.10, 82/4.60/4.23, 83/5.10/3.37, 84/5.96/2.87, 85/6.46/3.73, 86/5.60/4.23, 87/6.46/4.73, 88/5.60/5.23} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 5/120.00/390.00/0.4/Blue, 74/210.00/390.00/0.4/Green, 23/60.00/330.00/0.4/Orange} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 6/7, 7/3, 7/8, 8/4, 8/36, 9/1, 9/6, 10/9, 10/6, 11/9, 11/10, 12/17, 12/10, 13/11, 13/12, 14/11, 14/13, 14/16, 15/14, 15/13, 15/16, 15/17, 16/18, 16/19, 17/22, 17/18, 18/20, 18/19, 19/20, 19/21, 20/22, 20/21, 21/23, 21/24, 22/23, 23/25, 23/24, 24/25, 24/26, 25/27, 25/26, 26/28, 26/29, 27/78, 27/32, 28/27, 28/30, 29/28, 29/30, 29/31, 30/32, 30/31, 31/33, 31/34, 32/80, 32/35, 33/32, 33/34, 33/35, 34/39, 34/41, 35/42, 35/39, 36/5, 36/38, 37/8, 37/36, 38/5, 39/42, 39/41, 40/37, 40/38, 41/45, 41/47, 42/81, 42/88, 43/37, 43/40, 44/40, 44/38, 45/42, 45/48, 46/43, 46/44, 47/45, 47/48, 47/49, 48/50, 48/49, 49/51, 49/52, 50/51, 50/42, 50/88, 51/53, 51/52, 52/53, 52/54, 53/55, 53/54, 54/56, 54/57, 55/60, 55/56, 56/58, 56/57, 57/58, 57/59, 58/60, 58/59, 59/61, 59/62, 60/65, 60/61, 61/63, 61/62, 62/63, 62/64, 63/65, 63/64, 64/66, 64/67, 65/85, 65/66, 66/68, 66/67, 67/68, 67/69, 68/70, 68/69, 69/71, 69/72, 70/84, 70/71, 71/46, 71/72, 72/46, 72/44, 73/7, 73/8, 74/8, 74/43, 75/8, 75/74, 76/73, 76/75, 77/73, 77/76, 78/77, 78/79, 79/76, 79/82, 80/79, 80/42, 80/81, 81/82, 81/86, 82/83, 82/86, 83/75, 83/84, 84/74, 85/84, 85/70, 86/83, 86/87, 87/85, 87/55, 88/86, 88/87} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,88} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-50) -- (p-88); \draw[Green,very thick] (p-80) -- (p-81); \draw[Green,very thick] (p-47) -- (p-49); \draw[Green,very thick] (p-33) -- (p-35); \draw[Green,very thick] (p-29) -- (p-31); \draw[Green,very thick] (p-14) -- (p-16); \draw[Green,very thick] (p-15) -- (p-16); \draw[Green,very thick] (p-15) -- (p-17); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 5/120.00/390.00/0.4/Blue, 74/210.00/390.00/0.4/Green, 23/60.00/330.00/0.4/Orange} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/210, 2/330, 3/150, 4/30, 5/330, 6/360, 7/210, 8/330, 9/180, 10/60, 11/180, 12/348, 13/30, 14/150, 15/30, 16/150, 17/317, 18/360, 19/240, 20/60, 21/120, 22/47, 23/330, 24/210, 25/30, 26/90, 27/167, 28/240, 29/180, 30/360, 31/60, 32/240, 33/270, 34/30, 35/210, 36/120, 37/30, 38/360, 39/300, 40/90, 41/60, 42/60, 43/60, 44/240, 45/270, 46/180, 47/30, 48/270, 49/120, 50/30, 51/240, 52/60, 53/240, 54/360, 55/93, 56/210, 57/330, 58/210, 59/60, 60/137, 61/120, 62/360, 63/180, 64/300, 65/227, 66/90, 67/270, 68/150, 69/360, 70/330, 71/60, 72/360, 73/300, 74/360, 75/120, 76/60, 77/180, 78/257, 79/62, 80/180, 81/90, 82/150, 83/270, 84/210, 85/90, 86/240, 87/360, 88/270} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Darin verwendet Button "Feinjustieren(3)" folgende näherungsweise Ableitungsmatrix \sourceon 4.440892098500626e-15 , -0.0000015708025822291916, 0 -5.10702591327572e-15 , 5.038299732973428e-7 , 0 3.9968028886505635e-15, 0.0000018325966834042973, 0 \sourceoff Die dritte Spalte ist komplett Null, ich könnte also den dritten (orangen) Winkel alleine verstellen ohne dass sich die Kantenlängen ändern. Für die ersten drei Einsetzkanten stimmt das auch, allerdings ändern sich die letzten drei Einsetzkanten P14-P16, P15-P16, P15-P17. Für Button Feinjustieren müsste ich eigentlich diese letzten drei Einsetzkanten an den Anfang setzen und damit die Ableitungsmatrix bilden. Wie man solche Kanten herausfinden kann, dazu gab es schonmal Überlegungen in Beitrag No.630 letzter Absatz ab "Bei Button...". Die auszuwählenden Einsetzkanten sind dort als Anfügekanten bezeichnet. Ziemlich kompliziert das alles, es geht einfacher. Ich muss die Ableitungsmatrix nicht aus den drei Winkeln und den ersten drei Einsetzkanten bilden, sondern aus allen Winkeln und allen Einsetzkanten. Dann sieht die Matrix so aus \sourceon 4.440892098500626e-15, -0.0000015708025822291916, 0 -5.10702591327572e-15, 5.038299732973428e-7, 0 3.9968028886505635e-15, 0.0000018325966834042973, 0 -2.1649348980190553e-14, 0.000003728382380385753, 0 1.3100631690576847e-14,-5.794182773577461e-7, 0 -1.7453302114667224e-7, 0.000009126448137664056, 1.7453285150459408e-7 -3.4906585666405476e-7, 0.000008188297134559264, 3.490659944427321e-7 3.0229989467223106e-7, -0.0000074187649146129075, -3.0230001990538824e-7 \sourceoff Die Einträge ...e-14 und ...-e-15 betrachte ich als Null. Dann besteht die lineare Abhängigkeit jetzt aus der Gleichung 1 * erste Spalte + 0 * zweite Spalte + 1 * dritte Spalte = 0. Auf die Winkel übertragen, wenn ich den ersten (blauen) Winkel ein wenig ändere, muss ich den zweiten (grünen) Winkel unverändert lassen und den dritten (orangen) Winkel genau wie den ersten ändern. Das übernehme ich in die Eingabe 88 Knoten, 4×Grad 3, 80×Grad 4, 2×Grad 5, 2×Grad 7, 0 Überschneidungen 178 Kanten, minimal 0.99999999999991695532, maximal 1.00000000000007682743 $ %Eingabe war: % %Automatisch generierte Eingabe zu: #1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78); % % % % % % %P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(38,5,4,blauerWinkel); N(36,5,38); N(8,4,36); N(37,8,36); N(40,37,38); N(43,37,40); N(44,40,38); N(46,43,44); N(72,46,44); N(74,8,43); N(75,8,74); N(7,3,8); N(71,46,72); N(73,7,8); N(76,73,75); N(77,73,76); N(6,1,7); N(9,1,6); N(10,9,6); N(11,9,10); N(69,71,72); M(84,74,8,-180); N(70,84,71); N(83,75,84); N(85,84,70); N(68,70,69); N(67,68,69); N(66,68,67); N(64,66,67); N(65,85,66); N(63,65,64); N(62,63,64); N(61,63,62); N(59,61,62); N(60,65,61); N(58,60,59); N(57,58,59); N(56,58,57); N(54,56,57); N(55,60,56); N(87,85,55); N(53,55,54); N(86,83,87); N(88,86,87); N(52,53,54); N(82,83,86); N(51,53,52); N(79,76,82); N(81,82,86); N(42,81,88); N(49,51,52); N(50,51,42); N(78,77,79); N(80,79,42); N(48,50,49); N(45,42,48); N(47,45,48); N(41,45,47); N(39,42,41); N(34,39,41); N(35,42,39); N(32,80,35); N(33,32,34); N(27,78,32); N(31,33,34); N(30,32,31); N(28,27,30); N(29,28,30); N(26,28,29); N(25,27,26); N(24,25,26); N(23,25,24); N(21,23,24); M(22,23,25,blauerWinkel); N(20,22,21); N(19,20,21); N(18,20,19); N(16,18,19); N(17,22,18); N(12,17,10); N(13,11,12); N(14,11,13); N(15,14,13); %A(50,88); R(50,88,"green"); %A(80,81); R(80,81,"green"); %A(47,49); R(47,49,"green"); %A(33,35); R(33,35,"green"); %A(29,31); R(29,31,"green"); %A(14,16); R(14,16,"green"); %A(15,16); R(15,16,"green"); %A(15,17); R(15,17,"green"); % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/3.23/1.87, 8/4.23/1.87, 9/1.87/0.50, 10/1.87/1.50, 11/1.00/1.00, 12/2.37/2.37, 13/1.50/1.87, 14/0.50/1.87, 15/1.00/2.73, 16/0.00/2.73, 17/1.87/3.23, 18/0.87/3.23, 19/0.00/3.73, 20/0.87/4.23, 21/0.00/4.73, 22/1.87/4.23, 23/1.00/4.73, 24/0.50/5.60, 25/1.50/5.60, 26/1.00/6.46, 27/2.37/5.10, 28/1.87/5.96, 29/1.87/6.96, 30/2.73/6.46, 31/2.73/7.46, 32/3.23/5.60, 33/3.23/6.60, 34/3.73/7.46, 35/4.10/6.10, 36/4.73/1.00, 37/5.23/1.87, 38/5.60/0.50, 39/4.60/6.96, 40/6.10/1.37, 41/4.60/7.96, 42/5.10/6.10, 43/6.10/2.37, 44/6.60/0.50, 45/5.10/7.10, 46/6.60/1.50, 47/5.60/7.96, 48/6.10/7.10, 49/6.60/7.96, 50/6.10/6.10, 51/6.60/6.96, 52/7.46/7.46, 53/7.46/6.46, 54/8.33/6.96, 55/6.96/5.60, 56/7.83/6.10, 57/8.83/6.10, 58/8.33/5.23, 59/9.33/5.23, 60/7.46/4.73, 61/8.46/4.73, 62/9.33/4.23, 63/8.46/3.73, 64/9.33/3.23, 65/7.46/3.73, 66/8.33/3.23, 67/8.83/2.37, 68/7.83/2.37, 69/8.33/1.50, 70/6.96/2.87, 71/7.46/2.00, 72/7.46/1.00, 73/3.73/2.73, 74/5.10/2.37, 75/4.23/2.87, 76/3.73/3.73, 77/2.87/3.23, 78/2.87/4.23, 79/3.73/4.73, 80/4.23/5.60, 81/5.10/5.10, 82/4.60/4.23, 83/5.10/3.37, 84/5.96/2.87, 85/6.46/3.73, 86/5.60/4.23, 87/6.46/4.73, 88/5.60/5.23} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 5/120.00/390.00/0.4/Blue, 23/60.00/330.00/0.4/Blue} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 6/7, 7/3, 7/8, 8/4, 8/36, 9/1, 9/6, 10/9, 10/6, 11/9, 11/10, 12/17, 12/10, 13/11, 13/12, 14/11, 14/13, 14/16, 15/14, 15/13, 15/16, 15/17, 16/18, 16/19, 17/22, 17/18, 18/20, 18/19, 19/20, 19/21, 20/22, 20/21, 21/23, 21/24, 22/23, 23/25, 23/24, 24/25, 24/26, 25/27, 25/26, 26/28, 26/29, 27/78, 27/32, 28/27, 28/30, 29/28, 29/30, 29/31, 30/32, 30/31, 31/33, 31/34, 32/80, 32/35, 33/32, 33/34, 33/35, 34/39, 34/41, 35/42, 35/39, 36/5, 36/38, 37/8, 37/36, 38/5, 39/42, 39/41, 40/37, 40/38, 41/45, 41/47, 42/81, 42/88, 43/37, 43/40, 44/40, 44/38, 45/42, 45/48, 46/43, 46/44, 47/45, 47/48, 47/49, 48/50, 48/49, 49/51, 49/52, 50/51, 50/42, 50/88, 51/53, 51/52, 52/53, 52/54, 53/55, 53/54, 54/56, 54/57, 55/60, 55/56, 56/58, 56/57, 57/58, 57/59, 58/60, 58/59, 59/61, 59/62, 60/65, 60/61, 61/63, 61/62, 62/63, 62/64, 63/65, 63/64, 64/66, 64/67, 65/85, 65/66, 66/68, 66/67, 67/68, 67/69, 68/70, 68/69, 69/71, 69/72, 70/84, 70/71, 71/46, 71/72, 72/46, 72/44, 73/7, 73/8, 74/8, 74/43, 75/8, 75/74, 76/73, 76/75, 77/73, 77/76, 78/77, 78/79, 79/76, 79/82, 80/79, 80/42, 80/81, 81/82, 81/86, 82/83, 82/86, 83/75, 83/84, 84/74, 85/84, 85/70, 86/83, 86/87, 87/85, 87/55, 88/86, 88/87} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,88} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-50) -- (p-88); \draw[Green,very thick] (p-80) -- (p-81); \draw[Green,very thick] (p-47) -- (p-49); \draw[Green,very thick] (p-33) -- (p-35); \draw[Green,very thick] (p-29) -- (p-31); \draw[Green,very thick] (p-14) -- (p-16); \draw[Green,very thick] (p-15) -- (p-16); \draw[Green,very thick] (p-15) -- (p-17); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 5/120.00/390.00/0.4/Blue, 23/60.00/330.00/0.4/Blue} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/210, 2/330, 3/150, 4/30, 5/330, 6/360, 7/210, 8/330, 9/180, 10/60, 11/180, 12/347, 13/30, 14/270, 15/30, 16/240, 17/77, 18/360, 19/120, 20/360, 21/120, 22/48, 23/330, 24/90, 25/330, 26/90, 27/167, 28/300, 29/180, 30/360, 31/60, 32/240, 33/270, 34/30, 35/210, 36/120, 37/30, 38/360, 39/300, 40/90, 41/150, 42/60, 43/60, 44/240, 45/210, 46/180, 47/30, 48/270, 49/120, 50/30, 51/180, 52/60, 53/300, 54/90, 55/93, 56/210, 57/30, 58/210, 59/60, 60/257, 61/120, 62/300, 63/180, 64/30, 65/227, 66/90, 67/30, 68/150, 69/360, 70/330, 71/60, 72/360, 73/300, 74/360, 75/120, 76/60, 77/180, 78/257, 79/62, 80/180, 81/90, 82/150, 83/270, 84/210, 85/90, 86/330, 87/360, 88/270} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ und das passt. Allein die Änderung des blauen Winkels [Animation "Start_blauerWinkel"] macht den Graph beweglich. So einen Tipp auf Knopfdruck ohne extra GAP-Programm erhalten wäre nicht schlecht.


   Profil
StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
Mitteilungen: 4165
Wohnort: Raun
  Beitrag No.1900, eingetragen 2020-02-01

Hierzu neu Streichholzgraph-1898.htm mit Button "beweglich?". Ich beginne eine neue Version neben der bisherigen Streichholzgraph-1554.htm wegen möglicher Änderungen anderer Programmfunktionen. Zum Beispiel die Buttons für neue Eingabe geben jetzt stets Anzahl="s,ws" als Attribut im xml-Element "Feinjustieren" zurück für s Einsetzkanten und ws Winkel. Anschließendes Feinjustieren(s,ws) wirkt bei s>ws wie bisher als Feinjustieren(ws,ws), das kann sich aber auch noch ändern. Für den #467-2 ohne die beiden Kanten P22-P78 und P12-P77 erhalte ich nach Button neue Eingabe "wenig Winkel" jetzt 88 Knoten, 4×Grad 3, 80×Grad 4, 2×Grad 5, 2×Grad 7, 0 Überschneidungen 178 Kanten, minimal 0.99999999999998412381, maximal 1.00000000000001443290 einzustellende Kanten, Abstände und Winkel: |P42-P80|=1.00000000000000577316 |P75-P83|=1.00000000000000044409 |P86-P87|=1.00000000000000310862 |P85-P87|=1.00000000000000910383 |P55-P87|=1.00000000000000799361 |P60-P61|=1.00000000000000288658 |P65-P66|=1.00000000000001443290 |P65-P85|=0.99999999999998412381 $ %Eingabe war: % %#1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78); % % % % % % %P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(1,2); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,2,blauerWinkel); L(9,1,6); L(10,9,6); L(11,9,10); N(7,6,3); M(109,7,3,95.00000000000001); L(73,7,109); Q(8,7,4,ab(109,7,73,"gedreht"),D); M(110,8,4,35.000000000000014); L(37,8,110); M(111,5,2,-85.00000000000001); L(38,111,5); Q(36,8,5,ab(110,8,37,"gedreht"),ab(111,5,38,"gedreht")); M(112,37,8,154.99999999999997); L(43,37,112); M(113,38,5,-144.99999999999994); L(44,113,38); Q(40,37,38,ab(112,37,43,"gedreht"),ab(113,38,44,"gedreht")); M(114,44,38,-85.00000000000017); M(71,114,44,125.00000000000043); M(69,71,114,125.00000000000016); L(116,69,71); Q(115,71,114,ab(116,71,69,"gedreht"),D); Q(72,114,44,ab(115,114,69,71,"gedreht"),D); Q(46,43,44,D,ab(114,44,69,71,72,"gedreht")); M(117,8,4,125.00000000000001); L(75,8,117); Q(74,8,43,ab(117,8,75,"gedreht"),D); M(118,73,7,-144.99999999999994); L(77,73,118); Q(76,73,75,ab(118,73,77,"gedreht"),D); M(12,10,6,gruenerWinkel); M(119,11,9,95.00000000000006); L(14,11,119); L(15,14,119); L(16,14,15); Q(13,11,12,ab(119,11,14,15,16,"gedreht"),D); N(17,15,12); M(120,16,14,94.99999999999991); L(19,16,120); L(20,19,120); L(21,19,20); Q(18,16,17,ab(120,16,19,20,21,"gedreht"),D); N(22,20,17); M(121,21,19,95.00000000000006); L(24,21,121); L(25,24,121); L(26,24,25); Q(23,21,22,ab(121,21,24,25,26,"gedreht"),D); M(27,25,23,orangerWinkel); M(122,26,24,95.00000000000001); L(29,26,122); L(30,29,122); L(31,29,30); Q(28,26,27,ab(122,26,29,30,31,"gedreht"),D); N(32,30,27); M(123,31,29,95.00000000000009); L(34,31,123); M(124,32,27,-114.99999999999997); L(35,124,32); Q(33,31,32,ab(123,31,34,"gedreht"),ab(124,32,35,"gedreht")); M(125,34,31,154.99999999999991); L(41,34,125); M(126,35,32,-144.99999999999986); L(42,126,35); Q(39,34,35,ab(125,34,41,"gedreht"),ab(126,35,42,"gedreht")); M(127,41,34,95.00000000000006); L(47,41,127); L(48,47,127); L(49,47,48); Q(45,41,42,ab(127,41,47,48,49,"gedreht"),D); M(128,42,35,-174.99999999999991); L(88,128,42); Q(50,48,42,D,ab(128,42,88,"gedreht")); M(129,49,47,95.00000000000014); L(52,49,129); L(53,52,129); L(54,52,53); Q(51,49,50,ab(129,49,52,53,54,"gedreht"),D); N(78,27,77); N(79,78,76); N(80,32,79); M(130,42,35,34.999999999999915); L(81,42,130); A(80,42,ab(130,42,81,"gedreht")); M(131,81,42,155.0000000000003); M(83,131,81,-115.0000000000004); L(132,131,83); Q(86,81,131,D,ab(132,131,83,"gedreht")); Q(82,81,79,ab(131,81,83,86,"gedreht"),D); A(75,83); M(87,86,81,-84.99999999999967); L(133,86,87); A(88,86,ab(133,86,87,"gedreht")); N(84,83,74); M(134,84,74,155.00000000000026); L(85,84,134); Q(70,84,71,ab(134,84,85,"gedreht"),D); A(85,87); M(67,69,71,-85.00000000000058); M(64,67,69,185); L(66,67,64); L(136,67,66); Q(135,69,67,D,ab(136,67,64,66,"gedreht")); Q(68,70,69,D,ab(135,69,64,66,67,"gedreht")); M(56,54,52,94.99999999999955); L(57,54,56); L(58,57,56); L(137,57,58); M(62,64,66,-84.99999999999945); M(138,62,64,185); L(61,62,138); L(139,62,61); Q(63,64,62,D,ab(139,62,138,61,"gedreht")); Q(59,54,64,ab(137,54,56,57,58,"gedreht"),ab(138,64,61,62,63,"gedreht")); N(55,56,53); A(55,87); N(60,58,55); A(60,61); N(65,63,60); A(65,66); A(65,85); %R(42,80); // oder R(42,81); %R(75,83); %R(86,87); // oder R(86,88); %R(85,87); %R(55,87); %R(60,61); %R(65,66); %R(65,85); % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LimeGreen}{rgb}{0.20,0.80,0.20} \definecolor{Orange}{rgb}{1.00,0.64,0.00} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/3.23/1.87, 8/4.23/1.87, 9/1.87/0.50, 10/1.87/1.50, 11/1.00/1.00, 12/2.37/2.37, 13/1.50/1.87, 14/0.50/1.87, 15/1.00/2.73, 16/0.00/2.73, 17/1.87/3.23, 18/0.87/3.23, 19/0.00/3.73, 20/0.87/4.23, 21/0.00/4.73, 22/1.87/4.23, 23/1.00/4.73, 24/0.50/5.60, 25/1.50/5.60, 26/1.00/6.46, 27/2.37/5.10, 28/1.87/5.96, 29/1.87/6.96, 30/2.73/6.46, 31/2.73/7.46, 32/3.23/5.60, 33/3.23/6.60, 34/3.73/7.46, 35/4.10/6.10, 36/4.73/1.00, 37/5.23/1.87, 38/5.60/0.50, 39/4.60/6.96, 40/6.10/1.37, 41/4.60/7.96, 42/5.10/6.10, 43/6.10/2.37, 44/6.60/0.50, 45/5.10/7.10, 46/6.60/1.50, 47/5.60/7.96, 48/6.10/7.10, 49/6.60/7.96, 50/6.10/6.10, 51/6.60/6.96, 52/7.46/7.46, 53/7.46/6.46, 54/8.33/6.96, 55/6.96/5.60, 56/7.83/6.10, 57/8.83/6.10, 58/8.33/5.23, 59/9.33/5.23, 60/7.46/4.73, 61/8.46/4.73, 62/9.33/4.23, 63/8.46/3.73, 64/9.33/3.23, 65/7.46/3.73, 66/8.33/3.23, 67/8.83/2.37, 68/7.83/2.37, 69/8.33/1.50, 70/6.96/2.87, 71/7.46/2.00, 72/7.46/1.00, 73/3.73/2.73, 74/5.10/2.37, 75/4.23/2.87, 76/3.73/3.73, 77/2.87/3.23, 78/2.87/4.23, 79/3.73/4.73, 80/4.23/5.60, 81/5.10/5.10, 82/4.60/4.23, 83/5.10/3.37, 84/5.96/2.87, 85/6.46/3.73, 86/5.60/4.23, 87/6.46/4.73, 88/5.60/5.23} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/0.00/90.00/0.4/Blue, 10/330.00/420.00/0.4/Green, 25/240.00/330.00/0.4/Orange} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 7/6, 7/3, 8/7, 8/4, 9/1, 9/6, 10/9, 10/6, 11/9, 11/10, 12/10, 13/11, 13/12, 14/11, 14/13, 15/14, 15/13, 16/14, 16/15, 17/15, 17/12, 18/16, 18/17, 19/16, 19/18, 20/19, 20/18, 21/19, 21/20, 22/20, 22/17, 23/21, 23/22, 24/21, 24/23, 25/24, 25/23, 26/24, 26/25, 27/25, 28/26, 28/27, 29/26, 29/28, 30/29, 30/28, 31/29, 31/30, 32/30, 32/27, 33/31, 33/32, 34/31, 34/33, 35/33, 35/32, 36/8, 36/5, 37/8, 37/36, 38/36, 38/5, 39/34, 39/35, 40/37, 40/38, 41/34, 41/39, 42/39, 42/35, 43/37, 43/40, 44/40, 44/38, 45/41, 45/42, 46/43, 46/44, 47/41, 47/45, 48/47, 48/45, 49/47, 49/48, 50/48, 50/42, 51/49, 51/50, 52/49, 52/51, 53/52, 53/51, 54/52, 54/53, 55/56, 55/53, 55/87, 56/54, 57/54, 57/56, 58/57, 58/56, 59/57, 59/58, 59/62, 60/58, 60/55, 60/61, 61/62, 61/59, 62/64, 63/64, 63/61, 63/62, 64/67, 65/63, 65/60, 65/66, 65/85, 66/67, 66/64, 67/69, 68/70, 68/66, 68/67, 68/69, 69/71, 70/84, 70/71, 71/46, 72/69, 72/71, 72/46, 72/44, 73/7, 73/8, 74/8, 74/43, 75/8, 75/74, 75/83, 76/73, 76/75, 77/73, 77/76, 78/27, 78/77, 79/78, 79/76, 80/32, 80/79, 80/42, 81/42, 81/80, 82/81, 82/79, 83/82, 84/83, 84/74, 85/84, 85/70, 85/87, 86/81, 86/83, 86/82, 87/86, 88/50, 88/42, 88/86, 88/87} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,88} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[LimeGreen,very thick] (p-42) -- (p-80); \draw[LimeGreen,very thick] (p-75) -- (p-83); \draw[LimeGreen,very thick] (p-86) -- (p-87); \draw[LimeGreen,very thick] (p-85) -- (p-87); \draw[LimeGreen,very thick] (p-55) -- (p-87); \draw[LimeGreen,very thick] (p-60) -- (p-61); \draw[LimeGreen,very thick] (p-65) -- (p-66); \draw[LimeGreen,very thick] (p-65) -- (p-85); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/0.00/90.00/0.4/Blue, 10/330.00/420.00/0.4/Green, 25/240.00/330.00/0.4/Orange} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/210, 2/330, 3/150, 4/30, 5/330, 6/60, 7/210, 8/240, 9/180, 10/60, 11/270, 12/348, 13/30, 14/270, 15/30, 16/240, 17/318, 18/300, 19/240, 20/60, 21/120, 22/48, 23/330, 24/150, 25/330, 26/180, 27/258, 28/240, 29/180, 30/360, 31/60, 32/240, 33/270, 34/180, 35/360, 36/270, 37/180, 38/360, 39/90, 40/90, 41/60, 42/60, 43/60, 44/330, 45/270, 46/120, 47/150, 48/330, 49/120, 50/30, 51/240, 52/120, 53/300, 54/360, 55/93, 56/210, 57/90, 58/210, 59/330, 60/137, 61/180, 62/300, 63/180, 64/30, 65/318, 66/90, 67/330, 68/150, 69/360, 70/330, 71/120, 72/360, 73/90, 74/360, 75/120, 76/60, 77/180, 78/257, 79/123, 80/180, 81/90, 82/150, 83/270, 84/210, 85/90, 86/240, 87/360, 88/270} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Anschließender Button "beweglich?" sucht die lineare Abhängigkeit und packt sie gleich mit in die Eingabe zum Graph 88 Knoten, 4×Grad 3, 80×Grad 4, 2×Grad 5, 2×Grad 7, 0 Überschneidungen 178 Kanten, minimal 0.99999999999998412381, maximal 1.00000000000001443290 $ %Eingabe war: % %#1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78); % % % % %blauerWinkel=90+(0.9999981653287288)*(orangerWinkel-(89.99999999999994)); %gruenerWinkel=90+(-0.9999997980150385)*(orangerWinkel-(89.99999999999994)); %P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(1,2); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,2,blauerWinkel); L(9,1,6); L(10,9,6); L(11,9,10); N(7,6,3); M(109,7,3,95.00000000000001); L(73,7,109); Q(8,7,4,ab(109,7,73,"gedreht"),D); M(110,8,4,35.000000000000014); L(37,8,110); M(111,5,2,-85.00000000000001); L(38,111,5); Q(36,8,5,ab(110,8,37,"gedreht"),ab(111,5,38,"gedreht")); M(112,37,8,154.99999999999997); L(43,37,112); M(113,38,5,-144.99999999999994); L(44,113,38); Q(40,37,38,ab(112,37,43,"gedreht"),ab(113,38,44,"gedreht")); M(114,44,38,-85.00000000000017); M(71,114,44,125.00000000000043); M(69,71,114,125.00000000000016); L(116,69,71); Q(115,71,114,ab(116,71,69,"gedreht"),D); Q(72,114,44,ab(115,114,69,71,"gedreht"),D); Q(46,43,44,D,ab(114,44,69,71,72,"gedreht")); M(117,8,4,125.00000000000001); L(75,8,117); Q(74,8,43,ab(117,8,75,"gedreht"),D); M(118,73,7,-144.99999999999994); L(77,73,118); Q(76,73,75,ab(118,73,77,"gedreht"),D); M(12,10,6,gruenerWinkel); M(119,11,9,95.00000000000006); L(14,11,119); L(15,14,119); L(16,14,15); Q(13,11,12,ab(119,11,14,15,16,"gedreht"),D); N(17,15,12); M(120,16,14,94.99999999999991); L(19,16,120); L(20,19,120); L(21,19,20); Q(18,16,17,ab(120,16,19,20,21,"gedreht"),D); N(22,20,17); M(121,21,19,95.00000000000006); L(24,21,121); L(25,24,121); L(26,24,25); Q(23,21,22,ab(121,21,24,25,26,"gedreht"),D); M(27,25,23,orangerWinkel); M(122,26,24,95.00000000000001); L(29,26,122); L(30,29,122); L(31,29,30); Q(28,26,27,ab(122,26,29,30,31,"gedreht"),D); N(32,30,27); M(123,31,29,95.00000000000009); L(34,31,123); M(124,32,27,-114.99999999999997); L(35,124,32); Q(33,31,32,ab(123,31,34,"gedreht"),ab(124,32,35,"gedreht")); M(125,34,31,154.99999999999991); L(41,34,125); M(126,35,32,-144.99999999999986); L(42,126,35); Q(39,34,35,ab(125,34,41,"gedreht"),ab(126,35,42,"gedreht")); M(127,41,34,95.00000000000006); L(47,41,127); L(48,47,127); L(49,47,48); Q(45,41,42,ab(127,41,47,48,49,"gedreht"),D); M(128,42,35,-174.99999999999991); L(88,128,42); Q(50,48,42,D,ab(128,42,88,"gedreht")); M(129,49,47,95.00000000000014); L(52,49,129); L(53,52,129); L(54,52,53); Q(51,49,50,ab(129,49,52,53,54,"gedreht"),D); N(78,27,77); N(79,78,76); N(80,32,79); M(130,42,35,34.999999999999915); L(81,42,130); A(80,42,ab(130,42,81,"gedreht")); M(131,81,42,155.0000000000003); M(83,131,81,-115.0000000000004); L(132,131,83); Q(86,81,131,D,ab(132,131,83,"gedreht")); Q(82,81,79,ab(131,81,83,86,"gedreht"),D); A(75,83); M(87,86,81,-84.99999999999967); L(133,86,87); A(88,86,ab(133,86,87,"gedreht")); N(84,83,74); M(134,84,74,155.00000000000026); L(85,84,134); Q(70,84,71,ab(134,84,85,"gedreht"),D); A(85,87); M(67,69,71,-85.00000000000058); M(64,67,69,185); L(66,67,64); L(136,67,66); Q(135,69,67,D,ab(136,67,64,66,"gedreht")); Q(68,70,69,D,ab(135,69,64,66,67,"gedreht")); M(56,54,52,94.99999999999955); L(57,54,56); L(58,57,56); L(137,57,58); M(62,64,66,-84.99999999999945); M(138,62,64,185); L(61,62,138); L(139,62,61); Q(63,64,62,D,ab(139,62,138,61,"gedreht")); Q(59,54,64,ab(137,54,56,57,58,"gedreht"),ab(138,64,61,62,63,"gedreht")); N(55,56,53); A(55,87); N(60,58,55); A(60,61); N(65,63,60); A(65,66); A(65,85); %R(42,80); // oder R(42,81); %R(75,83); %R(86,87); // oder R(86,88); %R(85,87); %R(55,87); %R(60,61); %R(65,66); %R(65,85); % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{LimeGreen}{rgb}{0.20,0.80,0.20} \definecolor{Orange}{rgb}{1.00,0.64,0.00} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/3.23/1.87, 8/4.23/1.87, 9/1.87/0.50, 10/1.87/1.50, 11/1.00/1.00, 12/2.37/2.37, 13/1.50/1.87, 14/0.50/1.87, 15/1.00/2.73, 16/0.00/2.73, 17/1.87/3.23, 18/0.87/3.23, 19/0.00/3.73, 20/0.87/4.23, 21/0.00/4.73, 22/1.87/4.23, 23/1.00/4.73, 24/0.50/5.60, 25/1.50/5.60, 26/1.00/6.46, 27/2.37/5.10, 28/1.87/5.96, 29/1.87/6.96, 30/2.73/6.46, 31/2.73/7.46, 32/3.23/5.60, 33/3.23/6.60, 34/3.73/7.46, 35/4.10/6.10, 36/4.73/1.00, 37/5.23/1.87, 38/5.60/0.50, 39/4.60/6.96, 40/6.10/1.37, 41/4.60/7.96, 42/5.10/6.10, 43/6.10/2.37, 44/6.60/0.50, 45/5.10/7.10, 46/6.60/1.50, 47/5.60/7.96, 48/6.10/7.10, 49/6.60/7.96, 50/6.10/6.10, 51/6.60/6.96, 52/7.46/7.46, 53/7.46/6.46, 54/8.33/6.96, 55/6.96/5.60, 56/7.83/6.10, 57/8.83/6.10, 58/8.33/5.23, 59/9.33/5.23, 60/7.46/4.73, 61/8.46/4.73, 62/9.33/4.23, 63/8.46/3.73, 64/9.33/3.23, 65/7.46/3.73, 66/8.33/3.23, 67/8.83/2.37, 68/7.83/2.37, 69/8.33/1.50, 70/6.96/2.87, 71/7.46/2.00, 72/7.46/1.00, 73/3.73/2.73, 74/5.10/2.37, 75/4.23/2.87, 76/3.73/3.73, 77/2.87/3.23, 78/2.87/4.23, 79/3.73/4.73, 80/4.23/5.60, 81/5.10/5.10, 82/4.60/4.23, 83/5.10/3.37, 84/5.96/2.87, 85/6.46/3.73, 86/5.60/4.23, 87/6.46/4.73, 88/5.60/5.23} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 25/240.00/330.00/0.4/Orange} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 7/6, 7/3, 8/7, 8/4, 9/1, 9/6, 10/9, 10/6, 11/9, 11/10, 12/10, 13/11, 13/12, 14/11, 14/13, 15/14, 15/13, 16/14, 16/15, 17/15, 17/12, 18/16, 18/17, 19/16, 19/18, 20/19, 20/18, 21/19, 21/20, 22/20, 22/17, 23/21, 23/22, 24/21, 24/23, 25/24, 25/23, 26/24, 26/25, 27/25, 28/26, 28/27, 29/26, 29/28, 30/29, 30/28, 31/29, 31/30, 32/30, 32/27, 33/31, 33/32, 34/31, 34/33, 35/33, 35/32, 36/8, 36/5, 37/8, 37/36, 38/36, 38/5, 39/34, 39/35, 40/37, 40/38, 41/34, 41/39, 42/39, 42/35, 43/37, 43/40, 44/40, 44/38, 45/41, 45/42, 46/43, 46/44, 47/41, 47/45, 48/47, 48/45, 49/47, 49/48, 50/48, 50/42, 51/49, 51/50, 52/49, 52/51, 53/52, 53/51, 54/52, 54/53, 55/56, 55/53, 55/87, 56/54, 57/54, 57/56, 58/57, 58/56, 59/57, 59/58, 59/62, 60/58, 60/55, 60/61, 61/62, 61/59, 62/64, 63/64, 63/61, 63/62, 64/67, 65/63, 65/60, 65/66, 65/85, 66/67, 66/64, 67/69, 68/70, 68/66, 68/67, 68/69, 69/71, 70/84, 70/71, 71/46, 72/69, 72/71, 72/46, 72/44, 73/7, 73/8, 74/8, 74/43, 75/8, 75/74, 75/83, 76/73, 76/75, 77/73, 77/76, 78/27, 78/77, 79/78, 79/76, 80/32, 80/79, 80/42, 81/42, 81/80, 82/81, 82/79, 83/82, 84/83, 84/74, 85/84, 85/70, 85/87, 86/81, 86/83, 86/82, 87/86, 88/50, 88/42, 88/86, 88/87} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,88} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[LimeGreen,very thick] (p-42) -- (p-80); \draw[LimeGreen,very thick] (p-75) -- (p-83); \draw[LimeGreen,very thick] (p-86) -- (p-87); \draw[LimeGreen,very thick] (p-85) -- (p-87); \draw[LimeGreen,very thick] (p-55) -- (p-87); \draw[LimeGreen,very thick] (p-60) -- (p-61); \draw[LimeGreen,very thick] (p-65) -- (p-66); \draw[LimeGreen,very thick] (p-65) -- (p-85); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 25/240.00/330.00/0.4/Orange} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/210, 2/330, 3/150, 4/30, 5/330, 6/60, 7/210, 8/240, 9/180, 10/60, 11/270, 12/348, 13/30, 14/270, 15/30, 16/240, 17/318, 18/300, 19/240, 20/60, 21/120, 22/48, 23/330, 24/150, 25/330, 26/180, 27/258, 28/240, 29/180, 30/360, 31/60, 32/240, 33/270, 34/180, 35/360, 36/270, 37/180, 38/360, 39/90, 40/90, 41/60, 42/60, 43/60, 44/330, 45/270, 46/120, 47/150, 48/330, 49/120, 50/30, 51/240, 52/120, 53/300, 54/360, 55/93, 56/210, 57/90, 58/210, 59/330, 60/137, 61/180, 62/300, 63/180, 64/30, 65/318, 66/90, 67/330, 68/150, 69/360, 70/330, 71/120, 72/360, 73/90, 74/360, 75/120, 76/60, 77/180, 78/257, 79/123, 80/180, 81/90, 82/150, 83/270, 84/210, 85/90, 86/240, 87/360, 88/270} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ so dass man allein mit Button "+1" oder "+10"... oder Animationsknopf "Start_orangerWinkel" links neben dem Graph die Bewegung starten kann. Button "zurück" macht das alles wieder rückgängig. Nach Button neue Eingabe "egal wie" 88 Knoten, 4×Grad 3, 80×Grad 4, 2×Grad 5, 2×Grad 7, 0 Überschneidungen 178 Kanten, minimal 0.99999999999960431651, maximal 1.00000000000029243274 $ %Eingabe war: % %Automatisch generierte Eingabe zu: #1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78); nach Button neue Eingabe "egal wie" % % % % % % %P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(38,5,4,blauerWinkel); N(36,5,38); N(8,4,36); N(37,8,36); N(40,37,38); N(43,37,40); N(44,40,38); N(46,43,44); N(72,46,44); N(74,8,43); N(75,8,74); N(7,3,8); N(71,46,72); N(73,7,8); N(76,73,75); N(77,73,76); N(6,1,7); N(9,1,6); N(10,9,6); N(11,9,10); N(69,71,72); M(84,74,8,gruenerWinkel); N(70,84,71); N(83,75,84); N(85,84,70); N(68,70,69); N(67,68,69); N(66,68,67); N(64,66,67); N(65,85,66); N(63,65,64); N(62,63,64); N(61,63,62); N(59,61,62); N(60,65,61); N(58,60,59); N(57,58,59); N(56,58,57); N(54,56,57); N(55,60,56); N(87,85,55); N(53,55,54); N(86,83,87); N(88,86,87); N(52,53,54); N(82,83,86); N(51,53,52); N(79,76,82); N(81,82,86); N(42,81,88); N(49,51,52); N(50,51,42); N(78,77,79); N(80,79,42); N(48,50,49); N(45,42,48); N(47,45,48); N(41,45,47); N(39,42,41); N(34,39,41); N(35,42,39); N(32,80,35); N(33,32,34); N(27,78,32); N(31,33,34); N(30,32,31); N(28,27,30); N(29,28,30); N(26,28,29); N(25,27,26); N(24,25,26); N(23,25,24); N(21,23,24); M(22,23,25,orangerWinkel); N(20,22,21); N(19,20,21); N(18,20,19); N(16,18,19); N(17,22,18); N(12,17,10); N(13,11,12); N(14,11,13); N(15,14,13); %A(50,88); R(50,88,"green"); %A(80,81); R(80,81,"green"); %A(47,49); R(47,49,"green"); %A(33,35); R(33,35,"green"); %A(29,31); R(29,31,"green"); %A(14,16); R(14,16,"green"); %A(15,16); R(15,16,"green"); %A(15,17); R(15,17,"green"); % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/3.23/1.87, 8/4.23/1.87, 9/1.87/0.50, 10/1.87/1.50, 11/1.00/1.00, 12/2.37/2.37, 13/1.50/1.87, 14/0.50/1.87, 15/1.00/2.73, 16/0.00/2.73, 17/1.87/3.23, 18/0.87/3.23, 19/0.00/3.73, 20/0.87/4.23, 21/0.00/4.73, 22/1.87/4.23, 23/1.00/4.73, 24/0.50/5.60, 25/1.50/5.60, 26/1.00/6.46, 27/2.37/5.10, 28/1.87/5.96, 29/1.87/6.96, 30/2.73/6.46, 31/2.73/7.46, 32/3.23/5.60, 33/3.23/6.60, 34/3.73/7.46, 35/4.10/6.10, 36/4.73/1.00, 37/5.23/1.87, 38/5.60/0.50, 39/4.60/6.96, 40/6.10/1.37, 41/4.60/7.96, 42/5.10/6.10, 43/6.10/2.37, 44/6.60/0.50, 45/5.10/7.10, 46/6.60/1.50, 47/5.60/7.96, 48/6.10/7.10, 49/6.60/7.96, 50/6.10/6.10, 51/6.60/6.96, 52/7.46/7.46, 53/7.46/6.46, 54/8.33/6.96, 55/6.96/5.60, 56/7.83/6.10, 57/8.83/6.10, 58/8.33/5.23, 59/9.33/5.23, 60/7.46/4.73, 61/8.46/4.73, 62/9.33/4.23, 63/8.46/3.73, 64/9.33/3.23, 65/7.46/3.73, 66/8.33/3.23, 67/8.83/2.37, 68/7.83/2.37, 69/8.33/1.50, 70/6.96/2.87, 71/7.46/2.00, 72/7.46/1.00, 73/3.73/2.73, 74/5.10/2.37, 75/4.23/2.87, 76/3.73/3.73, 77/2.87/3.23, 78/2.87/4.23, 79/3.73/4.73, 80/4.23/5.60, 81/5.10/5.10, 82/4.60/4.23, 83/5.10/3.37, 84/5.96/2.87, 85/6.46/3.73, 86/5.60/4.23, 87/6.46/4.73, 88/5.60/5.23} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 5/120.00/390.00/0.4/Blue, 74/210.00/390.00/0.4/Green, 23/60.00/330.00/0.4/Orange} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 6/7, 7/3, 7/8, 8/4, 8/36, 9/1, 9/6, 10/9, 10/6, 11/9, 11/10, 12/17, 12/10, 13/11, 13/12, 14/11, 14/13, 14/16, 15/14, 15/13, 15/16, 15/17, 16/18, 16/19, 17/22, 17/18, 18/20, 18/19, 19/20, 19/21, 20/22, 20/21, 21/23, 21/24, 22/23, 23/25, 23/24, 24/25, 24/26, 25/27, 25/26, 26/28, 26/29, 27/78, 27/32, 28/27, 28/30, 29/28, 29/30, 29/31, 30/32, 30/31, 31/33, 31/34, 32/80, 32/35, 33/32, 33/34, 33/35, 34/39, 34/41, 35/42, 35/39, 36/5, 36/38, 37/8, 37/36, 38/5, 39/42, 39/41, 40/37, 40/38, 41/45, 41/47, 42/81, 42/88, 43/37, 43/40, 44/40, 44/38, 45/42, 45/48, 46/43, 46/44, 47/45, 47/48, 47/49, 48/50, 48/49, 49/51, 49/52, 50/51, 50/42, 50/88, 51/53, 51/52, 52/53, 52/54, 53/55, 53/54, 54/56, 54/57, 55/60, 55/56, 56/58, 56/57, 57/58, 57/59, 58/60, 58/59, 59/61, 59/62, 60/65, 60/61, 61/63, 61/62, 62/63, 62/64, 63/65, 63/64, 64/66, 64/67, 65/85, 65/66, 66/68, 66/67, 67/68, 67/69, 68/70, 68/69, 69/71, 69/72, 70/84, 70/71, 71/46, 71/72, 72/46, 72/44, 73/7, 73/8, 74/8, 74/43, 75/8, 75/74, 76/73, 76/75, 77/73, 77/76, 78/77, 78/79, 79/76, 79/82, 80/79, 80/42, 80/81, 81/82, 81/86, 82/83, 82/86, 83/75, 83/84, 84/74, 85/84, 85/70, 86/83, 86/87, 87/85, 87/55, 88/86, 88/87} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,88} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-50) -- (p-88); \draw[Green,very thick] (p-80) -- (p-81); \draw[Green,very thick] (p-47) -- (p-49); \draw[Green,very thick] (p-33) -- (p-35); \draw[Green,very thick] (p-29) -- (p-31); \draw[Green,very thick] (p-14) -- (p-16); \draw[Green,very thick] (p-15) -- (p-16); \draw[Green,very thick] (p-15) -- (p-17); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 5/120.00/390.00/0.4/Blue, 74/210.00/390.00/0.4/Green, 23/60.00/330.00/0.4/Orange} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/210, 2/330, 3/150, 4/30, 5/330, 6/360, 7/210, 8/330, 9/180, 10/60, 11/180, 12/347, 13/30, 14/270, 15/30, 16/240, 17/77, 18/300, 19/120, 20/60, 21/120, 22/48, 23/330, 24/210, 25/30, 26/90, 27/167, 28/240, 29/180, 30/360, 31/60, 32/240, 33/270, 34/30, 35/210, 36/120, 37/30, 38/360, 39/300, 40/90, 41/60, 42/60, 43/60, 44/240, 45/270, 46/180, 47/30, 48/270, 49/120, 50/30, 51/240, 52/60, 53/240, 54/360, 55/93, 56/210, 57/330, 58/210, 59/60, 60/137, 61/120, 62/360, 63/180, 64/300, 65/227, 66/90, 67/270, 68/150, 69/360, 70/330, 71/60, 72/360, 73/300, 74/360, 75/120, 76/60, 77/180, 78/257, 79/62, 80/180, 81/90, 82/150, 83/270, 84/210, 85/90, 86/240, 87/360, 88/270} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ liefert Button "beweglich?" ebenfalls einen beweglichen Graph 88 Knoten, 4×Grad 3, 80×Grad 4, 2×Grad 5, 2×Grad 7, 0 Überschneidungen 178 Kanten, minimal 0.99999999999960431651, maximal 1.00000000000029243274 $ %Eingabe war: % %Automatisch generierte Eingabe zu: #1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78); nach Button neue Eingabe "egal wie" % % % % %blauerWinkel=-90+(0.9999576819615411)*(orangerWinkel-(-90.00000000000018)); %gruenerWinkel=-179.9999999999996+(3.305192664070729e-7)*(orangerWinkel-(-90.00000000000018)); %P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(38,5,4,blauerWinkel); N(36,5,38); N(8,4,36); N(37,8,36); N(40,37,38); N(43,37,40); N(44,40,38); N(46,43,44); N(72,46,44); N(74,8,43); N(75,8,74); N(7,3,8); N(71,46,72); N(73,7,8); N(76,73,75); N(77,73,76); N(6,1,7); N(9,1,6); N(10,9,6); N(11,9,10); N(69,71,72); M(84,74,8,gruenerWinkel); N(70,84,71); N(83,75,84); N(85,84,70); N(68,70,69); N(67,68,69); N(66,68,67); N(64,66,67); N(65,85,66); N(63,65,64); N(62,63,64); N(61,63,62); N(59,61,62); N(60,65,61); N(58,60,59); N(57,58,59); N(56,58,57); N(54,56,57); N(55,60,56); N(87,85,55); N(53,55,54); N(86,83,87); N(88,86,87); N(52,53,54); N(82,83,86); N(51,53,52); N(79,76,82); N(81,82,86); N(42,81,88); N(49,51,52); N(50,51,42); N(78,77,79); N(80,79,42); N(48,50,49); N(45,42,48); N(47,45,48); N(41,45,47); N(39,42,41); N(34,39,41); N(35,42,39); N(32,80,35); N(33,32,34); N(27,78,32); N(31,33,34); N(30,32,31); N(28,27,30); N(29,28,30); N(26,28,29); N(25,27,26); N(24,25,26); N(23,25,24); N(21,23,24); M(22,23,25,orangerWinkel); N(20,22,21); N(19,20,21); N(18,20,19); N(16,18,19); N(17,22,18); N(12,17,10); N(13,11,12); N(14,11,13); N(15,14,13); %A(50,88); R(50,88,"green"); %A(80,81); R(80,81,"green"); %A(47,49); R(47,49,"green"); %A(33,35); R(33,35,"green"); %A(29,31); R(29,31,"green"); %A(14,16); R(14,16,"green"); %A(15,16); R(15,16,"green"); %A(15,17); R(15,17,"green"); % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/3.23/1.87, 8/4.23/1.87, 9/1.87/0.50, 10/1.87/1.50, 11/1.00/1.00, 12/2.37/2.37, 13/1.50/1.87, 14/0.50/1.87, 15/1.00/2.73, 16/0.00/2.73, 17/1.87/3.23, 18/0.87/3.23, 19/0.00/3.73, 20/0.87/4.23, 21/0.00/4.73, 22/1.87/4.23, 23/1.00/4.73, 24/0.50/5.60, 25/1.50/5.60, 26/1.00/6.46, 27/2.37/5.10, 28/1.87/5.96, 29/1.87/6.96, 30/2.73/6.46, 31/2.73/7.46, 32/3.23/5.60, 33/3.23/6.60, 34/3.73/7.46, 35/4.10/6.10, 36/4.73/1.00, 37/5.23/1.87, 38/5.60/0.50, 39/4.60/6.96, 40/6.10/1.37, 41/4.60/7.96, 42/5.10/6.10, 43/6.10/2.37, 44/6.60/0.50, 45/5.10/7.10, 46/6.60/1.50, 47/5.60/7.96, 48/6.10/7.10, 49/6.60/7.96, 50/6.10/6.10, 51/6.60/6.96, 52/7.46/7.46, 53/7.46/6.46, 54/8.33/6.96, 55/6.96/5.60, 56/7.83/6.10, 57/8.83/6.10, 58/8.33/5.23, 59/9.33/5.23, 60/7.46/4.73, 61/8.46/4.73, 62/9.33/4.23, 63/8.46/3.73, 64/9.33/3.23, 65/7.46/3.73, 66/8.33/3.23, 67/8.83/2.37, 68/7.83/2.37, 69/8.33/1.50, 70/6.96/2.87, 71/7.46/2.00, 72/7.46/1.00, 73/3.73/2.73, 74/5.10/2.37, 75/4.23/2.87, 76/3.73/3.73, 77/2.87/3.23, 78/2.87/4.23, 79/3.73/4.73, 80/4.23/5.60, 81/5.10/5.10, 82/4.60/4.23, 83/5.10/3.37, 84/5.96/2.87, 85/6.46/3.73, 86/5.60/4.23, 87/6.46/4.73, 88/5.60/5.23} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 23/60.00/330.00/0.4/Orange} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 6/7, 7/3, 7/8, 8/4, 8/36, 9/1, 9/6, 10/9, 10/6, 11/9, 11/10, 12/17, 12/10, 13/11, 13/12, 14/11, 14/13, 14/16, 15/14, 15/13, 15/16, 15/17, 16/18, 16/19, 17/22, 17/18, 18/20, 18/19, 19/20, 19/21, 20/22, 20/21, 21/23, 21/24, 22/23, 23/25, 23/24, 24/25, 24/26, 25/27, 25/26, 26/28, 26/29, 27/78, 27/32, 28/27, 28/30, 29/28, 29/30, 29/31, 30/32, 30/31, 31/33, 31/34, 32/80, 32/35, 33/32, 33/34, 33/35, 34/39, 34/41, 35/42, 35/39, 36/5, 36/38, 37/8, 37/36, 38/5, 39/42, 39/41, 40/37, 40/38, 41/45, 41/47, 42/81, 42/88, 43/37, 43/40, 44/40, 44/38, 45/42, 45/48, 46/43, 46/44, 47/45, 47/48, 47/49, 48/50, 48/49, 49/51, 49/52, 50/51, 50/42, 50/88, 51/53, 51/52, 52/53, 52/54, 53/55, 53/54, 54/56, 54/57, 55/60, 55/56, 56/58, 56/57, 57/58, 57/59, 58/60, 58/59, 59/61, 59/62, 60/65, 60/61, 61/63, 61/62, 62/63, 62/64, 63/65, 63/64, 64/66, 64/67, 65/85, 65/66, 66/68, 66/67, 67/68, 67/69, 68/70, 68/69, 69/71, 69/72, 70/84, 70/71, 71/46, 71/72, 72/46, 72/44, 73/7, 73/8, 74/8, 74/43, 75/8, 75/74, 76/73, 76/75, 77/73, 77/76, 78/77, 78/79, 79/76, 79/82, 80/79, 80/42, 80/81, 81/82, 81/86, 82/83, 82/86, 83/75, 83/84, 84/74, 85/84, 85/70, 86/83, 86/87, 87/85, 87/55, 88/86, 88/87} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,88} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-50) -- (p-88); \draw[Green,very thick] (p-80) -- (p-81); \draw[Green,very thick] (p-47) -- (p-49); \draw[Green,very thick] (p-33) -- (p-35); \draw[Green,very thick] (p-29) -- (p-31); \draw[Green,very thick] (p-14) -- (p-16); \draw[Green,very thick] (p-15) -- (p-16); \draw[Green,very thick] (p-15) -- (p-17); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 23/60.00/330.00/0.4/Orange} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/210, 2/330, 3/150, 4/30, 5/330, 6/360, 7/210, 8/330, 9/180, 10/60, 11/180, 12/347, 13/30, 14/270, 15/30, 16/240, 17/77, 18/300, 19/120, 20/60, 21/120, 22/48, 23/330, 24/210, 25/30, 26/90, 27/167, 28/240, 29/180, 30/360, 31/60, 32/240, 33/270, 34/30, 35/210, 36/120, 37/30, 38/360, 39/300, 40/90, 41/60, 42/60, 43/60, 44/240, 45/270, 46/180, 47/30, 48/270, 49/120, 50/30, 51/240, 52/60, 53/240, 54/360, 55/93, 56/210, 57/330, 58/210, 59/60, 60/137, 61/120, 62/360, 63/180, 64/300, 65/227, 66/90, 67/270, 68/150, 69/360, 70/330, 71/60, 72/360, 73/300, 74/360, 75/120, 76/60, 77/180, 78/257, 79/62, 80/180, 81/90, 82/150, 83/270, 84/210, 85/90, 86/240, 87/360, 88/270} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ und sogar nach Button neue Eingabe "Rahmen zuerst" mit den vielen einzustellenden Winkeln 88 Knoten, 4×Grad 3, 80×Grad 4, 2×Grad 5, 2×Grad 7, 0 Überschneidungen 178 Kanten, minimal 0.99999999999980404564, maximal 1.00000000000011546319 $ %Eingabe war: % %#1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78); % % % % % % % % % % % % % % % % % %P[1]=[0,0]; P[9]=[-43.30127018922193,25.000000000000004]; D=ab(1,9); A(9,1); N(6,9,1); N(10,9,6); N(11,9,10); M(14,11,9,blauerWinkel); N(13,14,11); N(15,14,13); N(16,14,15); M(19,16,14,gruenerWinkel); N(18,19,16); N(20,19,18); N(21,19,20); M(24,21,19,orangerWinkel); N(23,24,21); N(25,24,23); N(26,24,25); M(29,26,24,vierterWinkel); N(28,29,26); N(30,29,28); N(31,29,30); M(34,31,29,fuenfterWinkel); N(33,34,31); M(41,34,31,sechsterWinkel); N(39,41,34); M(47,41,34,siebenterWinkel); N(45,47,41); N(48,47,45); N(49,47,48); M(52,49,47,achterWinkel); N(51,52,49); N(53,52,51); N(54,52,53); M(57,54,52,neunterWinkel); N(56,57,54); N(58,57,56); N(59,57,58); M(62,59,57,zehnterWinkel); N(61,62,59); N(63,62,61); N(64,62,63); M(67,64,62,elfterWinkel); N(66,67,64); N(68,67,66); N(69,67,68); M(72,69,67,zwölfterWinkel); N(71,72,69); N(46,72,71); N(44,72,46); M(40,44,72,dreizehnterWinkel); N(38,44,40); Q(5,38,1,1*D,2*D); A(5,38); A(5,1); H(2,1,5,2); A(2,1); L(3,1,2); H(5,38,5,1); A(5,38); L(36,5,38); A(2,5); L(4,2,5); A(3,4); N(7,6,3); N(8,4,36); N(12,13,10); N(17,18,12); N(22,23,17); N(27,28,25); N(32,33,27); N(35,39,32); N(37,36,40); N(42,45,35); N(43,40,46); N(50,51,42); N(55,56,53); N(60,61,55); N(65,66,60); N(70,71,68); N(73,7,8); N(74,8,43); N(75,8,74); N(80,42,32); N(81,42,80); N(84,74,70); N(85,84,70); N(87,85,55); N(88,87,42); M(78,27,28,vierzehnterWinkel); N(76,73,75); N(77,76,78); N(79,76,80); N(82,81,79); N(83,84,82); N(86,87,88); %A(8,7); R(8,7,"green"); %A(17,15); R(17,15,"green"); %A(22,20); R(22,20,"green"); %A(32,30); R(32,30,"green"); %A(35,33); R(35,33,"green"); %A(37,8); R(37,8,"green"); %A(42,39); R(42,39,"green"); %A(43,37); R(43,37,"green"); %A(50,48); R(50,48,"green"); %A(60,58); R(60,58,"green"); %A(65,63); R(65,63,"green"); %A(85,65); R(85,65,"green"); %A(88,50); R(88,50,"green"); %A(77,73); R(77,73,"green"); %A(79,78); R(79,78,"green"); %A(83,75); R(83,75,"green"); %A(86,81); R(86,81,"green"); %A(86,83); R(86,83,"green"); %A(86,82); R(86,82,"green"); % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LightBlue}{rgb}{0.68,0.84,0.90} \definecolor{LightCoral}{rgb}{0.94,0.50,0.50} \definecolor{LightCyan}{rgb}{0.88,1.00,1.00} \definecolor{LightGoldenrodYellow}{rgb}{0.98,0.98,0.82} \definecolor{LightGreen}{rgb}{0.56,0.93,0.56} \definecolor{LightGray}{rgb}{0.82,0.82,0.82} \definecolor{LightPink}{rgb}{1.00,0.71,0.75} \definecolor{LightSalmon}{rgb}{1.00,0.63,0.48} \definecolor{Lime}{rgb}{0.00,1.00,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/3.23/1.87, 8/4.23/1.87, 9/1.87/0.50, 10/1.87/1.50, 11/1.00/1.00, 12/2.37/2.37, 13/1.50/1.87, 14/0.50/1.87, 15/1.00/2.73, 16/0.00/2.73, 17/1.87/3.23, 18/0.87/3.23, 19/0.00/3.73, 20/0.87/4.23, 21/0.00/4.73, 22/1.87/4.23, 23/1.00/4.73, 24/0.50/5.60, 25/1.50/5.60, 26/1.00/6.46, 27/2.37/5.10, 28/1.87/5.96, 29/1.87/6.96, 30/2.73/6.46, 31/2.73/7.46, 32/3.23/5.60, 33/3.23/6.60, 34/3.73/7.46, 35/4.10/6.10, 36/4.73/1.00, 37/5.23/1.87, 38/5.60/0.50, 39/4.60/6.96, 40/6.10/1.37, 41/4.60/7.96, 42/5.10/6.10, 43/6.10/2.37, 44/6.60/0.50, 45/5.10/7.10, 46/6.60/1.50, 47/5.60/7.96, 48/6.10/7.10, 49/6.60/7.96, 50/6.10/6.10, 51/6.60/6.96, 52/7.46/7.46, 53/7.46/6.46, 54/8.33/6.96, 55/6.96/5.60, 56/7.83/6.10, 57/8.83/6.10, 58/8.33/5.23, 59/9.33/5.23, 60/7.46/4.73, 61/8.46/4.73, 62/9.33/4.23, 63/8.46/3.73, 64/9.33/3.23, 65/7.46/3.73, 66/8.33/3.23, 67/8.83/2.37, 68/7.83/2.37, 69/8.33/1.50, 70/6.96/2.87, 71/7.46/2.00, 72/7.46/1.00, 73/3.73/2.73, 74/5.10/2.37, 75/4.23/2.87, 76/3.73/3.73, 77/2.87/3.23, 78/2.87/4.23, 79/3.73/4.73, 80/4.23/5.60, 81/5.10/5.10, 82/4.60/4.23, 83/5.10/3.37, 84/5.96/2.87, 85/6.46/3.73, 86/5.60/4.23, 87/6.46/4.73, 88/5.60/5.23} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 11/330.00/480.00/0.4/Blue, 16/300.00/450.00/0.4/Green, 21/270.00/420.00/0.4/Orange, 26/240.00/390.00/0.4/Violet, 31/210.00/360.00/0.4/Teal, 34/180.00/390.00/0.4/Lime, 41/210.00/360.00/0.4/LightBlue, 49/180.00/330.00/0.4/LightCoral, 54/150.00/300.00/0.4/LightCyan, 59/120.00/270.00/0.4/LightGoldenrodYellow, 64/90.00/240.00/0.4/LightGreen, 69/60.00/210.00/0.4/LightGray, 44/30.00/120.00/0.4/LightPink, 27/120.00/300.00/0.4/LightSalmon} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 2/5, 3/1, 3/2, 3/4, 4/2, 4/5, 5/38, 6/9, 6/1, 7/6, 7/3, 8/4, 8/36, 8/7, 9/1, 10/9, 10/6, 11/9, 11/10, 12/13, 12/10, 13/14, 13/11, 14/11, 15/14, 15/13, 16/14, 16/15, 17/18, 17/12, 17/15, 18/19, 18/16, 19/16, 20/19, 20/18, 21/19, 21/20, 22/23, 22/17, 22/20, 23/24, 23/21, 24/21, 25/24, 25/23, 26/24, 26/25, 27/28, 27/25, 28/29, 28/26, 29/26, 30/29, 30/28, 31/29, 31/30, 32/33, 32/27, 32/30, 33/34, 33/31, 34/31, 35/39, 35/32, 35/33, 36/5, 36/38, 37/36, 37/40, 37/8, 38/44, 38/40, 39/41, 39/34, 40/44, 41/34, 42/45, 42/35, 42/39, 43/40, 43/46, 43/37, 44/72, 44/46, 45/47, 45/41, 46/72, 46/71, 47/41, 48/47, 48/45, 49/47, 49/48, 50/51, 50/42, 50/48, 51/52, 51/49, 52/49, 53/52, 53/51, 54/52, 54/53, 55/56, 55/53, 56/57, 56/54, 57/54, 58/57, 58/56, 59/57, 59/58, 60/61, 60/55, 60/58, 61/62, 61/59, 62/59, 63/62, 63/61, 64/62, 64/63, 65/66, 65/60, 65/63, 66/67, 66/64, 67/64, 68/67, 68/66, 69/67, 69/68, 70/71, 70/68, 71/72, 71/69, 72/69, 73/7, 73/8, 74/8, 74/43, 75/8, 75/74, 76/73, 76/75, 77/76, 77/78, 77/73, 78/27, 79/76, 79/80, 79/78, 80/42, 80/32, 81/42, 81/80, 82/81, 82/79, 83/84, 83/82, 83/75, 84/74, 84/70, 85/84, 85/70, 85/65, 86/87, 86/88, 86/81, 86/83, 86/82, 87/85, 87/55, 88/87, 88/42, 88/50} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,88} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-8) -- (p-7); \draw[Green,very thick] (p-17) -- (p-15); \draw[Green,very thick] (p-22) -- (p-20); \draw[Green,very thick] (p-32) -- (p-30); \draw[Green,very thick] (p-35) -- (p-33); \draw[Green,very thick] (p-37) -- (p-8); \draw[Green,very thick] (p-42) -- (p-39); \draw[Green,very thick] (p-43) -- (p-37); \draw[Green,very thick] (p-50) -- (p-48); \draw[Green,very thick] (p-60) -- (p-58); \draw[Green,very thick] (p-65) -- (p-63); \draw[Green,very thick] (p-85) -- (p-65); \draw[Green,very thick] (p-88) -- (p-50); \draw[Green,very thick] (p-77) -- (p-73); \draw[Green,very thick] (p-79) -- (p-78); \draw[Green,very thick] (p-83) -- (p-75); \draw[Green,very thick] (p-86) -- (p-81); \draw[Green,very thick] (p-86) -- (p-83); \draw[Green,very thick] (p-86) -- (p-82); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 11/330.00/480.00/0.4/Blue, 16/300.00/450.00/0.4/Green, 21/270.00/420.00/0.4/Orange, 26/240.00/390.00/0.4/Violet, 31/210.00/360.00/0.4/Teal, 34/180.00/390.00/0.4/Lime, 41/210.00/360.00/0.4/LightBlue, 49/180.00/330.00/0.4/LightCoral, 54/150.00/300.00/0.4/LightCyan, 59/120.00/270.00/0.4/LightGoldenrodYellow, 64/90.00/240.00/0.4/LightGreen, 69/60.00/210.00/0.4/LightGray, 44/30.00/120.00/0.4/LightPink, 27/120.00/300.00/0.4/LightSalmon} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/210, 2/330, 3/150, 4/30, 5/330, 6/60, 7/210, 8/240, 9/180, 10/60, 11/180, 12/348, 13/30, 14/210, 15/30, 16/150, 17/318, 18/300, 19/180, 20/60, 21/210, 22/48, 23/270, 24/90, 25/30, 26/90, 27/258, 28/300, 29/180, 30/300, 31/150, 32/240, 33/270, 34/180, 35/210, 36/270, 37/180, 38/360, 39/300, 40/90, 41/60, 42/150, 43/60, 44/330, 45/270, 46/180, 47/150, 48/330, 49/120, 50/30, 51/180, 52/360, 53/240, 54/360, 55/93, 56/150, 57/30, 58/210, 59/330, 60/137, 61/180, 62/360, 63/180, 64/30, 65/227, 66/90, 67/30, 68/210, 69/270, 70/330, 71/60, 72/360, 73/90, 74/360, 75/120, 76/60, 77/180, 78/257, 79/123, 80/180, 81/300, 82/210, 83/270, 84/210, 85/90, 86/30, 87/360, 88/120} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ findet Button "beweglich?" eine Beweglichkeit. 88 Knoten, 4×Grad 3, 80×Grad 4, 2×Grad 5, 2×Grad 7, 0 Überschneidungen 178 Kanten, minimal 0.99999999999980404564, maximal 1.00000000000011546319 $ %Eingabe war: % %#1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78); % % % % %blauerWinkel=150.00000000000009+(0.9999983168393314)*(dreizehnterWinkel-(90)); %gruenerWinkel=150+(-0.9999983168393296)*(dreizehnterWinkel-(90)); %orangerWinkel=150.0000000000002+(0.9999987575491853)*(dreizehnterWinkel-(90)); %vierterWinkel=149.99999999999974+(-1.0000001604326674)*(dreizehnterWinkel-(90)); %fuenfterWinkel=150.00000000000063+(1.0000024741707787)*(dreizehnterWinkel-(90)); %sechsterWinkel=-150.00000000000074+(-1.000004852037189)*(dreizehnterWinkel-(90)); %siebenterWinkel=150.00000000000063+(1.000004049339543)*(dreizehnterWinkel-(90)); %achterWinkel=149.99999999999918+(-1.0000014811475222)*(dreizehnterWinkel-(90)); %neunterWinkel=150+(1.0000023821281057)*(dreizehnterWinkel-(90)); %zehnterWinkel=150.0000000000002+(-1.0000010600001117)*(dreizehnterWinkel-(90)); %elfterWinkel=150.00000000000006+(1.0000010758308997)*(dreizehnterWinkel-(90)); %zwölfterWinkel=149.99999999999966+(-1.000000418101856)*(dreizehnterWinkel-(90)); %vierzehnterWinkel=179.99999999999943+(6.8801574023397e-7)*(dreizehnterWinkel-(90)); %P[1]=[0,0]; P[9]=[-43.30127018922193,25.000000000000004]; D=ab(1,9); A(9,1); N(6,9,1); N(10,9,6); N(11,9,10); M(14,11,9,blauerWinkel); N(13,14,11); N(15,14,13); N(16,14,15); M(19,16,14,gruenerWinkel); N(18,19,16); N(20,19,18); N(21,19,20); M(24,21,19,orangerWinkel); N(23,24,21); N(25,24,23); N(26,24,25); M(29,26,24,vierterWinkel); N(28,29,26); N(30,29,28); N(31,29,30); M(34,31,29,fuenfterWinkel); N(33,34,31); M(41,34,31,sechsterWinkel); N(39,41,34); M(47,41,34,siebenterWinkel); N(45,47,41); N(48,47,45); N(49,47,48); M(52,49,47,achterWinkel); N(51,52,49); N(53,52,51); N(54,52,53); M(57,54,52,neunterWinkel); N(56,57,54); N(58,57,56); N(59,57,58); M(62,59,57,zehnterWinkel); N(61,62,59); N(63,62,61); N(64,62,63); M(67,64,62,elfterWinkel); N(66,67,64); N(68,67,66); N(69,67,68); M(72,69,67,zwölfterWinkel); N(71,72,69); N(46,72,71); N(44,72,46); M(40,44,72,dreizehnterWinkel); N(38,44,40); Q(5,38,1,1*D,2*D); A(5,38); A(5,1); H(2,1,5,2); A(2,1); L(3,1,2); H(5,38,5,1); A(5,38); L(36,5,38); A(2,5); L(4,2,5); A(3,4); N(7,6,3); N(8,4,36); N(12,13,10); N(17,18,12); N(22,23,17); N(27,28,25); N(32,33,27); N(35,39,32); N(37,36,40); N(42,45,35); N(43,40,46); N(50,51,42); N(55,56,53); N(60,61,55); N(65,66,60); N(70,71,68); N(73,7,8); N(74,8,43); N(75,8,74); N(80,42,32); N(81,42,80); N(84,74,70); N(85,84,70); N(87,85,55); N(88,87,42); M(78,27,28,vierzehnterWinkel); N(76,73,75); N(77,76,78); N(79,76,80); N(82,81,79); N(83,84,82); N(86,87,88); %A(8,7); R(8,7,"green"); %A(17,15); R(17,15,"green"); %A(22,20); R(22,20,"green"); %A(32,30); R(32,30,"green"); %A(35,33); R(35,33,"green"); %A(37,8); R(37,8,"green"); %A(42,39); R(42,39,"green"); %A(43,37); R(43,37,"green"); %A(50,48); R(50,48,"green"); %A(60,58); R(60,58,"green"); %A(65,63); R(65,63,"green"); %A(85,65); R(85,65,"green"); %A(88,50); R(88,50,"green"); %A(77,73); R(77,73,"green"); %A(79,78); R(79,78,"green"); %A(83,75); R(83,75,"green"); %A(86,81); R(86,81,"green"); %A(86,83); R(86,83,"green"); %A(86,82); R(86,82,"green"); % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LightPink}{rgb}{1.00,0.71,0.75} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/3.23/1.87, 8/4.23/1.87, 9/1.87/0.50, 10/1.87/1.50, 11/1.00/1.00, 12/2.37/2.37, 13/1.50/1.87, 14/0.50/1.87, 15/1.00/2.73, 16/0.00/2.73, 17/1.87/3.23, 18/0.87/3.23, 19/0.00/3.73, 20/0.87/4.23, 21/0.00/4.73, 22/1.87/4.23, 23/1.00/4.73, 24/0.50/5.60, 25/1.50/5.60, 26/1.00/6.46, 27/2.37/5.10, 28/1.87/5.96, 29/1.87/6.96, 30/2.73/6.46, 31/2.73/7.46, 32/3.23/5.60, 33/3.23/6.60, 34/3.73/7.46, 35/4.10/6.10, 36/4.73/1.00, 37/5.23/1.87, 38/5.60/0.50, 39/4.60/6.96, 40/6.10/1.37, 41/4.60/7.96, 42/5.10/6.10, 43/6.10/2.37, 44/6.60/0.50, 45/5.10/7.10, 46/6.60/1.50, 47/5.60/7.96, 48/6.10/7.10, 49/6.60/7.96, 50/6.10/6.10, 51/6.60/6.96, 52/7.46/7.46, 53/7.46/6.46, 54/8.33/6.96, 55/6.96/5.60, 56/7.83/6.10, 57/8.83/6.10, 58/8.33/5.23, 59/9.33/5.23, 60/7.46/4.73, 61/8.46/4.73, 62/9.33/4.23, 63/8.46/3.73, 64/9.33/3.23, 65/7.46/3.73, 66/8.33/3.23, 67/8.83/2.37, 68/7.83/2.37, 69/8.33/1.50, 70/6.96/2.87, 71/7.46/2.00, 72/7.46/1.00, 73/3.73/2.73, 74/5.10/2.37, 75/4.23/2.87, 76/3.73/3.73, 77/2.87/3.23, 78/2.87/4.23, 79/3.73/4.73, 80/4.23/5.60, 81/5.10/5.10, 82/4.60/4.23, 83/5.10/3.37, 84/5.96/2.87, 85/6.46/3.73, 86/5.60/4.23, 87/6.46/4.73, 88/5.60/5.23} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 44/30.00/120.00/0.4/LightPink} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 2/5, 3/1, 3/2, 3/4, 4/2, 4/5, 5/38, 6/9, 6/1, 7/6, 7/3, 8/4, 8/36, 8/7, 9/1, 10/9, 10/6, 11/9, 11/10, 12/13, 12/10, 13/14, 13/11, 14/11, 15/14, 15/13, 16/14, 16/15, 17/18, 17/12, 17/15, 18/19, 18/16, 19/16, 20/19, 20/18, 21/19, 21/20, 22/23, 22/17, 22/20, 23/24, 23/21, 24/21, 25/24, 25/23, 26/24, 26/25, 27/28, 27/25, 28/29, 28/26, 29/26, 30/29, 30/28, 31/29, 31/30, 32/33, 32/27, 32/30, 33/34, 33/31, 34/31, 35/39, 35/32, 35/33, 36/5, 36/38, 37/36, 37/40, 37/8, 38/44, 38/40, 39/41, 39/34, 40/44, 41/34, 42/45, 42/35, 42/39, 43/40, 43/46, 43/37, 44/72, 44/46, 45/47, 45/41, 46/72, 46/71, 47/41, 48/47, 48/45, 49/47, 49/48, 50/51, 50/42, 50/48, 51/52, 51/49, 52/49, 53/52, 53/51, 54/52, 54/53, 55/56, 55/53, 56/57, 56/54, 57/54, 58/57, 58/56, 59/57, 59/58, 60/61, 60/55, 60/58, 61/62, 61/59, 62/59, 63/62, 63/61, 64/62, 64/63, 65/66, 65/60, 65/63, 66/67, 66/64, 67/64, 68/67, 68/66, 69/67, 69/68, 70/71, 70/68, 71/72, 71/69, 72/69, 73/7, 73/8, 74/8, 74/43, 75/8, 75/74, 76/73, 76/75, 77/76, 77/78, 77/73, 78/27, 79/76, 79/80, 79/78, 80/42, 80/32, 81/42, 81/80, 82/81, 82/79, 83/84, 83/82, 83/75, 84/74, 84/70, 85/84, 85/70, 85/65, 86/87, 86/88, 86/81, 86/83, 86/82, 87/85, 87/55, 88/87, 88/42, 88/50} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,88} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-8) -- (p-7); \draw[Green,very thick] (p-17) -- (p-15); \draw[Green,very thick] (p-22) -- (p-20); \draw[Green,very thick] (p-32) -- (p-30); \draw[Green,very thick] (p-35) -- (p-33); \draw[Green,very thick] (p-37) -- (p-8); \draw[Green,very thick] (p-42) -- (p-39); \draw[Green,very thick] (p-43) -- (p-37); \draw[Green,very thick] (p-50) -- (p-48); \draw[Green,very thick] (p-60) -- (p-58); \draw[Green,very thick] (p-65) -- (p-63); \draw[Green,very thick] (p-85) -- (p-65); \draw[Green,very thick] (p-88) -- (p-50); \draw[Green,very thick] (p-77) -- (p-73); \draw[Green,very thick] (p-79) -- (p-78); \draw[Green,very thick] (p-83) -- (p-75); \draw[Green,very thick] (p-86) -- (p-81); \draw[Green,very thick] (p-86) -- (p-83); \draw[Green,very thick] (p-86) -- (p-82); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 44/30.00/120.00/0.4/LightPink} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/210, 2/330, 3/150, 4/30, 5/330, 6/60, 7/210, 8/240, 9/180, 10/60, 11/180, 12/348, 13/30, 14/210, 15/30, 16/150, 17/318, 18/300, 19/180, 20/60, 21/210, 22/48, 23/270, 24/90, 25/30, 26/90, 27/258, 28/300, 29/180, 30/300, 31/150, 32/240, 33/270, 34/180, 35/210, 36/270, 37/180, 38/360, 39/300, 40/90, 41/60, 42/150, 43/60, 44/330, 45/270, 46/180, 47/150, 48/330, 49/120, 50/30, 51/180, 52/360, 53/240, 54/360, 55/93, 56/150, 57/30, 58/210, 59/330, 60/137, 61/180, 62/360, 63/180, 64/30, 65/227, 66/90, 67/30, 68/210, 69/270, 70/330, 71/60, 72/360, 73/90, 74/360, 75/120, 76/60, 77/180, 78/257, 79/123, 80/180, 81/300, 82/210, 83/270, 84/210, 85/90, 86/30, 87/360, 88/120} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Das hatte ich nicht erwartet. Weitere Beispielgraphen aber gar nicht erst versuchen, die gehen alle nicht. Bis hierher sind das nur ausgewählte Testbeispiele zum Ausprobieren als Demoversion. Es ist nicht immer so, daß die lineare Abhängigkeit zwischen den Winkeln über das gesamte Bewegungsintervall hinweg erhalten bleibt. Allgemein gilt das nur annähernd für kleinste Bewegungsschritte, danach muss man den Graph neu zurechtziehen und die nächste Bewegungsrichtung bestimmen. Oder höhere Ableitungen zur Bestimmung der Bewegung auswerten. Zuguterletzt macht dann die begrenzte Rechengenauigkeit noch einen Strich durch die Rechnung. Hierzu gleich als Beispiel obiger Graph nach zweimal Button neue Eingabe "wenig Winkel" 88 Knoten, 4×Grad 3, 80×Grad 4, 2×Grad 5, 2×Grad 7, 0 Überschneidungen 178 Kanten, minimal 0.99999999999999800160, maximal 1.00000000000001798561 $ %Eingabe war: % %#1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78); % % % % % % %P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(1,2); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,2,blauerWinkel); L(9,1,6); L(10,9,6); L(11,9,10); N(7,6,3); M(109,7,3,95.00000000000001); L(73,7,109); Q(8,7,4,ab(109,7,73,"gedreht"),D); M(110,8,4,34.99999999999997); L(37,8,110); M(111,5,2,275.00000000000006); L(38,111,5); Q(36,8,5,ab(110,8,37,"gedreht"),ab(111,5,38,"gedreht")); M(112,37,8,155.00000000000003); L(43,37,112); M(113,38,5,215); L(44,113,38); Q(40,37,38,ab(112,37,43,"gedreht"),ab(113,38,44,"gedreht")); M(114,44,38,275); M(71,114,44,125.00000000000001); M(69,71,114,125); L(116,69,71); Q(115,71,114,ab(116,71,69,"gedreht"),D); Q(72,114,44,ab(115,114,69,71,"gedreht"),D); Q(46,43,44,D,ab(114,44,69,71,72,"gedreht")); M(117,8,4,125.00000000000001); L(75,8,117); Q(74,8,43,ab(117,8,75,"gedreht"),D); M(118,73,7,215); L(77,73,118); Q(76,73,75,ab(118,73,77,"gedreht"),D); M(12,10,6,gruenerWinkel); M(119,11,9,95.00000000000006); L(14,11,119); L(15,14,119); L(16,14,15); Q(13,11,12,ab(119,11,14,15,16,"gedreht"),D); N(17,15,12); M(120,16,14,94.99999999999991); L(19,16,120); L(20,19,120); L(21,19,20); Q(18,16,17,ab(120,16,19,20,21,"gedreht"),D); N(22,20,17); M(121,21,19,95.00000000000014); L(24,21,121); L(25,24,121); L(26,24,25); Q(23,21,22,ab(121,21,24,25,26,"gedreht"),D); M(27,25,23,orangerWinkel); M(122,26,24,95); L(29,26,122); L(30,29,122); L(31,29,30); Q(28,26,27,ab(122,26,29,30,31,"gedreht"),D); N(32,30,27); M(123,31,29,95.00000000000011); L(34,31,123); M(124,32,27,244.99999999999986); L(35,124,32); Q(33,31,32,ab(123,31,34,"gedreht"),ab(124,32,35,"gedreht")); M(125,34,31,154.99999999999974); L(41,34,125); M(126,35,32,215.00000000000034); L(42,126,35); Q(39,34,35,ab(125,34,41,"gedreht"),ab(126,35,42,"gedreht")); M(127,41,34,95.00000000000016); L(47,41,127); L(48,47,127); L(49,47,48); Q(45,41,42,ab(127,41,47,48,49,"gedreht"),D); M(128,42,35,184.9999999999999); L(88,128,42); Q(50,48,42,D,ab(128,42,88,"gedreht")); M(129,49,47,95.0000000000004); L(52,49,129); L(53,52,129); L(54,52,53); Q(51,49,50,ab(129,49,52,53,54,"gedreht"),D); N(78,27,77); N(79,78,76); N(80,32,79); M(130,42,35,35.0000000000003); L(81,42,130); A(80,42,ab(130,42,81,"gedreht")); M(82,81,42,154.99999999999943); L(86,81,82); L(131,86,82); Q(83,81,75,ab(131,81,82,86,"gedreht"),D); A(79,82); M(87,86,81,275.00000000000057); L(132,86,87); A(88,86,ab(132,86,87,"gedreht")); N(55,87,53); M(133,54,52,94.9999999999983); L(57,54,133); L(58,57,133); L(59,57,58); Q(56,54,55,ab(133,54,57,58,59,"gedreht"),D); N(60,58,55); M(134,59,57,95.00000000000199); L(62,59,134); M(135,62,59,124.99999999999986); L(64,62,135); Q(63,62,134,ab(135,62,64,"gedreht"),D); Q(61,59,60,ab(134,59,62,63,64,"gedreht"),D); M(66,64,62,94.99999999999955); L(67,64,66); L(68,67,66); L(136,67,68); A(69,64,ab(136,64,66,67,68,"gedreht")); N(65,63,60); A(65,66); N(70,71,68); M(84,70,68,214.9999999999997); L(137,84,70); Q(85,70,65,ab(137,70,84,"gedreht"),D); A(83,84); A(74,84); A(85,87); %R(42,80); // oder R(42,81); %R(79,82); %R(86,87); // oder R(86,88); %R(64,66); // oder R(64,67); %R(65,66); %R(83,84); %R(74,84); %R(85,87); % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LimeGreen}{rgb}{0.20,0.80,0.20} \definecolor{Orange}{rgb}{1.00,0.64,0.00} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/3.23/1.87, 8/4.23/1.87, 9/1.87/0.50, 10/1.87/1.50, 11/1.00/1.00, 12/2.37/2.37, 13/1.50/1.87, 14/0.50/1.87, 15/1.00/2.73, 16/0.00/2.73, 17/1.87/3.23, 18/0.87/3.23, 19/0.00/3.73, 20/0.87/4.23, 21/0.00/4.73, 22/1.87/4.23, 23/1.00/4.73, 24/0.50/5.60, 25/1.50/5.60, 26/1.00/6.46, 27/2.37/5.10, 28/1.87/5.96, 29/1.87/6.96, 30/2.73/6.46, 31/2.73/7.46, 32/3.23/5.60, 33/3.23/6.60, 34/3.73/7.46, 35/4.10/6.10, 36/4.73/1.00, 37/5.23/1.87, 38/5.60/0.50, 39/4.60/6.96, 40/6.10/1.37, 41/4.60/7.96, 42/5.10/6.10, 43/6.10/2.37, 44/6.60/0.50, 45/5.10/7.10, 46/6.60/1.50, 47/5.60/7.96, 48/6.10/7.10, 49/6.60/7.96, 50/6.10/6.10, 51/6.60/6.96, 52/7.46/7.46, 53/7.46/6.46, 54/8.33/6.96, 55/6.96/5.60, 56/7.83/6.10, 57/8.83/6.10, 58/8.33/5.23, 59/9.33/5.23, 60/7.46/4.73, 61/8.46/4.73, 62/9.33/4.23, 63/8.46/3.73, 64/9.33/3.23, 65/7.46/3.73, 66/8.33/3.23, 67/8.83/2.37, 68/7.83/2.37, 69/8.33/1.50, 70/6.96/2.87, 71/7.46/2.00, 72/7.46/1.00, 73/3.73/2.73, 74/5.10/2.37, 75/4.23/2.87, 76/3.73/3.73, 77/2.87/3.23, 78/2.87/4.23, 79/3.73/4.73, 80/4.23/5.60, 81/5.10/5.10, 82/4.60/4.23, 83/5.10/3.37, 84/5.96/2.87, 85/6.46/3.73, 86/5.60/4.23, 87/6.46/4.73, 88/5.60/5.23} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/0.00/90.00/0.4/Blue, 10/330.00/420.00/0.4/Green, 25/240.00/330.00/0.4/Orange} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 7/6, 7/3, 8/7, 8/4, 9/1, 9/6, 10/9, 10/6, 11/9, 11/10, 12/10, 13/11, 13/12, 14/11, 14/13, 15/14, 15/13, 16/14, 16/15, 17/15, 17/12, 18/16, 18/17, 19/16, 19/18, 20/19, 20/18, 21/19, 21/20, 22/20, 22/17, 23/21, 23/22, 24/21, 24/23, 25/24, 25/23, 26/24, 26/25, 27/25, 28/26, 28/27, 29/26, 29/28, 30/29, 30/28, 31/29, 31/30, 32/30, 32/27, 33/31, 33/32, 34/31, 34/33, 35/33, 35/32, 36/8, 36/5, 37/8, 37/36, 38/36, 38/5, 39/34, 39/35, 40/37, 40/38, 41/34, 41/39, 42/39, 42/35, 43/37, 43/40, 44/40, 44/38, 45/41, 45/42, 46/43, 46/44, 47/41, 47/45, 48/47, 48/45, 49/47, 49/48, 50/48, 50/42, 51/49, 51/50, 52/49, 52/51, 53/52, 53/51, 54/52, 54/53, 55/87, 55/53, 56/54, 56/55, 57/54, 57/56, 58/57, 58/56, 59/57, 59/58, 60/58, 60/55, 61/59, 61/60, 62/59, 62/61, 63/62, 63/61, 64/62, 64/63, 65/63, 65/60, 65/66, 66/64, 67/64, 67/66, 68/67, 68/66, 69/71, 69/67, 69/68, 70/71, 70/68, 71/46, 72/69, 72/71, 72/46, 72/44, 73/7, 73/8, 74/8, 74/43, 74/84, 75/8, 75/74, 76/73, 76/75, 77/73, 77/76, 78/27, 78/77, 79/78, 79/76, 79/82, 80/32, 80/79, 80/42, 81/42, 81/80, 82/81, 83/82, 83/86, 83/75, 83/84, 84/70, 85/70, 85/84, 85/65, 85/87, 86/81, 86/82, 87/86, 88/50, 88/42, 88/86, 88/87} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,88} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[LimeGreen,very thick] (p-42) -- (p-80); \draw[LimeGreen,very thick] (p-79) -- (p-82); \draw[LimeGreen,very thick] (p-86) -- (p-87); \draw[LimeGreen,very thick] (p-64) -- (p-66); \draw[LimeGreen,very thick] (p-65) -- (p-66); \draw[LimeGreen,very thick] (p-83) -- (p-84); \draw[LimeGreen,very thick] (p-74) -- (p-84); \draw[LimeGreen,very thick] (p-85) -- (p-87); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/0.00/90.00/0.4/Blue, 10/330.00/420.00/0.4/Green, 25/240.00/330.00/0.4/Orange} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/210, 2/330, 3/150, 4/30, 5/330, 6/60, 7/210, 8/240, 9/180, 10/60, 11/270, 12/348, 13/30, 14/270, 15/30, 16/240, 17/318, 18/300, 19/240, 20/60, 21/120, 22/48, 23/330, 24/210, 25/30, 26/180, 27/258, 28/300, 29/120, 30/300, 31/60, 32/240, 33/270, 34/30, 35/210, 36/270, 37/30, 38/360, 39/90, 40/90, 41/60, 42/60, 43/60, 44/330, 45/210, 46/180, 47/150, 48/270, 49/120, 50/30, 51/180, 52/360, 53/240, 54/360, 55/92, 56/210, 57/30, 58/210, 59/60, 60/258, 61/120, 62/60, 63/240, 64/30, 65/318, 66/90, 67/270, 68/210, 69/360, 70/330, 71/120, 72/360, 73/90, 74/360, 75/120, 76/60, 77/180, 78/257, 79/123, 80/180, 81/300, 82/210, 83/270, 84/210, 85/90, 86/240, 87/360, 88/120} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ dann Button "beweglich?" - und weg sind die Winkel. $ %Eingabe war: % %#1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78); % % % %blauerWinkel=90; %gruenerWinkel=90; %orangerWinkel=89.99999999999994; %P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(1,2); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,2,blauerWinkel); L(9,1,6); L(10,9,6); L(11,9,10); N(7,6,3); M(109,7,3,95.00000000000001); L(73,7,109); Q(8,7,4,ab(109,7,73,"gedreht"),D); M(110,8,4,34.99999999999997); L(37,8,110); M(111,5,2,275.00000000000006); L(38,111,5); Q(36,8,5,ab(110,8,37,"gedreht"),ab(111,5,38,"gedreht")); M(112,37,8,155.00000000000003); L(43,37,112); M(113,38,5,215); L(44,113,38); Q(40,37,38,ab(112,37,43,"gedreht"),ab(113,38,44,"gedreht")); M(114,44,38,275); M(71,114,44,125.00000000000001); M(69,71,114,125); L(116,69,71); Q(115,71,114,ab(116,71,69,"gedreht"),D); Q(72,114,44,ab(115,114,69,71,"gedreht"),D); Q(46,43,44,D,ab(114,44,69,71,72,"gedreht")); M(117,8,4,125.00000000000001); L(75,8,117); Q(74,8,43,ab(117,8,75,"gedreht"),D); M(118,73,7,215); L(77,73,118); Q(76,73,75,ab(118,73,77,"gedreht"),D); M(12,10,6,gruenerWinkel); M(119,11,9,95.00000000000006); L(14,11,119); L(15,14,119); L(16,14,15); Q(13,11,12,ab(119,11,14,15,16,"gedreht"),D); N(17,15,12); M(120,16,14,94.99999999999991); L(19,16,120); L(20,19,120); L(21,19,20); Q(18,16,17,ab(120,16,19,20,21,"gedreht"),D); N(22,20,17); M(121,21,19,95.00000000000014); L(24,21,121); L(25,24,121); L(26,24,25); Q(23,21,22,ab(121,21,24,25,26,"gedreht"),D); M(27,25,23,orangerWinkel); M(122,26,24,95); L(29,26,122); L(30,29,122); L(31,29,30); Q(28,26,27,ab(122,26,29,30,31,"gedreht"),D); N(32,30,27); M(123,31,29,95.00000000000011); L(34,31,123); M(124,32,27,244.99999999999986); L(35,124,32); Q(33,31,32,ab(123,31,34,"gedreht"),ab(124,32,35,"gedreht")); M(125,34,31,154.99999999999974); L(41,34,125); M(126,35,32,215.00000000000034); L(42,126,35); Q(39,34,35,ab(125,34,41,"gedreht"),ab(126,35,42,"gedreht")); M(127,41,34,95.00000000000016); L(47,41,127); L(48,47,127); L(49,47,48); Q(45,41,42,ab(127,41,47,48,49,"gedreht"),D); M(128,42,35,184.9999999999999); L(88,128,42); Q(50,48,42,D,ab(128,42,88,"gedreht")); M(129,49,47,95.0000000000004); L(52,49,129); L(53,52,129); L(54,52,53); Q(51,49,50,ab(129,49,52,53,54,"gedreht"),D); N(78,27,77); N(79,78,76); N(80,32,79); M(130,42,35,35.0000000000003); L(81,42,130); A(80,42,ab(130,42,81,"gedreht")); M(82,81,42,154.99999999999943); L(86,81,82); L(131,86,82); Q(83,81,75,ab(131,81,82,86,"gedreht"),D); A(79,82); M(87,86,81,275.00000000000057); L(132,86,87); A(88,86,ab(132,86,87,"gedreht")); N(55,87,53); M(133,54,52,94.9999999999983); L(57,54,133); L(58,57,133); L(59,57,58); Q(56,54,55,ab(133,54,57,58,59,"gedreht"),D); N(60,58,55); M(134,59,57,95.00000000000199); L(62,59,134); M(135,62,59,124.99999999999986); L(64,62,135); Q(63,62,134,ab(135,62,64,"gedreht"),D); Q(61,59,60,ab(134,59,62,63,64,"gedreht"),D); M(66,64,62,94.99999999999955); L(67,64,66); L(68,67,66); L(136,67,68); A(69,64,ab(136,64,66,67,68,"gedreht")); N(65,63,60); A(65,66); N(70,71,68); M(84,70,68,214.9999999999997); L(137,84,70); Q(85,70,65,ab(137,70,84,"gedreht"),D); A(83,84); A(74,84); A(85,87); %R(42,80); // oder R(42,81); %R(79,82); %R(86,87); // oder R(86,88); %R(64,66); // oder R(64,67); %R(65,66); %R(83,84); %R(74,84); %R(85,87); % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{LimeGreen}{rgb}{0.20,0.80,0.20} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73205080756887808136/0.00000000000000000000, 2/3.73205080756887808136/0.00000000000000000000, 3/3.23205080756887808136/0.86602540378443859659, 4/4.23205080756887852544/0.86602540378443859659, 5/4.73205080756887852544/0.00000000000000000000, 6/2.73205080756887808136/1.00000000000000000000, 7/3.23205080756887808136/1.86602540378443837454, 8/4.23205080756887852544/1.86602540378443881863, 9/1.86602540378443970681/0.50000000000000011102, 10/1.86602540378443970681/1.50000000000000000000, 11/1.00000000000000111022/1.00000000000000022204, 12/2.36602540378443970681/2.36602540378443837454, 13/1.50000000000000066613/1.86602540378443926272, 14/0.50000000000000055511/1.86602540378443837454, 15/1.00000000000000000000/2.73205080756887763727, 16/0.00000000000000000000/2.73205080756887674909, 17/1.86602540378443904068/3.23205080756887674909, 18/0.86602540378443904068/3.23205080756887630500, 19/0.00000000000000113687/3.73205080756887674909, 20/0.86602540378443959579/4.23205080756887674909, 21/0.00000000000000170530/4.73205080756887674909, 22/1.86602540378443970681/4.23205080756887674909, 23/1.00000000000000177636/4.73205080756887852544, 24/0.49999999999999972244/5.59807621135331512363, 25/1.49999999999999911182/5.59807621135331867634, 26/0.99999999999999633626/6.46410161513775349817, 27/2.36602540378443837454/5.09807621135331956452, 28/1.86602540378443615410/5.96410161513775616271, 29/1.86602540378443393365/6.96410161513775616271, 30/2.73205080756887452864/6.46410161513775705089, 31/2.73205080756887142002/7.46410161513775971542, 32/3.23205080756887674909/5.59807621135331956452, 33/3.23205080756886786730/6.59807621135331956452, 34/3.73205080756887053184/7.46410161513775882725, 35/4.09807621135331157092/6.09807621135332755813, 36/4.73205080756887852544/1.00000000000000000000, 37/5.23205080756887852544/1.86602540378443881863, 38/5.59807621135331689999/0.50000000000000000000, 39/4.59807621135331334727/6.96410161513776504449, 40/6.09807621135331601181/1.36602540378443837454, 41/4.59807621135330535367/7.96410161513776682085, 42/5.09807621135331157092/6.09807621135332489359, 43/6.09807621135331689999/2.36602540378443926272, 44/6.59807621135331601181/0.50000000000000011102, 45/5.09807621135330091278/7.09807621135332489359, 46/6.59807621135331601181/1.50000000000000000000, 47/5.59807621135330535367/7.96410161513776060360, 48/6.09807621135330002460/7.09807621135332045270, 49/6.59807621135330446549/7.96410161513775527453, 50/6.09807621135331157092/6.09807621135332045270, 51/6.59807621135331867634/6.96410161513775527453, 52/7.46410161513775083364/7.46410161513776682085, 53/7.46410161513776415632/6.46410161513776682085, 54/8.33012701892219631361/6.96410161513777925535, 55/6.96410161513775705089/5.59807621135332933449, 56/7.83012701892218743183/6.09807621135334532170, 57/8.83012701892218920818/6.09807621135333377538, 58/8.33012701892217499733/5.23205080756890072990, 59/9.33012701892217677369/5.23205080756888740723, 60/7.46410161513774639275/4.73205080756888474269, 61/8.46410161513774639275/4.73205080756887142002, 62/9.33012701892219098454/4.23205080756888740723, 63/8.46410161513776237996/3.73205080756887186411, 64/9.33012701892221052447/3.23205080756888740723, 65/7.46410161513776326814/3.73205080756888429860, 66/8.33012701892220164268/3.23205080756887541682, 67/8.83012701892219808997/2.36602540378443526592, 68/7.83012701892219720179/2.36602540378443926272, 69/8.33012701892219453725/1.49999999999999866773, 70/6.96410161513775971542/2.86602540378444015090, 71/7.46410161513775527453/1.99999999999999911182, 72/7.46410161513775527453/0.99999999999999966693, 73/3.73205080756887808136/2.73205080756887763727, 74/5.09807621135331689999/2.36602540378443837454, 75/4.23205080756887852544/2.86602540378443926272, 76/3.73205080756887941362/3.73205080756887763727, 77/2.86602540378443970681/3.23205080756887852544, 78/2.86602540378443526592/4.23205080756887941362, 79/3.73205080756887452864/4.73205080756887763727, 80/4.23205080756887674909/5.59807621135331512363, 81/5.09807621135332134088/5.09807621135332311724, 82/4.59807621135331689999/4.23205080756888740723, 83/5.09807621135331245910/3.36602540378444681224, 84/5.96410161513775882725/2.86602540378444547997, 85/6.46410161513776326814/3.73205080756888163407, 86/5.59807621135331601181/4.23205080756888296634, 87/6.46410161513775083364/4.73205080756889273630, 88/5.59807621135330713003/5.23205080756888474269} \coordinate (p-\i) at (\x,\y); %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 7/6, 7/3, 8/7, 8/4, 9/1, 9/6, 10/9, 10/6, 11/9, 11/10, 12/10, 13/11, 13/12, 14/11, 14/13, 15/14, 15/13, 16/14, 16/15, 17/15, 17/12, 18/16, 18/17, 19/16, 19/18, 20/19, 20/18, 21/19, 21/20, 22/20, 22/17, 23/21, 23/22, 24/21, 24/23, 25/24, 25/23, 26/24, 26/25, 27/25, 28/26, 28/27, 29/26, 29/28, 30/29, 30/28, 31/29, 31/30, 32/30, 32/27, 33/31, 33/32, 34/31, 34/33, 35/33, 35/32, 36/8, 36/5, 37/8, 37/36, 38/36, 38/5, 39/34, 39/35, 40/37, 40/38, 41/34, 41/39, 42/39, 42/35, 43/37, 43/40, 44/40, 44/38, 45/41, 45/42, 46/43, 46/44, 47/41, 47/45, 48/47, 48/45, 49/47, 49/48, 50/48, 50/42, 51/49, 51/50, 52/49, 52/51, 53/52, 53/51, 54/52, 54/53, 55/87, 55/53, 56/54, 56/55, 57/54, 57/56, 58/57, 58/56, 59/57, 59/58, 60/58, 60/55, 61/59, 61/60, 62/59, 62/61, 63/62, 63/61, 64/62, 64/63, 65/63, 65/60, 65/66, 66/64, 67/64, 67/66, 68/67, 68/66, 69/71, 69/67, 69/68, 70/71, 70/68, 71/46, 72/69, 72/71, 72/46, 72/44, 73/7, 73/8, 74/8, 74/43, 74/84, 75/8, 75/74, 76/73, 76/75, 77/73, 77/76, 78/27, 78/77, 79/78, 79/76, 79/82, 80/32, 80/79, 80/42, 81/42, 81/80, 82/81, 83/82, 83/86, 83/75, 83/84, 84/70, 85/70, 85/84, 85/65, 85/87, 86/81, 86/82, 87/86, 88/50, 88/42, 88/86, 88/87} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,88} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[LimeGreen,very thick] (p-42) -- (p-80); \draw[LimeGreen,very thick] (p-79) -- (p-82); \draw[LimeGreen,very thick] (p-86) -- (p-87); \draw[LimeGreen,very thick] (p-64) -- (p-66); \draw[LimeGreen,very thick] (p-65) -- (p-66); \draw[LimeGreen,very thick] (p-83) -- (p-84); \draw[LimeGreen,very thick] (p-74) -- (p-84); \draw[LimeGreen,very thick] (p-85) -- (p-87); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/210, 2/330, 3/150, 4/30, 5/330, 6/60, 7/210, 8/240, 9/180, 10/60, 11/270, 12/348, 13/30, 14/270, 15/30, 16/240, 17/318, 18/300, 19/240, 20/60, 21/120, 22/48, 23/330, 24/210, 25/30, 26/180, 27/258, 28/300, 29/120, 30/300, 31/60, 32/240, 33/270, 34/30, 35/210, 36/270, 37/30, 38/360, 39/90, 40/90, 41/60, 42/60, 43/60, 44/330, 45/210, 46/180, 47/150, 48/270, 49/120, 50/30, 51/180, 52/360, 53/240, 54/360, 55/92, 56/210, 57/30, 58/210, 59/60, 60/258, 61/120, 62/60, 63/240, 64/30, 65/318, 66/90, 67/270, 68/210, 69/360, 70/330, 71/120, 72/360, 73/90, 74/360, 75/120, 76/60, 77/180, 78/257, 79/123, 80/180, 81/300, 82/210, 83/270, 84/210, 85/90, 86/240, 87/360, 88/120} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Soll heißen, das Streichholzprogramm hält den Graph für starr, was aber nicht stimmt. Aus irgendeinem Grund kommt bei nochmaligem Button neue Eingabe "wenig Winkel" eine leicht geänderte Eingabereihenfolge heraus, was ja erlaubt ist. Jedoch in der zugehörigen Ableitungsmatrix \sourceon [-1.7453229972375084e-9, -3.760648903394781e-9, -2.0153387847443582e-9], [-2.908885798902361e-9, -2.2370962859952215e-9, 6.717787437438005e-10], [-5.817710757582972e-10, -1.7573775767942834e-9, -1.1756151607755783e-9], [ 0.000027487164666828434, 0.000017865575814846046,-3.781552848636238e-9], [-0.000023807840509260103,-0.000015478709333827112,-5.038305328497472e-10], [-0.00001587414215609151, -0.00001032160139780025, -2.0153323454508154e-9], [ 0.00003968170818802186, 0.00002579868326224588, -7.557414694048248e-10], [-0.000031752590419209525,-0.000020649053289911734,-4.5345052157586e-9] \sourceoff ist es beim besten Willen nicht möglich, die erwartete lineare Abhängigkeit erste minus zweite plus dritte Spalte gleich Null herauszulesen. Die Matrix genauer annähern mit kleineren Winkeländerungen bringt auch keine wesentliche Verbesserung. Das kann nur an einer ungünstigen Eingabevariante des Graphen liegen und man würde bei einem unbekannten Graph zu Recht erstmal "unbeweglich" annehmen. So gesehen ist der Button neue Eingabe "Rahmen zuerst" mit den vielen einzustellenden Winkeln vielleicht doch nicht so verkehrt, weil vom Rand ausgehend die Berechnung der inneren Kanten in relativ wenig Schritten erfolgt.


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StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
Mitteilungen: 4165
Wohnort: Raun
  Beitrag No.1901, eingetragen 2020-02-08

Nächster Graph #1894-1 nächste Programmversion Streichholzgraph-1898.htm mit Testbutton "Newtonpolynom(10)". Der Graph ist bereits als Startbild eingestellt (Graph #1894-1 markieren, ins große Eingabefenster kopieren und Button "neu zeichnen" geht auch). Anschließend Button neue Eingabe "Rahmen zuerst" gefolgt von Button "beweglich?" ergibt $ %Eingabe war: % %#1894-1 % % % % %blauerWinkel=148.95502437185988+(0.1410406669571719)*(neunterWinkel-(104.47751218593004)); %gruenerWinkel=135.52248781407008+(-0.6307535182062247)*(neunterWinkel-(104.47751218593004)); %orangerWinkel=104.47751218592992+(1.0000032572318647)*(neunterWinkel-(104.47751218593004)); %vierterWinkel=75.52248781407012+(-0.6307527345561197)*(neunterWinkel-(104.47751218593004)); %fuenfterWinkel=88.95502437185985+(0.14104184543139073)*(neunterWinkel-(104.47751218593004)); %sechsterWinkel=106.56746344221015+(-0.02057818663278938)*(neunterWinkel-(104.47751218593004)); %siebenterWinkel=148.95502437185982+(0.14103841595938466)*(neunterWinkel-(104.47751218593004)); %achterWinkel=135.52248781406996+(-0.6307501277441359)*(neunterWinkel-(104.47751218593004)); %P[5]=[81.1989530225137,-23.620797303099177]; P[2]=[31.54207889274424,-17.773160886543337]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(8,1,2,blauerWinkel); N(7,8,1); N(9,8,7); N(10,8,9); M(16,10,8,gruenerWinkel); N(15,16,10); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(31,36,35); M(30,31,36,vierterWinkel); N(29,31,30); N(28,29,30); N(22,29,28); M(24,22,29,fuenfterWinkel); N(23,22,24); N(25,23,24); N(26,23,25); M(43,26,23,sechsterWinkel); N(41,26,43); N(42,41,43); N(40,41,42); M(46,40,41,siebenterWinkel); N(45,46,40); N(47,46,45); N(48,46,47); M(53,48,46,achterWinkel); N(52,53,48); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(67,71,70); Q(59,67,5,2*D,2*D); A(59,67); A(59,5); H(60,5,59,2); A(60,5); L(62,5,60); H(65,67,59,2); A(65,67); L(66,65,67); A(65,59); L(64,59,65); A(64,66); A(60,59); L(61,60,59); A(62,61); N(6,3,4); N(11,7,6); N(20,37,17); N(27,25,24); N(32,27,28); N(38,35,20); N(44,42,43); N(49,45,44); N(57,72,54); N(63,62,61); N(68,63,64); N(73,70,57); N(19,20,15); N(56,57,52); N(12,11,6); N(21,20,19); N(33,27,32); N(39,38,20); N(50,49,44); N(58,57,56); N(69,63,68); N(74,73,57); N(13,69,12); N(14,39,21); N(34,33,50); N(51,74,58); %A(14,12); R(14,12,"green"); %A(14,13); R(14,13,"green"); %A(14,33); R(14,33,"green"); %A(34,14); R(34,14,"green"); %A(51,13); R(51,13,"green"); %A(51,50); R(51,50,"green"); %A(51,34); R(51,34,"green"); %A(51,69); R(51,69,"green"); % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LightCyan}{rgb}{0.88,1.00,1.00} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.85122958682191840474/0.23390545666223369614, 2/2.84436706941730799159/0.11695272833111684807, 3/2.44908236189626027368/1.03551138187480851194, 4/3.44221984449164963848/0.91855865354369181652, 5/3.83750455201269735639/0.00000000000000000000, 6/3.04693513697060236467/1.83711730708738363305, 7/1.98627496519078117210/1.22474487139158894067, 8/1.06066017177982319097/0.84627789235802786116, 9/1.19570555014868573629/1.83711730708738318896, 10/0.27009075673772781068/1.45865032805382210945, 11/2.12132034355964416150/2.21558428612094360233, 12/2.91188975860173870913/2.82795672181673873880, 13/3.83750455201268492189/2.44948974278314768327, 14/3.70245917364383281267/3.44032915751253476344, 15/1.06066017177982208075/2.07102276374961702388, 16/0.13504537836886390534/2.44948974278317699316, 17/0.92561479341095842521/3.06186217847897212962, 18/0.00000000000000000000/3.44032915751253165482, 19/1.98627496519077983983/2.44948974278317788134, 20/1.85122958682191640634/3.44032915751253298708, 21/2.77684438023287460950/3.06186217847897301780, 22/1.85122958682191174340/6.64675285836283347152, 23/2.84436706941730133025/6.76370558669395283147, 24/2.44908236189625583279/5.84514693315025990472, 25/3.44221984449164519759/5.96209966148137926467, 26/3.83750455201269069505/6.88065831502507219142, 27/3.04693513697060014422/5.04354100793768633793, 28/1.98627496519077717529/5.65591344363347836577, 29/1.06066017177981830599/6.03438042266703700278, 30/1.19570555014868351584/5.04354100793768278521, 31/0.27009075673772470205/5.42200798697124142222, 32/2.12132034355964282923/4.66507402890412414820, 33/2.91188975860173915322/4.05270159320833123218, 34/3.83750455201269602412/4.43116857224189519826, 35/1.06066017177982030439/4.80963555127544761802, 36/0.13504537836886276736/4.43116857224188631648, 37/0.92561479341095787010/3.81879613654609251228, 38/1.98627496519077850756/4.43116857224188809283, 39/2.77684438023287372133/3.81879613654609428863, 40/5.82377951720347031284/6.64675285836284324148, 41/4.83064203460808005985/6.76370558669395816054, 42/5.22592674212912911003/5.84514693315026701015, 43/4.23278925953373974522/5.96209966148138192921, 44/4.62807396705478879539/5.04354100793769077882, 45/5.68873413883460798957/5.65591344363348724755, 46/6.61434893224556574864/6.03438042266705032546, 47/6.47930355387670431355/5.04354100793769610789, 48/7.40491834728766207263/5.42200798697125740944, 49/5.55368876046574744265/4.66507402890413302998, 50/4.76311934542365467138/4.05270159320833567307, 51/3.97254993038155967966/3.44032915751253964842, 52/6.61434893224556752500/4.80963555127546271706, 53/7.53996372565652528408/4.43116857224190230369, 54/6.74939431061443162463/3.81879613654610761131, 55/7.67500910402539027189/3.44032915751254764203, 56/5.68873413883461065410/4.43116857224189875097, 57/5.82377951720347475373/3.44032915751254364523, 58/4.89816472379251610647/3.81879613654610272633, 59/5.82377951720347475373/0.23390545666225651122, 60/4.83064203460808716528/0.11695272833112821398, 61/5.22592674212912378096/1.03551138187482494324, 62/4.23278925953373530433/0.91855865354369670150, 63/4.62807396705477192000/1.83711730708739295892, 64/5.68873413883461687135/1.22474487139161203331, 65/6.61434893224557374225/0.84627789235804673496, 66/6.47930355387671408351/1.83711730708740250684, 67/7.40491834728767095442/1.45865032805383720849, 68/5.55368876046572612637/2.21558428612096269816, 69/4.76311934542362536149/2.82795672181674939694, 70/6.61434893224557374225/2.07102276374962901428, 71/7.53996372565652972497/2.44948974278319253628, 72/6.74939431061443340099/3.06186217847898456412, 73/5.68873413883461509499/2.44948974278318853948, 74/4.89816472379251877101/3.06186217847898056732} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 55/97.76/202.24/0.4/LightCyan} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 1/3, 2/5, 3/2, 3/4, 4/2, 4/5, 6/3, 6/4, 7/8, 7/1, 8/1, 9/8, 9/7, 10/8, 10/9, 11/7, 11/6, 12/11, 12/6, 13/69, 13/12, 14/39, 14/21, 14/12, 14/13, 14/33, 15/16, 15/10, 16/10, 17/16, 17/15, 18/16, 18/17, 19/20, 19/15, 20/37, 20/17, 21/20, 21/19, 22/29, 22/28, 23/22, 23/24, 24/22, 25/23, 25/24, 26/23, 26/25, 27/25, 27/24, 28/29, 28/30, 29/31, 29/30, 30/31, 31/36, 31/35, 32/27, 32/28, 33/27, 33/32, 34/33, 34/50, 34/14, 35/36, 35/37, 36/18, 36/37, 37/18, 38/35, 38/20, 39/38, 39/20, 40/41, 40/42, 41/26, 41/43, 42/41, 42/43, 43/26, 44/42, 44/43, 45/46, 45/40, 46/40, 47/46, 47/45, 48/46, 48/47, 49/45, 49/44, 50/49, 50/44, 51/74, 51/58, 51/13, 51/50, 51/34, 51/69, 52/53, 52/48, 53/48, 54/53, 54/52, 55/53, 55/54, 56/57, 56/52, 57/72, 57/54, 58/57, 58/56, 60/5, 60/59, 61/60, 61/59, 62/5, 62/60, 62/61, 63/62, 63/61, 64/59, 64/65, 64/66, 65/67, 65/59, 66/65, 66/67, 67/71, 67/70, 68/63, 68/64, 69/63, 69/68, 70/71, 70/72, 71/55, 71/72, 72/55, 73/70, 73/57, 74/73, 74/57} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,74} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-14) -- (p-12); \draw[Green,very thick] (p-14) -- (p-13); \draw[Green,very thick] (p-14) -- (p-33); \draw[Green,very thick] (p-34) -- (p-14); \draw[Green,very thick] (p-51) -- (p-13); \draw[Green,very thick] (p-51) -- (p-50); \draw[Green,very thick] (p-51) -- (p-34); \draw[Green,very thick] (p-51) -- (p-69); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 55/97.76/202.24/0.4/LightCyan} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/292, 2/323, 3/83, 4/23, 5/323, 6/308, 7/52, 8/232, 9/52, 10/172, 11/188, 12/68, 13/232, 14/68, 15/308, 16/128, 17/68, 18/128, 19/248, 20/232, 21/8, 22/68, 23/37, 24/217, 25/37, 26/37, 27/277, 28/308, 29/68, 30/248, 31/188, 32/172, 33/292, 34/52, 35/352, 36/232, 37/352, 38/112, 39/352, 40/23, 41/83, 42/263, 43/263, 44/263, 45/232, 46/52, 47/232, 48/352, 49/8, 50/248, 51/112, 52/128, 53/308, 54/248, 55/308, 56/68, 57/308, 58/188, 59/337, 60/277, 61/97, 62/157, 63/232, 64/128, 65/8, 66/128, 67/8, 68/352, 69/112, 70/172, 71/52, 72/172, 73/292, 74/172} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ mit einem frei beweglichen Winkel, der Graph ist beweglich. Wird dieser Winkel mit Buttons "+1" oder "-1" verstellt, so entstehen recht schnell unpassende Kanten. Die lineare Annäherung der Winkeländerung (aus der Ableitunsmatrix abgekesen) ist zu ungenau. Nach jeder Winkeländerung um +1 müsste der Graph neu zurechtgezogen werden. Das habe ich für 10 Winkeländerungen durchgeführt und die entstehenden Winkeländerungen in Newtonpolynome gepackt. Wer das im Streichholzprogramm selber ausprobieren will, nochmal mit #1894-1 starten, dann Button neue Eingabe "Rahmen zuerst", dann Testbutton "Newtonpolynom(10)" (befindet sich bei den Testfunktionen und -Graphen) und nach etlichen Sekunden wird am Seitenende eine Liste von Newtonpolynomen ausgegeben. Diese in obigen Graph (der nach Button "beweglich?") anstelle der linearen Polynome blauerWinkel=... einsetzen, dann noch die Animationswinkelbereiche und -zeit anpassen (15 s von neunterWinkel+25° bis neunterWinkel-35°) dann Button "neu zeichnen" und man erhält $ %Eingabe war: % %#1894-1 % % % % %blauerWinkel=148.88671009447805+(neunterWinkel-104)/1*((0.1408448774476483)+(neunterWinkel-105)/2*((-0.008544615548174761)+(neunterWinkel-106)/3*((-0.00010376917674648212)+(neunterWinkel-107)/4*((0.00000560396125592888)+(neunterWinkel-108)/5*((3.061999223064049e-7)+(neunterWinkel-109)/6*((-1.3431559864329756e-8)+(neunterWinkel-110)/7*((-1.8478090169082861e-9)+(neunterWinkel-111)/8*((4.780531526193954e-11)+(neunterWinkel-112)/9*((5.6559201766503975e-12)))))))))); %gruenerWinkel=135.82460766621898+(neunterWinkel-104)/1*((-0.6305662265546346)+(neunterWinkel-105)/2*((0.008175628854985462)+(neunterWinkel-106)/3*((0.000047319122813860304)+(neunterWinkel-107)/4*((-0.0000025056787364974298)+(neunterWinkel-108)/5*((-1.4848583873572352e-7)+(neunterWinkel-109)/6*((6.16401507613773e-9)+(neunterWinkel-110)/7*((9.677592061052565e-10)+(neunterWinkel-111)/8*((-5.150013748789206e-11)+(neunterWinkel-112)/9*((6.076561476220377e-11)))))))))); %orangerWinkel=104.00000000000078+(neunterWinkel-104)/1*((1.0000000000006537)+(neunterWinkel-105)/2*((-5.087485988042317e-12)+(neunterWinkel-106)/3*((1.1453948900452815e-11)+(neunterWinkel-107)/4*((-1.6839862837514374e-11)+(neunterWinkel-108)/5*((1.7564616427989677e-11)+(neunterWinkel-109)/6*((-9.15179043659009e-12)+(neunterWinkel-110)/7*((-1.3642420526593924e-11)+(neunterWinkel-111)/8*((5.5862869885459077e-11)+(neunterWinkel-112)/9*((-1.2396128568070708e-10)))))))))); %vierterWinkel=75.82460766621898+(neunterWinkel-104)/1*((-0.6305662265546061)+(neunterWinkel-105)/2*((0.008175628854914407)+(neunterWinkel-106)/3*((0.000047319122970179706)+(neunterWinkel-107)/4*((-0.000002505679034925379)+(neunterWinkel-108)/5*((-1.4848531293409906e-7)+(neunterWinkel-109)/6*((6.163105581435957e-9)+(neunterWinkel-110)/7*((9.693650326880743e-10)+(neunterWinkel-111)/8*((-5.441336270450847e-11)+(neunterWinkel-112)/9*((6.609468528040452e-11)))))))))); %fuenfterWinkel=88.88671009447798+(neunterWinkel-104)/1*((0.1408448774476767)+(neunterWinkel-105)/2*((-0.008544615548217394)+(neunterWinkel-106)/3*((-0.00010376917664700613)+(neunterWinkel-107)/4*((0.000005603961028555204)+(neunterWinkel-108)/5*((3.0620041968631995e-7)+(neunterWinkel-109)/6*((-1.343258304586925e-8)+(neunterWinkel-110)/7*((-1.845833708102873e-9)+(neunterWinkel-111)/8*((4.4224179873708636e-11)+(neunterWinkel-112)/9*((1.1667111721180845e-11)))))))))); %sechsterWinkel=106.57736447860536+(neunterWinkel-104)/1*((-0.02055730178675219)+(neunterWinkel-105)/2*((0.0007379733913097652)+(neunterWinkel-106)/3*((0.00011290009688025293)+(neunterWinkel-107)/4*((-0.000006196548966386217)+(neunterWinkel-108)/5*((-3.1544495016078145e-7)+(neunterWinkel-109)/6*((1.4544255577675358e-8)+(neunterWinkel-110)/7*((1.7711556665744865e-9)+(neunterWinkel-111)/8*((-3.9676706364843994e-11)+(neunterWinkel-112)/9*((-3.133493464702042e-11)))))))))); %siebenterWinkel=148.88671009447785+(neunterWinkel-104)/1*((0.14084487744770513)+(neunterWinkel-105)/2*((-0.008544615547720014)+(neunterWinkel-106)/3*((-0.00010376917805388075)+(neunterWinkel-107)/4*((0.000005603963501243925)+(neunterWinkel-108)/5*((3.06197023292043e-7)+(neunterWinkel-109)/6*((-1.3428717693386716e-8)+(neunterWinkel-110)/7*((-1.8495143194741104e-9)+(neunterWinkel-111)/8*((4.723688107333146e-11)+(neunterWinkel-112)/9*((9.208633855450898e-12)))))))))); %achterWinkel=135.82460766621944+(neunterWinkel-104)/1*((-0.6305662265542082)+(neunterWinkel-105)/2*((0.008175628851887495)+(neunterWinkel-106)/3*((0.000047319129691913986)+(neunterWinkel-107)/4*((-0.00000250568871251744)+(neunterWinkel-108)/5*((-1.484757206071663e-7)+(neunterWinkel-109)/6*((6.159467602628865e-9)+(neunterWinkel-110)/7*((9.578400295140455e-10)+(neunterWinkel-111)/8*((-1.5262457964126952e-11)+(neunterWinkel-112)/9*((-1.6967760529951192e-11)))))))))); %P[5]=[81.1989530225137,-23.620797303099177]; P[2]=[31.54207889274424,-17.773160886543337]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(8,1,2,blauerWinkel); N(7,8,1); N(9,8,7); N(10,8,9); M(16,10,8,gruenerWinkel); N(15,16,10); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(31,36,35); M(30,31,36,vierterWinkel); N(29,31,30); N(28,29,30); N(22,29,28); M(24,22,29,fuenfterWinkel); N(23,22,24); N(25,23,24); N(26,23,25); M(43,26,23,sechsterWinkel); N(41,26,43); N(42,41,43); N(40,41,42); M(46,40,41,siebenterWinkel); N(45,46,40); N(47,46,45); N(48,46,47); M(53,48,46,achterWinkel); N(52,53,48); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(67,71,70); Q(59,67,5,2*D,2*D); A(59,67); A(59,5); H(60,5,59,2); A(60,5); L(62,5,60); H(65,67,59,2); A(65,67); L(66,65,67); A(65,59); L(64,59,65); A(64,66); A(60,59); L(61,60,59); A(62,61); N(6,3,4); N(11,7,6); N(20,37,17); N(27,25,24); N(32,27,28); N(38,35,20); N(44,42,43); N(49,45,44); N(57,72,54); N(63,62,61); N(68,63,64); N(73,70,57); N(19,20,15); N(56,57,52); N(12,11,6); N(21,20,19); N(33,27,32); N(39,38,20); N(50,49,44); N(58,57,56); N(69,63,68); N(74,73,57); N(13,69,12); N(14,39,21); N(34,33,50); N(51,74,58); %A(14,12); R(14,12,"green"); %A(14,13); R(14,13,"green"); %A(14,33); R(14,33,"green"); %A(34,14); R(34,14,"green"); %A(51,13); R(51,13,"green"); %A(51,50); R(51,50,"green"); %A(51,34); R(51,34,"green"); %A(51,69); R(51,69,"green"); % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LightCyan}{rgb}{0.88,1.00,1.00} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.85122958682189819868/0.23390545666223369614, 2/2.84436706941728756348/0.11695272833111684807, 3/2.44908236189623984558/1.03551138187480851194, 4/3.44221984449163009856/0.91855865354369181652, 5/3.83750455201267737237/0.00000000000000000000, 6/3.04693513697058193657/1.83711730708738363305, 7/1.98627496519075608106/1.22474487139158938476, 8/1.06066017177980009834/0.84627789235802408641, 9/1.19570555014865798071/1.83711730708737985829, 10/0.27009075673770166492/1.45865032805381455994, 11/2.12132034355962373340/2.21558428612094360233, 12/2.91188975860171872512/2.82795672181673873880, 13/3.83750455201269602412/2.44948974278322628706, 14/3.70245917364381194048/3.44032915751253076664, 15/1.06066017177980409514/2.07102276374959926031, 16/0.13504537836885083246/2.44948974278317122000, 17/0.92561479341095298512/3.06186217847895569832, 18/0.00000000000000000000/3.44032915751252765801, 19/1.98627496519075696924/2.44948974278317255227, 20/1.85122958682190597024/3.44032915751252899028, 21/2.77684438023285951047/3.06186217847895703059, 22/1.85122958682188731849/6.64675285836283169516, 23/2.84436706941727601716/6.76370558669395638418, 24/2.44908236189623629286/5.84514693315026256926, 25/3.44221984449162521358/5.96209966148138637010, 26/3.83750455201266493788/6.88065831502508196138, 27/3.04693513697058415701/5.04354100793769166700, 28/1.98627496519075075199/5.65591344363347658941, 29/1.06066017177979254882/6.03438042266703700278, 30/1.19570555014865620436/5.04354100793768189703, 31/0.27009075673769800119/5.42200798697124142222, 32/2.12132034355962950656/4.66507402890412414820, 33/2.91188975860172893917/4.05270159320833656125, 34/3.83750455201267914873/4.43116857224191651454, 35/1.06066017177980209674/4.80963555127545827617, 36/0.13504537836884941693/4.43116857224188454012, 37/0.92561479341095276308/3.81879613654610139406, 38/1.98627496519075497083/4.43116857224188542830, 39/2.77684438023285906638/3.81879613654610228224, 40/5.82377951720344544384/6.64675285836285478780, 41/4.83064203460805519086/6.76370558669396881868, 42/5.22592674212910690557/5.84514693315027766829, 43/4.23278925953371576441/5.96209966148139081099, 44/4.62807396705476747911/5.04354100793770232514, 45/5.68873413883458223239/5.65591344363350057023, 46/6.61434893224553910329/6.03438042266705920724, 47/6.47930355387667589184/5.04354100793770410149, 48/7.40491834728763365092/5.42200798697126362669, 49/5.55368876046572612637/4.66507402890414457630, 50/4.76311934542363335510/4.05270159320834721939, 51/3.97254993038151438256/3.44032915751257428738, 52/6.61434893224553288604/4.80963555127547603973, 53/7.53996372565648798059/4.43116857224190940912, 54/6.74939431061438899206/3.81879613654612048990, 55/7.67500910402534497479/3.44032915751255341519, 56/5.68873413883457246243/4.43116857224192006726, 57/5.82377951720342945663/3.44032915751256407333, 58/4.89816472379247436209/3.81879613654613025986, 59/5.82377951720346143105/0.23390545666220380339, 60/4.83064203460806940171/0.11695272833110192945, 61/5.22592674212913177456/1.03551138187478763975, 62/4.23278925953373885704/0.91855865354368582132, 63/4.62807396705480122989/1.83711730708737164264, 64/5.68873413883456446882/1.22474487139155430171, 65/6.61434893224553466240/0.84627789235802430845, 66/6.47930355387663947653/1.83711730708737452922, 67/7.40491834728761055828/1.45865032805384498005, 68/5.55368876046576609440/2.21558428612091784515, 69/4.76311934542367954037/2.82795672181672452794, 70/6.61434893224551689883/2.07102276374964278105, 71/7.53996372565647643427/2.44948974278319964171, 72/6.74939431061438455117/3.06186217847899699862, 73/5.68873413883456180429/2.44948974278320985576, 74/4.89816472379246992119/3.06186217847900854494} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 55/97.76/202.24/0.4/LightCyan} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 1/3, 2/5, 3/2, 3/4, 4/2, 4/5, 6/3, 6/4, 7/8, 7/1, 8/1, 9/8, 9/7, 10/8, 10/9, 11/7, 11/6, 12/11, 12/6, 13/69, 13/12, 14/39, 14/21, 14/12, 14/13, 14/33, 15/16, 15/10, 16/10, 17/16, 17/15, 18/16, 18/17, 19/20, 19/15, 20/37, 20/17, 21/20, 21/19, 22/29, 22/28, 23/22, 23/24, 24/22, 25/23, 25/24, 26/23, 26/25, 27/25, 27/24, 28/29, 28/30, 29/31, 29/30, 30/31, 31/36, 31/35, 32/27, 32/28, 33/27, 33/32, 34/33, 34/50, 34/14, 35/36, 35/37, 36/18, 36/37, 37/18, 38/35, 38/20, 39/38, 39/20, 40/41, 40/42, 41/26, 41/43, 42/41, 42/43, 43/26, 44/42, 44/43, 45/46, 45/40, 46/40, 47/46, 47/45, 48/46, 48/47, 49/45, 49/44, 50/49, 50/44, 51/74, 51/58, 51/13, 51/50, 51/34, 51/69, 52/53, 52/48, 53/48, 54/53, 54/52, 55/53, 55/54, 56/57, 56/52, 57/72, 57/54, 58/57, 58/56, 60/5, 60/59, 61/60, 61/59, 62/5, 62/60, 62/61, 63/62, 63/61, 64/59, 64/65, 64/66, 65/67, 65/59, 66/65, 66/67, 67/71, 67/70, 68/63, 68/64, 69/63, 69/68, 70/71, 70/72, 71/55, 71/72, 72/55, 73/70, 73/57, 74/73, 74/57} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,74} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-14) -- (p-12); \draw[Green,very thick] (p-14) -- (p-13); \draw[Green,very thick] (p-14) -- (p-33); \draw[Green,very thick] (p-34) -- (p-14); \draw[Green,very thick] (p-51) -- (p-13); \draw[Green,very thick] (p-51) -- (p-50); \draw[Green,very thick] (p-51) -- (p-34); \draw[Green,very thick] (p-51) -- (p-69); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 55/97.76/202.24/0.4/LightCyan} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/203, 2/323, 3/83, 4/23, 5/217, 6/83, 7/352, 8/172, 9/112, 10/172, 11/188, 12/188, 13/308, 14/292, 15/308, 16/188, 17/68, 18/128, 19/248, 20/128, 21/8, 22/157, 23/157, 24/157, 25/337, 26/37, 27/277, 28/308, 29/68, 30/308, 31/112, 32/172, 33/292, 34/52, 35/352, 36/112, 37/292, 38/112, 39/352, 40/112, 41/143, 42/23, 43/263, 44/128, 45/232, 46/112, 47/292, 48/68, 49/8, 50/8, 51/112, 52/188, 53/8, 54/188, 55/52, 56/68, 57/52, 58/188, 59/337, 60/337, 61/37, 62/217, 63/232, 64/128, 65/8, 66/128, 67/8, 68/352, 69/352, 70/232, 71/352, 72/172, 73/292, 74/172} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Äußerlich kein Unterschied, nur in der Eingabe sind die Polynome ersetzt. Anstelle der Umformungsschritte kann man den Graph auch von hier aus ins Streichholzprogramm kopieren. Anschließend mit Button "Kanten" die Beschriftung ausschalten und mit Knopf "Start_neunterWinkel" links vom Graph die Animation starten. Button "Newtonpolynom(10)" hat noch viele viele Mängel und ist auch nicht als endgültige Lösung gedacht, deshalb nur Testbutton. Es soll nur ein Test sein, ob das ein halbwegs brauchbares Ergebnis liefert, dass man wenigstens ungefähr die Beweglichkeit im Blick hat und so Kanten zum Um- und Einsetzen suchen kann.


   Profil
StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
Mitteilungen: 4165
Wohnort: Raun
  Beitrag No.1902, eingetragen 2020-02-15

Weitere Newtonpolynome: Im letzten Graph setze ich Kante P9-P11 ein und entferne dafür Kante P4-P6 und ebenso alle dazu symmetrischen Kanten. Dann Button neue Eingabe "Rahmen zuerst" und vor dem Testbutton "Newtonpolynom(10)" setze ich noch blauerWinkel an das Ende der Liste der Winkel, damit dieser als Parameter in den Newtonpolynomen erscheint. neunterWinkel als Parameter ergab kein brauchbares Ergebnis und nach verschiedenen anderen Versuchen habe ich schließlich folgenden Graph erhalten 74 Knoten, 16×Grad 3, 54×Grad 4, 4×Grad 6, 0 Überschneidungen 144 Kanten, minimal 0.99999999999990096811, maximal 1.00000000000010635937 $ %Eingabe war: % %#1902_1a = #1894-1 mit 4 umgelegten Kanten, dann blauerWinkel+10*1 % % % % %gruenerWinkel=135.52248781407005+(blauerWinkel-148.95502437185988)*((-0.13401954390838)+(blauerWinkel-149.95502437185988)*((-0.01563260986196724)+(blauerWinkel-150.95502437185988)*((0.00017091138651418683)+(blauerWinkel-151.95502437185988)*((-0.000001846049790070005)+(blauerWinkel-152.95502437185988)*((2.2553862777385804e-9)+(blauerWinkel-153.95502437185988)*((3.220487580294345e-11)+(blauerWinkel-154.95502437185988)*((-5.102390467712281e-12)+(blauerWinkel-155.95502437185988)*((5.0566958004057103e-14)+(blauerWinkel-156.95502437185988)*((-2.4870562162008914e-15)+(blauerWinkel-157.95502437185988)*((1.4262547123617674e-17))))))))))); %orangerWinkel=104.47751218592991+(blauerWinkel-148.95502437185988)*((0.13357316342579395)+(blauerWinkel-149.95502437185988)*((0.01520338351935635)+(blauerWinkel-150.95502437185988)*((-0.00016144706818484641)+(blauerWinkel-151.95502437185988)*((0.0000021058598237052236)+(blauerWinkel-152.95502437185988)*((-1.0005154749137547e-8)+(blauerWinkel-153.95502437185988)*((2.0668908559974283e-10)+(blauerWinkel-154.95502437185988)*((3.64730327071304e-12)+(blauerWinkel-155.95502437185988)*((-5.0157761548087156e-14)+(blauerWinkel-156.95502437185988)*((4.0883228625250085e-15)+(blauerWinkel-157.95502437185988)*((-3.432488515719872e-17))))))))))); %vierterWinkel=75.52248781407012+(blauerWinkel-148.95502437185988)*((-0.13401954390846527)+(blauerWinkel-149.95502437185988)*((-0.015632609861931712)+(blauerWinkel-150.95502437185988)*((0.00017091138651655532)+(blauerWinkel-151.95502437185988)*((-0.0000018460497977675557)+(blauerWinkel-152.95502437185988)*((2.2553906594196878e-9)+(blauerWinkel-153.95502437185988)*((3.220323760711625e-11)+(blauerWinkel-154.95502437185988)*((-5.101933690271561e-12)+(blauerWinkel-155.95502437185988)*((5.046298475415152e-14)+(blauerWinkel-156.95502437185988)*((-2.465439180228494e-15)+(blauerWinkel-157.95502437185988)*((9.825572171682454e-18))))))))))); %fuenfterWinkel=88.95502437185979+(blauerWinkel-148.95502437185988)*((0.9999999999984368)+(blauerWinkel-149.95502437185988)*((1.8474111129762605e-12)+(blauerWinkel-150.95502437185988)*((-1.0444978215673473e-12)+(blauerWinkel-151.95502437185988)*((3.8487731520338763e-13)+(blauerWinkel-152.95502437185988)*((-1.1013412404281553e-13)+(blauerWinkel-153.95502437185988)*((2.7257208835686063e-14)+(blauerWinkel-154.95502437185988)*((-6.132660516977055e-15)+(blauerWinkel-155.95502437185988)*((1.284686642780538e-15)+(blauerWinkel-156.95502437185988)*((-2.5587997329455987e-16)+(blauerWinkel-157.95502437185988)*((4.881065177752363e-17))))))))))); %sechsterWinkel=106.56746344221033+(blauerWinkel-148.95502437185988)*((-1.8655340756059786)+(blauerWinkel-149.95502437185988)*((0.016061836201068047)+(blauerWinkel-150.95502437185988)*((-0.000180375702915588)+(blauerWinkel-151.95502437185988)*((0.0000015862390672083393)+(blauerWinkel-152.95502437185988)*((5.494573921775703e-9)+(blauerWinkel-153.95502437185988)*((-2.711455159165118e-10)+(blauerWinkel-154.95502437185988)*((6.568025840994326e-12)+(blauerWinkel-155.95502437185988)*((-5.323466533701143e-14)+(blauerWinkel-156.95502437185988)*((1.3469139527593563e-15)+(blauerWinkel-157.95502437185988)*((-8.337050312758024e-17))))))))))); %siebenterWinkel=148.95502437185985+(blauerWinkel-148.95502437185988)*((0.9999999999983515)+(blauerWinkel-149.95502437185988)*((1.9184653865522705e-12)+(blauerWinkel-150.95502437185988)*((-1.0705510552118842e-12)+(blauerWinkel-151.95502437185988)*((3.943512183468556e-13)+(blauerWinkel-152.95502437185988)*((-1.1558161835030962e-13)+(blauerWinkel-153.95502437185988)*((3.0000693287648675e-14)+(blauerWinkel-154.95502437185988)*((-7.156180410155296e-15)+(blauerWinkel-155.95502437185988)*((1.5803936642600644e-15)+(blauerWinkel-156.95502437185988)*((-3.253521301088466e-16)+(blauerWinkel-157.95502437185988)*((6.255627017764463e-17))))))))))); %achterWinkel=135.52248781407008+(blauerWinkel-148.95502437185988)*((-0.13401954390860737)+(blauerWinkel-149.95502437185988)*((-0.015632609861739866)+(blauerWinkel-150.95502437185988)*((0.00017091138641471085)+(blauerWinkel-151.95502437185988)*((-0.0000018460497687537228)+(blauerWinkel-152.95502437185988)*((2.2553872251279913e-9)+(blauerWinkel-153.95502437185988)*((3.220227048003076e-11)+(blauerWinkel-154.95502437185988)*((-5.101200590709603e-12)+(blauerWinkel-155.95502437185988)*((5.0189834646261943e-14)+(blauerWinkel-156.95502437185988)*((-2.3890746299755062e-15)+(blauerWinkel-157.95502437185988)*((-7.675616697290482e-18))))))))))); %neunterWinkel=104.47751218592991+(blauerWinkel-148.95502437185988)*((0.1335731634261208)+(blauerWinkel-149.95502437185988)*((0.015203383518979763)+(blauerWinkel-150.95502437185988)*((-0.0001614470679811575)+(blauerWinkel-151.95502437185988)*((0.000002105859759164254)+(blauerWinkel-152.95502437185988)*((-1.0005143143605743e-8)+(blauerWinkel-153.95502437185988)*((2.0668863164203418e-10)+(blauerWinkel-154.95502437185988)*((3.646880328511662e-12)+(blauerWinkel-155.95502437185988)*((-4.9992461642598194e-14)+(blauerWinkel-156.95502437185988)*((4.048221676833542e-15)+(blauerWinkel-157.95502437185988)*((-2.6508286772677843e-17))))))))))); %P[5]=[81.19895302251417,-23.62079730309884]; P[2]=[31.542078892744694,-17.773160886543025]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(8,1,2,blauerWinkel); N(7,8,1); N(9,8,7); N(10,8,9); M(16,10,8,gruenerWinkel); N(15,16,10); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(31,36,35); M(30,31,36,vierterWinkel); N(29,31,30); N(28,29,30); N(22,29,28); M(24,22,29,fuenfterWinkel); N(23,22,24); N(25,23,24); N(26,23,25); M(43,26,23,sechsterWinkel); N(41,26,43); N(42,41,43); N(40,41,42); M(46,40,41,siebenterWinkel); N(45,46,40); N(47,46,45); N(48,46,47); M(53,48,46,achterWinkel); N(52,53,48); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(67,71,70); Q(59,67,5,2*D,2*D); A(59,67); A(59,5); H(60,5,59,2); A(60,5); L(62,5,60); H(65,67,59,2); A(65,67); L(66,65,67); A(65,59); L(64,59,65); A(64,66); A(60,59); L(61,60,59); A(62,61); N(11,9,7); N(20,37,17); N(32,28,30); N(38,35,20); N(49,47,45); N(57,72,54); N(68,64,66); N(73,70,57); N(6,11,3); N(19,20,15); N(27,24,32); N(44,49,42); N(56,57,52); N(63,61,68); N(12,11,6); N(21,20,19); N(33,27,32); N(39,38,20); N(50,49,44); N(58,57,56); N(69,63,68); N(74,73,57); N(13,69,12); N(14,33,13); N(34,14,50); N(51,69,34); %A(14,39); R(14,39,"green"); %A(14,21); R(14,21,"green"); %A(14,12); R(14,12,"green"); %A(34,33); R(34,33,"green"); %A(51,74); R(51,74,"green"); %A(51,58); R(51,58,"green"); %A(51,13); R(51,13,"green"); %A(51,50); R(51,50,"green"); % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.85/0.23, 2/2.84/0.12, 3/2.45/1.04, 4/3.44/0.92, 5/3.84/0.00, 6/3.05/1.84, 7/1.99/1.22, 8/1.06/0.85, 9/1.20/1.84, 10/0.27/1.46, 11/2.12/2.22, 12/2.91/2.83, 13/3.84/2.45, 14/3.70/3.44, 15/1.06/2.07, 16/0.14/2.45, 17/0.93/3.06, 18/0.00/3.44, 19/1.99/2.45, 20/1.85/3.44, 21/2.78/3.06, 22/1.85/6.65, 23/2.84/6.76, 24/2.45/5.85, 25/3.44/5.96, 26/3.84/6.88, 27/3.05/5.04, 28/1.99/5.66, 29/1.06/6.03, 30/1.20/5.04, 31/0.27/5.42, 32/2.12/4.67, 33/2.91/4.05, 34/3.84/4.43, 35/1.06/4.81, 36/0.14/4.43, 37/0.93/3.82, 38/1.99/4.43, 39/2.78/3.82, 40/5.82/6.65, 41/4.83/6.76, 42/5.23/5.85, 43/4.23/5.96, 44/4.63/5.04, 45/5.69/5.66, 46/6.61/6.03, 47/6.48/5.04, 48/7.40/5.42, 49/5.55/4.67, 50/4.76/4.05, 51/3.97/3.44, 52/6.61/4.81, 53/7.54/4.43, 54/6.75/3.82, 55/7.68/3.44, 56/5.69/4.43, 57/5.82/3.44, 58/4.90/3.82, 59/5.82/0.23, 60/4.83/0.12, 61/5.23/1.04, 62/4.23/0.92, 63/4.63/1.84, 64/5.69/1.22, 65/6.61/0.85, 66/6.48/1.84, 67/7.40/1.46, 68/5.55/2.22, 69/4.76/2.83, 70/6.61/2.07, 71/7.54/2.45, 72/6.75/3.06, 73/5.69/2.45, 74/4.90/3.06} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/353.28/502.24/0.4/Blue} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 1/3, 2/5, 3/2, 3/4, 4/2, 4/5, 6/11, 6/3, 7/8, 7/1, 8/1, 9/8, 9/7, 10/8, 10/9, 11/9, 11/7, 12/11, 12/6, 13/69, 13/12, 14/33, 14/13, 14/39, 14/21, 14/12, 15/16, 15/10, 16/10, 17/16, 17/15, 18/16, 18/17, 19/20, 19/15, 20/37, 20/17, 21/20, 21/19, 22/29, 22/28, 23/22, 23/24, 24/22, 25/23, 25/24, 26/23, 26/25, 27/24, 27/32, 28/29, 28/30, 29/31, 29/30, 30/31, 31/36, 31/35, 32/28, 32/30, 33/27, 33/32, 34/14, 34/50, 34/33, 35/36, 35/37, 36/18, 36/37, 37/18, 38/35, 38/20, 39/38, 39/20, 40/41, 40/42, 41/26, 41/43, 42/41, 42/43, 43/26, 44/49, 44/42, 45/46, 45/40, 46/40, 47/46, 47/45, 48/46, 48/47, 49/47, 49/45, 50/49, 50/44, 51/69, 51/34, 51/74, 51/58, 51/13, 51/50, 52/53, 52/48, 53/48, 54/53, 54/52, 55/53, 55/54, 56/57, 56/52, 57/72, 57/54, 58/57, 58/56, 60/5, 60/59, 61/60, 61/59, 62/5, 62/60, 62/61, 63/61, 63/68, 64/59, 64/65, 64/66, 65/67, 65/59, 66/65, 66/67, 67/71, 67/70, 68/64, 68/66, 69/63, 69/68, 70/71, 70/72, 71/55, 71/72, 72/55, 73/70, 73/57, 74/73, 74/57} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,74} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/353.28/502.24/0.4/Blue} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/203, 2/263, 3/83, 4/23, 5/217, 6/308, 7/292, 8/172, 9/112, 10/172, 11/52, 12/188, 13/232, 14/68, 15/308, 16/248, 17/68, 18/232, 19/248, 20/128, 21/8, 22/68, 23/97, 24/217, 25/277, 26/37, 27/52, 28/68, 29/68, 30/248, 31/112, 32/308, 33/172, 34/128, 35/52, 36/232, 37/352, 38/112, 39/352, 40/112, 41/143, 42/263, 43/263, 44/128, 45/232, 46/52, 47/232, 48/68, 49/8, 50/248, 51/112, 52/188, 53/308, 54/248, 55/52, 56/68, 57/308, 58/188, 59/337, 60/277, 61/37, 62/97, 63/232, 64/128, 65/308, 66/8, 67/292, 68/128, 69/112, 70/172, 71/292, 72/112, 73/292, 74/172} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ [Graph ins große Eingabefenster des Streichholzprogramms kopieren, dann Buttons "neu zeichnen", "Ausrichten", "Kanten" und schließlich Animationsknopf "Start_blauerWinkel" links neben dem Graph"] Zwei Bilder für größeren und kleineren blauerWinkel: $ %Eingabe war: % %#1902_1a = #1894-1 mit 4 umgelegten Kanten, dann blauerWinkel+10*1 % % % % %gruenerWinkel=135.52248781407005+(blauerWinkel-148.95502437185988)*((-0.13401954390838)+(blauerWinkel-149.95502437185988)*((-0.01563260986196724)+(blauerWinkel-150.95502437185988)*((0.00017091138651418683)+(blauerWinkel-151.95502437185988)*((-0.000001846049790070005)+(blauerWinkel-152.95502437185988)*((2.2553862777385804e-9)+(blauerWinkel-153.95502437185988)*((3.220487580294345e-11)+(blauerWinkel-154.95502437185988)*((-5.102390467712281e-12)+(blauerWinkel-155.95502437185988)*((5.0566958004057103e-14)+(blauerWinkel-156.95502437185988)*((-2.4870562162008914e-15)+(blauerWinkel-157.95502437185988)*((1.4262547123617674e-17))))))))))); %orangerWinkel=104.47751218592991+(blauerWinkel-148.95502437185988)*((0.13357316342579395)+(blauerWinkel-149.95502437185988)*((0.01520338351935635)+(blauerWinkel-150.95502437185988)*((-0.00016144706818484641)+(blauerWinkel-151.95502437185988)*((0.0000021058598237052236)+(blauerWinkel-152.95502437185988)*((-1.0005154749137547e-8)+(blauerWinkel-153.95502437185988)*((2.0668908559974283e-10)+(blauerWinkel-154.95502437185988)*((3.64730327071304e-12)+(blauerWinkel-155.95502437185988)*((-5.0157761548087156e-14)+(blauerWinkel-156.95502437185988)*((4.0883228625250085e-15)+(blauerWinkel-157.95502437185988)*((-3.432488515719872e-17))))))))))); %vierterWinkel=75.52248781407012+(blauerWinkel-148.95502437185988)*((-0.13401954390846527)+(blauerWinkel-149.95502437185988)*((-0.015632609861931712)+(blauerWinkel-150.95502437185988)*((0.00017091138651655532)+(blauerWinkel-151.95502437185988)*((-0.0000018460497977675557)+(blauerWinkel-152.95502437185988)*((2.2553906594196878e-9)+(blauerWinkel-153.95502437185988)*((3.220323760711625e-11)+(blauerWinkel-154.95502437185988)*((-5.101933690271561e-12)+(blauerWinkel-155.95502437185988)*((5.046298475415152e-14)+(blauerWinkel-156.95502437185988)*((-2.465439180228494e-15)+(blauerWinkel-157.95502437185988)*((9.825572171682454e-18))))))))))); %fuenfterWinkel=88.95502437185979+(blauerWinkel-148.95502437185988)*((0.9999999999984368)+(blauerWinkel-149.95502437185988)*((1.8474111129762605e-12)+(blauerWinkel-150.95502437185988)*((-1.0444978215673473e-12)+(blauerWinkel-151.95502437185988)*((3.8487731520338763e-13)+(blauerWinkel-152.95502437185988)*((-1.1013412404281553e-13)+(blauerWinkel-153.95502437185988)*((2.7257208835686063e-14)+(blauerWinkel-154.95502437185988)*((-6.132660516977055e-15)+(blauerWinkel-155.95502437185988)*((1.284686642780538e-15)+(blauerWinkel-156.95502437185988)*((-2.5587997329455987e-16)+(blauerWinkel-157.95502437185988)*((4.881065177752363e-17))))))))))); %sechsterWinkel=106.56746344221033+(blauerWinkel-148.95502437185988)*((-1.8655340756059786)+(blauerWinkel-149.95502437185988)*((0.016061836201068047)+(blauerWinkel-150.95502437185988)*((-0.000180375702915588)+(blauerWinkel-151.95502437185988)*((0.0000015862390672083393)+(blauerWinkel-152.95502437185988)*((5.494573921775703e-9)+(blauerWinkel-153.95502437185988)*((-2.711455159165118e-10)+(blauerWinkel-154.95502437185988)*((6.568025840994326e-12)+(blauerWinkel-155.95502437185988)*((-5.323466533701143e-14)+(blauerWinkel-156.95502437185988)*((1.3469139527593563e-15)+(blauerWinkel-157.95502437185988)*((-8.337050312758024e-17))))))))))); %siebenterWinkel=148.95502437185985+(blauerWinkel-148.95502437185988)*((0.9999999999983515)+(blauerWinkel-149.95502437185988)*((1.9184653865522705e-12)+(blauerWinkel-150.95502437185988)*((-1.0705510552118842e-12)+(blauerWinkel-151.95502437185988)*((3.943512183468556e-13)+(blauerWinkel-152.95502437185988)*((-1.1558161835030962e-13)+(blauerWinkel-153.95502437185988)*((3.0000693287648675e-14)+(blauerWinkel-154.95502437185988)*((-7.156180410155296e-15)+(blauerWinkel-155.95502437185988)*((1.5803936642600644e-15)+(blauerWinkel-156.95502437185988)*((-3.253521301088466e-16)+(blauerWinkel-157.95502437185988)*((6.255627017764463e-17))))))))))); %achterWinkel=135.52248781407008+(blauerWinkel-148.95502437185988)*((-0.13401954390860737)+(blauerWinkel-149.95502437185988)*((-0.015632609861739866)+(blauerWinkel-150.95502437185988)*((0.00017091138641471085)+(blauerWinkel-151.95502437185988)*((-0.0000018460497687537228)+(blauerWinkel-152.95502437185988)*((2.2553872251279913e-9)+(blauerWinkel-153.95502437185988)*((3.220227048003076e-11)+(blauerWinkel-154.95502437185988)*((-5.101200590709603e-12)+(blauerWinkel-155.95502437185988)*((5.0189834646261943e-14)+(blauerWinkel-156.95502437185988)*((-2.3890746299755062e-15)+(blauerWinkel-157.95502437185988)*((-7.675616697290482e-18))))))))))); %neunterWinkel=104.47751218592991+(blauerWinkel-148.95502437185988)*((0.1335731634261208)+(blauerWinkel-149.95502437185988)*((0.015203383518979763)+(blauerWinkel-150.95502437185988)*((-0.0001614470679811575)+(blauerWinkel-151.95502437185988)*((0.000002105859759164254)+(blauerWinkel-152.95502437185988)*((-1.0005143143605743e-8)+(blauerWinkel-153.95502437185988)*((2.0668863164203418e-10)+(blauerWinkel-154.95502437185988)*((3.646880328511662e-12)+(blauerWinkel-155.95502437185988)*((-4.9992461642598194e-14)+(blauerWinkel-156.95502437185988)*((4.048221676833542e-15)+(blauerWinkel-157.95502437185988)*((-2.6508286772677843e-17))))))))))); %P[5]=[31.74219649117,-79.36949187458876]; P[2]=[-14.33674095819476,-59.95991888759268]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(8,1,2,blauerWinkel); N(7,8,1); N(9,8,7); N(10,8,9); M(16,10,8,gruenerWinkel); N(15,16,10); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(31,36,35); M(30,31,36,vierterWinkel); N(29,31,30); N(28,29,30); N(22,29,28); M(24,22,29,fuenfterWinkel); N(23,22,24); N(25,23,24); N(26,23,25); M(43,26,23,sechsterWinkel); N(41,26,43); N(42,41,43); N(40,41,42); M(46,40,41,siebenterWinkel); N(45,46,40); N(47,46,45); N(48,46,47); M(53,48,46,achterWinkel); N(52,53,48); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(67,71,70); Q(59,67,5,2*D,2*D); A(59,67); A(59,5); H(60,5,59,2); A(60,5); L(62,5,60); H(65,67,59,2); A(65,67); L(66,65,67); A(65,59); L(64,59,65); A(64,66); A(60,59); L(61,60,59); A(62,61); N(11,9,7); N(20,37,17); N(32,28,30); N(38,35,20); N(49,47,45); N(57,72,54); N(68,64,66); N(73,70,57); N(6,11,3); N(19,20,15); N(27,24,32); N(44,49,42); N(56,57,52); N(63,61,68); N(12,11,6); N(21,20,19); N(33,27,32); N(39,38,20); N(50,49,44); N(58,57,56); N(69,63,68); N(74,73,57); N(13,69,12); N(14,33,13); N(34,14,50); N(51,69,34); %A(14,39); R(14,39,"green"); %A(14,21); R(14,21,"green"); %A(14,12); R(14,12,"green"); %A(34,33); R(34,33,"green"); %A(51,74); R(51,74,"green"); %A(51,58); R(51,58,"green"); %A(51,13); R(51,13,"green"); %A(51,50); R(51,50,"green"); % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.80/0.78, 2/2.72/0.39, 3/2.60/1.38, 4/3.52/0.99, 5/3.64/0.00, 6/2.84/2.35, 7/1.87/1.77, 8/0.97/1.33, 9/1.04/2.33, 10/0.14/1.89, 11/1.93/2.77, 12/2.75/3.35, 13/3.64/2.89, 14/3.594/3.887, 15/0.97/2.45, 16/0.07/2.89, 17/0.90/3.45, 18/0.00/3.89, 19/1.87/2.89, 20/1.80/3.89, 21/2.70/3.45, 22/1.80/7.00, 23/2.72/7.39, 24/2.60/6.39, 25/3.52/6.78, 26/3.64/7.77, 27/2.84/5.42, 28/1.87/6.00, 29/0.97/6.44, 30/1.04/5.44, 31/0.14/5.88, 32/1.93/5.00, 33/2.75/4.43, 34/3.64/4.89, 35/0.97/5.32, 36/0.07/4.88, 37/0.90/4.33, 38/1.87/4.88, 39/2.70/4.33, 40/5.49/7.00, 41/4.56/7.39, 42/4.69/6.39, 43/3.77/6.78, 44/4.44/5.42, 45/5.42/6.00, 46/6.32/6.44, 47/6.25/5.44, 48/7.15/5.88, 49/5.35/5.00, 50/4.53/4.43, 51/3.690/3.887, 52/6.32/5.32, 53/7.21/4.88, 54/6.39/4.33, 55/7.28/3.89, 56/5.42/4.88, 57/5.49/3.89, 58/4.59/4.33, 59/5.49/0.78, 60/4.56/0.39, 61/4.69/1.38, 62/3.77/0.99, 63/4.44/2.35, 64/5.42/1.77, 65/6.32/1.33, 66/6.25/2.33, 67/7.15/1.89, 68/5.35/2.77, 69/4.53/3.35, 70/6.32/2.45, 71/7.21/2.89, 72/6.39/3.45, 73/5.42/2.89, 74/4.59/3.45} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/337.16/506.11/0.4/Blue} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 1/3, 2/5, 3/2, 3/4, 4/2, 4/5, 6/11, 6/3, 7/8, 7/1, 8/1, 9/8, 9/7, 10/8, 10/9, 11/9, 11/7, 12/11, 12/6, 13/69, 13/12, 14/33, 14/13, 14/39, 14/21, 14/12, 15/16, 15/10, 16/10, 17/16, 17/15, 18/16, 18/17, 19/20, 19/15, 20/37, 20/17, 21/20, 21/19, 22/29, 22/28, 23/22, 23/24, 24/22, 25/23, 25/24, 26/23, 26/25, 27/24, 27/32, 28/29, 28/30, 29/31, 29/30, 30/31, 31/36, 31/35, 32/28, 32/30, 33/27, 33/32, 34/14, 34/50, 34/33, 35/36, 35/37, 36/18, 36/37, 37/18, 38/35, 38/20, 39/38, 39/20, 40/41, 40/42, 41/26, 41/43, 42/41, 42/43, 43/26, 44/49, 44/42, 45/46, 45/40, 46/40, 47/46, 47/45, 48/46, 48/47, 49/47, 49/45, 50/49, 50/44, 51/69, 51/34, 51/74, 51/58, 51/13, 51/50, 52/53, 52/48, 53/48, 54/53, 54/52, 55/53, 55/54, 56/57, 56/52, 57/72, 57/54, 58/57, 58/56, 60/5, 60/59, 61/60, 61/59, 62/5, 62/60, 62/61, 63/61, 63/68, 64/59, 64/65, 64/66, 65/67, 65/59, 66/65, 66/67, 67/71, 67/70, 68/64, 68/66, 69/63, 69/68, 70/71, 70/72, 71/55, 71/72, 72/55, 73/70, 73/57, 74/73, 74/57} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,74} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/337.16/506.11/0.4/Blue} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/187, 2/187, 3/127, 4/7, 5/233, 6/305, 7/356, 8/176, 9/116, 10/176, 11/56, 12/65, 13/303, 14/297, 15/4, 16/184, 17/4, 18/124, 19/244, 20/124, 21/4, 22/173, 23/173, 24/293, 25/353, 26/127, 27/55, 28/4, 29/124, 30/184, 31/184, 32/175, 33/295, 34/57, 35/356, 36/116, 37/356, 38/116, 39/356, 40/7, 41/7, 42/307, 43/187, 44/125, 45/116, 46/116, 47/356, 48/64, 49/5, 50/3, 51/243, 52/124, 53/4, 54/184, 55/56, 56/64, 57/56, 58/184, 59/353, 60/353, 61/53, 62/173, 63/235, 64/124, 65/304, 66/124, 67/296, 68/124, 69/357, 70/176, 71/356, 72/116, 73/296, 74/176} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ $ %Eingabe war: % %#1902_1a = #1894-1 mit 4 umgelegten Kanten, dann blauerWinkel+10*1 % % % % %gruenerWinkel=135.52248781407005+(blauerWinkel-148.95502437185988)*((-0.13401954390838)+(blauerWinkel-149.95502437185988)*((-0.01563260986196724)+(blauerWinkel-150.95502437185988)*((0.00017091138651418683)+(blauerWinkel-151.95502437185988)*((-0.000001846049790070005)+(blauerWinkel-152.95502437185988)*((2.2553862777385804e-9)+(blauerWinkel-153.95502437185988)*((3.220487580294345e-11)+(blauerWinkel-154.95502437185988)*((-5.102390467712281e-12)+(blauerWinkel-155.95502437185988)*((5.0566958004057103e-14)+(blauerWinkel-156.95502437185988)*((-2.4870562162008914e-15)+(blauerWinkel-157.95502437185988)*((1.4262547123617674e-17))))))))))); %orangerWinkel=104.47751218592991+(blauerWinkel-148.95502437185988)*((0.13357316342579395)+(blauerWinkel-149.95502437185988)*((0.01520338351935635)+(blauerWinkel-150.95502437185988)*((-0.00016144706818484641)+(blauerWinkel-151.95502437185988)*((0.0000021058598237052236)+(blauerWinkel-152.95502437185988)*((-1.0005154749137547e-8)+(blauerWinkel-153.95502437185988)*((2.0668908559974283e-10)+(blauerWinkel-154.95502437185988)*((3.64730327071304e-12)+(blauerWinkel-155.95502437185988)*((-5.0157761548087156e-14)+(blauerWinkel-156.95502437185988)*((4.0883228625250085e-15)+(blauerWinkel-157.95502437185988)*((-3.432488515719872e-17))))))))))); %vierterWinkel=75.52248781407012+(blauerWinkel-148.95502437185988)*((-0.13401954390846527)+(blauerWinkel-149.95502437185988)*((-0.015632609861931712)+(blauerWinkel-150.95502437185988)*((0.00017091138651655532)+(blauerWinkel-151.95502437185988)*((-0.0000018460497977675557)+(blauerWinkel-152.95502437185988)*((2.2553906594196878e-9)+(blauerWinkel-153.95502437185988)*((3.220323760711625e-11)+(blauerWinkel-154.95502437185988)*((-5.101933690271561e-12)+(blauerWinkel-155.95502437185988)*((5.046298475415152e-14)+(blauerWinkel-156.95502437185988)*((-2.465439180228494e-15)+(blauerWinkel-157.95502437185988)*((9.825572171682454e-18))))))))))); %fuenfterWinkel=88.95502437185979+(blauerWinkel-148.95502437185988)*((0.9999999999984368)+(blauerWinkel-149.95502437185988)*((1.8474111129762605e-12)+(blauerWinkel-150.95502437185988)*((-1.0444978215673473e-12)+(blauerWinkel-151.95502437185988)*((3.8487731520338763e-13)+(blauerWinkel-152.95502437185988)*((-1.1013412404281553e-13)+(blauerWinkel-153.95502437185988)*((2.7257208835686063e-14)+(blauerWinkel-154.95502437185988)*((-6.132660516977055e-15)+(blauerWinkel-155.95502437185988)*((1.284686642780538e-15)+(blauerWinkel-156.95502437185988)*((-2.5587997329455987e-16)+(blauerWinkel-157.95502437185988)*((4.881065177752363e-17))))))))))); %sechsterWinkel=106.56746344221033+(blauerWinkel-148.95502437185988)*((-1.8655340756059786)+(blauerWinkel-149.95502437185988)*((0.016061836201068047)+(blauerWinkel-150.95502437185988)*((-0.000180375702915588)+(blauerWinkel-151.95502437185988)*((0.0000015862390672083393)+(blauerWinkel-152.95502437185988)*((5.494573921775703e-9)+(blauerWinkel-153.95502437185988)*((-2.711455159165118e-10)+(blauerWinkel-154.95502437185988)*((6.568025840994326e-12)+(blauerWinkel-155.95502437185988)*((-5.323466533701143e-14)+(blauerWinkel-156.95502437185988)*((1.3469139527593563e-15)+(blauerWinkel-157.95502437185988)*((-8.337050312758024e-17))))))))))); %siebenterWinkel=148.95502437185985+(blauerWinkel-148.95502437185988)*((0.9999999999983515)+(blauerWinkel-149.95502437185988)*((1.9184653865522705e-12)+(blauerWinkel-150.95502437185988)*((-1.0705510552118842e-12)+(blauerWinkel-151.95502437185988)*((3.943512183468556e-13)+(blauerWinkel-152.95502437185988)*((-1.1558161835030962e-13)+(blauerWinkel-153.95502437185988)*((3.0000693287648675e-14)+(blauerWinkel-154.95502437185988)*((-7.156180410155296e-15)+(blauerWinkel-155.95502437185988)*((1.5803936642600644e-15)+(blauerWinkel-156.95502437185988)*((-3.253521301088466e-16)+(blauerWinkel-157.95502437185988)*((6.255627017764463e-17))))))))))); %achterWinkel=135.52248781407008+(blauerWinkel-148.95502437185988)*((-0.13401954390860737)+(blauerWinkel-149.95502437185988)*((-0.015632609861739866)+(blauerWinkel-150.95502437185988)*((0.00017091138641471085)+(blauerWinkel-151.95502437185988)*((-0.0000018460497687537228)+(blauerWinkel-152.95502437185988)*((2.2553872251279913e-9)+(blauerWinkel-153.95502437185988)*((3.220227048003076e-11)+(blauerWinkel-154.95502437185988)*((-5.101200590709603e-12)+(blauerWinkel-155.95502437185988)*((5.0189834646261943e-14)+(blauerWinkel-156.95502437185988)*((-2.3890746299755062e-15)+(blauerWinkel-157.95502437185988)*((-7.675616697290482e-18))))))))))); %neunterWinkel=104.47751218592991+(blauerWinkel-148.95502437185988)*((0.1335731634261208)+(blauerWinkel-149.95502437185988)*((0.015203383518979763)+(blauerWinkel-150.95502437185988)*((-0.0001614470679811575)+(blauerWinkel-151.95502437185988)*((0.000002105859759164254)+(blauerWinkel-152.95502437185988)*((-1.0005143143605743e-8)+(blauerWinkel-153.95502437185988)*((2.0668863164203418e-10)+(blauerWinkel-154.95502437185988)*((3.646880328511662e-12)+(blauerWinkel-155.95502437185988)*((-4.9992461642598194e-14)+(blauerWinkel-156.95502437185988)*((4.048221676833542e-15)+(blauerWinkel-157.95502437185988)*((-2.6508286772677843e-17))))))))))); %P[5]=[120.71208750145257,-10.495143621012147]; P[2]=[70.81218587654718,-13.657392476614973]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(8,1,2,blauerWinkel); N(7,8,1); N(9,8,7); N(10,8,9); M(16,10,8,gruenerWinkel); N(15,16,10); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(31,36,35); M(30,31,36,vierterWinkel); N(29,31,30); N(28,29,30); N(22,29,28); M(24,22,29,fuenfterWinkel); N(23,22,24); N(25,23,24); N(26,23,25); M(43,26,23,sechsterWinkel); N(41,26,43); N(42,41,43); N(40,41,42); M(46,40,41,siebenterWinkel); N(45,46,40); N(47,46,45); N(48,46,47); M(53,48,46,achterWinkel); N(52,53,48); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(67,71,70); Q(59,67,5,2*D,2*D); A(59,67); A(59,5); H(60,5,59,2); A(60,5); L(62,5,60); H(65,67,59,2); A(65,67); L(66,65,67); A(65,59); L(64,59,65); A(64,66); A(60,59); L(61,60,59); A(62,61); N(11,9,7); N(20,37,17); N(32,28,30); N(38,35,20); N(49,47,45); N(57,72,54); N(68,64,66); N(73,70,57); N(6,11,3); N(19,20,15); N(27,24,32); N(44,49,42); N(56,57,52); N(63,61,68); N(12,11,6); N(21,20,19); N(33,27,32); N(39,38,20); N(50,49,44); N(58,57,56); N(69,63,68); N(74,73,57); N(13,69,12); N(14,33,13); N(34,14,50); N(51,69,34); %A(14,39); R(14,39,"green"); %A(14,21); R(14,21,"green"); %A(14,12); R(14,12,"green"); %A(34,33); R(34,33,"green"); %A(51,74); R(51,74,"green"); %A(51,58); R(51,58,"green"); %A(51,13); R(51,13,"green"); %A(51,50); R(51,50,"green"); % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.85/0.00, 2/2.85/0.06, 3/2.29/0.90, 4/3.29/0.96, 5/3.84/0.13, 6/3.02/1.58, 7/1.98/0.99, 8/1.05/0.61, 9/1.18/1.60, 10/0.26/1.22, 11/2.11/1.98, 12/2.91/2.57, 13/3.84/2.21, 14/3.69/3.20, 15/1.05/1.82, 16/0.13/2.21, 17/0.92/2.82, 18/0.00/3.20, 19/1.98/2.21, 20/1.85/3.20, 21/2.77/2.82, 22/1.85/6.40, 23/2.85/6.33, 24/2.29/5.50, 25/3.29/5.44, 26/3.84/6.27, 27/3.02/4.82, 28/1.98/5.41, 29/1.05/5.79, 30/1.18/4.80, 31/0.26/5.18, 32/2.11/4.41, 33/2.91/3.82, 34/3.84/4.19, 35/1.05/4.57, 36/0.13/4.19, 37/0.92/3.58, 38/1.98/4.19, 39/2.77/3.58, 40/5.84/6.40, 41/4.84/6.33, 42/5.40/5.50, 43/4.40/5.44, 44/4.67/4.82, 45/5.71/5.41, 46/6.63/5.79, 47/6.51/4.80, 48/7.43/5.18, 49/5.58/4.41, 50/4.78/3.82, 51/3.99/3.20, 52/6.64/4.57, 53/7.56/4.19, 54/6.77/3.58, 55/7.69/3.20, 56/5.71/4.19, 57/5.84/3.20, 58/4.92/3.58, 59/5.84/0.00, 60/4.84/0.06, 61/5.40/0.90, 62/4.40/0.96, 63/4.67/1.58, 64/5.71/0.99, 65/6.63/0.61, 66/6.51/1.60, 67/7.43/1.22, 68/5.58/1.98, 69/4.78/2.57, 70/6.64/1.82, 71/7.56/2.21, 72/6.77/2.82, 73/5.71/2.21, 74/4.92/2.82} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/3.63/142.58/0.4/Blue} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 1/3, 2/5, 3/2, 3/4, 4/2, 4/5, 6/11, 6/3, 7/8, 7/1, 8/1, 9/8, 9/7, 10/8, 10/9, 11/9, 11/7, 12/11, 12/6, 13/69, 13/12, 14/33, 14/13, 14/39, 14/21, 14/12, 15/16, 15/10, 16/10, 17/16, 17/15, 18/16, 18/17, 19/20, 19/15, 20/37, 20/17, 21/20, 21/19, 22/29, 22/28, 23/22, 23/24, 24/22, 25/23, 25/24, 26/23, 26/25, 27/24, 27/32, 28/29, 28/30, 29/31, 29/30, 30/31, 31/36, 31/35, 32/28, 32/30, 33/27, 33/32, 34/14, 34/50, 34/33, 35/36, 35/37, 36/18, 36/37, 37/18, 38/35, 38/20, 39/38, 39/20, 40/41, 40/42, 41/26, 41/43, 42/41, 42/43, 43/26, 44/49, 44/42, 45/46, 45/40, 46/40, 47/46, 47/45, 48/46, 48/47, 49/47, 49/45, 50/49, 50/44, 51/69, 51/34, 51/74, 51/58, 51/13, 51/50, 52/53, 52/48, 53/48, 54/53, 54/52, 55/53, 55/54, 56/57, 56/52, 57/72, 57/54, 58/57, 58/56, 60/5, 60/59, 61/60, 61/59, 62/5, 62/60, 62/61, 63/61, 63/68, 64/59, 64/65, 64/66, 65/67, 65/59, 66/65, 66/67, 67/71, 67/70, 68/64, 68/66, 69/63, 69/68, 70/71, 70/72, 71/55, 71/72, 72/55, 73/70, 73/57, 74/73, 74/57} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,74} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/3.63/142.58/0.4/Blue} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/214, 2/334, 3/154, 4/34, 5/334, 6/306, 7/53, 8/173, 9/113, 10/173, 11/53, 12/189, 13/231, 14/69, 15/307, 16/187, 17/67, 18/127, 19/247, 20/233, 21/7, 22/146, 23/146, 24/266, 25/326, 26/154, 27/54, 28/67, 29/67, 30/187, 31/113, 32/307, 33/171, 34/129, 35/353, 36/233, 37/293, 38/113, 39/353, 40/113, 41/154, 42/334, 43/214, 44/126, 45/233, 46/113, 47/353, 48/67, 49/233, 50/246, 51/111, 52/127, 53/67, 54/247, 55/307, 56/67, 57/53, 58/187, 59/247, 60/206, 61/26, 62/86, 63/234, 64/127, 65/307, 66/127, 67/293, 68/127, 69/114, 70/173, 71/293, 72/173, 73/293, 74/173} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Zufällig habe ich dann noch eine Bewegungsmöglichkeit gefunden, bei der der oberste Knoten P26 nach außen und der unterste Knoten P5 nach innen bewegt wird. $ %Eingabe war: % %#1902_1c = #1894-1 mit 4 umgelegten Kanten, dann blauerWinkel=138+10*1 % % % % %gruenerWinkel=134.02217398627073+(blauerWinkel-138)*((0.33863056790141854)+(blauerWinkel-139)*((-0.020425597796361217)+(blauerWinkel-140)*((0.00012591747007206777)+(blauerWinkel-141)*((-1.6782361456080253e-7)+(blauerWinkel-142)*((-5.10587625512926e-9)+(blauerWinkel-143)*((-5.73784378035447e-10)+(blauerWinkel-144)*((1.7203660718255866e-11)+(blauerWinkel-145)*((-1.8288228075388755e-13)+(blauerWinkel-146)*((-2.8274462916897133e-15)+(blauerWinkel-147)*((-1.0871584379996863e-8))))))))))); %orangerWinkel=105.9584582600583+(blauerWinkel-138)*((-0.3354217042569161)+(blauerWinkel-139)*((0.020273471044319535)+(blauerWinkel-140)*((-0.00012750497954291026)+(blauerWinkel-141)*((5.102121741392337e-7)+(blauerWinkel-142)*((-8.54838795305568e-9)+(blauerWinkel-143)*((8.758419767217454e-10)+(blauerWinkel-144)*((-2.0858201938099876e-11)+(blauerWinkel-145)*((1.7920761875748829e-13)+(blauerWinkel-146)*((4.136334622017823e-15)+(blauerWinkel-147)*((1.0964366102717062e-8))))))))))); %vierterWinkel=74.03945099335755+(blauerWinkel-138)*((0.3360019979627964)+(blauerWinkel-139)*((-0.020307756998917625)+(blauerWinkel-140)*((0.00012447453548247722)+(blauerWinkel-141)*((-5.133324603908348e-7)+(blauerWinkel-142)*((9.860567710500534e-9)+(blauerWinkel-143)*((-8.274150352529208e-10)+(blauerWinkel-144)*((1.9842588242755387e-11)+(blauerWinkel-145)*((-1.5015713541300292e-13)+(blauerWinkel-146)*((-4.670925608277748e-15)+(blauerWinkel-147)*((-1.0660105930766685e-8))))))))))); %fuenfterWinkel=97.43016871071936+(blauerWinkel-138)*((-1.1229762192709387)+(blauerWinkel-139)*((0.007160463156708374)+(blauerWinkel-140)*((-0.000012708070556755047)+(blauerWinkel-141)*((-0.0000010831081874348074)+(blauerWinkel-142)*((5.5091601799024e-9)+(blauerWinkel-143)*((3.796474246087483e-10)+(blauerWinkel-144)*((-3.5389032092830534e-12)+(blauerWinkel-145)*((-2.770482256302422e-13)+(blauerWinkel-146)*((1.246617937249165e-14)+(blauerWinkel-147)*((3.2229361552503416e-7))))))))))); %sechsterWinkel=92.05994788126162+(blauerWinkel-138)*((1.8225329525087233)+(blauerWinkel-139)*((0.003217098771855831)+(blauerWinkel-140)*((0.00005680942219044027)+(blauerWinkel-141)*((4.0591844966778903e-7)+(blauerWinkel-142)*((1.76164661525039e-8)+(blauerWinkel-143)*((-3.7049346306947657e-10)+(blauerWinkel-144)*((-4.971467329474287e-12)+(blauerWinkel-145)*((4.764041013444236e-13)+(blauerWinkel-146)*((-1.3956032095490156e-14)+(blauerWinkel-147)*((-6.16767933321335e-7))))))))))); %siebenterWinkel=157.4301687107192+(blauerWinkel-138)*((-1.1229762192706403)+(blauerWinkel-139)*((0.007160463156424157)+(blauerWinkel-140)*((-0.000012708070438331257)+(blauerWinkel-141)*((-0.0000010831082176328741)+(blauerWinkel-142)*((5.509167522177534e-9)+(blauerWinkel-143)*((3.79645273243191e-10)+(blauerWinkel-144)*((-3.53830545109976e-12)+(blauerWinkel-145)*((-2.7718568181449936e-13)+(blauerWinkel-146)*((1.2493944737976288e-14)+(blauerWinkel-147)*((3.222936155195046e-7))))))))))); %achterWinkel=134.03945099335772+(blauerWinkel-138)*((0.33600199796262586)+(blauerWinkel-139)*((-0.02030775699883236)+(blauerWinkel-140)*((0.00012447453548247722)+(blauerWinkel-141)*((-5.133324746016895e-7)+(blauerWinkel-142)*((9.860573631689773e-9)+(blauerWinkel-143)*((-8.274163181772673e-10)+(blauerWinkel-144)*((1.984272922346768e-11)+(blauerWinkel-145)*((-1.5014092263971942e-13)+(blauerWinkel-146)*((-4.685023675967204e-15)+(blauerWinkel-147)*((-1.0660105926090826e-8))))))))))); %neunterWinkel=105.95845826005805+(blauerWinkel-138)*((-0.33542170425687345)+(blauerWinkel-139)*((0.020273471044440328)+(blauerWinkel-140)*((-0.00012750497965186014)+(blauerWinkel-141)*((5.10212214995441e-7)+(blauerWinkel-142)*((-8.548394466364995e-9)+(blauerWinkel-143)*((8.758412859166843e-10)+(blauerWinkel-144)*((-2.0857513952367783e-11)+(blauerWinkel-145)*((1.7898804132962844e-13)+(blauerWinkel-146)*((4.184698833487993e-15)+(blauerWinkel-147)*((1.0964366094332629e-8))))))))))); %P[5]=[113.53195298149822,13.1016955924527]; P[2]=[63.687443166521255,9.161538069629813]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(8,1,2,blauerWinkel); N(7,8,1); N(9,8,7); N(10,8,9); M(16,10,8,gruenerWinkel); N(15,16,10); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(31,36,35); M(30,31,36,vierterWinkel); N(29,31,30); N(28,29,30); N(22,29,28); M(24,22,29,fuenfterWinkel); N(23,22,24); N(25,23,24); N(26,23,25); M(43,26,23,sechsterWinkel); N(41,26,43); N(42,41,43); N(40,41,42); M(46,40,41,siebenterWinkel); N(45,46,40); N(47,46,45); N(48,46,47); M(53,48,46,achterWinkel); N(52,53,48); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(67,71,70); Q(59,67,5,2*D,2*D); A(59,67); A(59,5); H(60,5,59,2); A(60,5); L(62,5,60); H(65,67,59,2); A(65,67); L(66,65,67); A(65,59); L(64,59,65); A(64,66); A(60,59); L(61,60,59); A(62,61); N(11,9,7); N(20,37,17); N(32,28,30); N(38,35,20); N(49,47,45); N(57,72,54); N(68,64,66); N(73,70,57); N(6,11,3); N(19,20,15); N(27,24,32); N(44,49,42); N(56,57,52); N(63,61,68); N(12,11,6); N(21,20,19); N(33,27,32); N(39,38,20); N(50,49,44); N(58,57,56); N(69,63,68); N(74,73,57); N(13,69,12); N(14,33,13); N(34,14,50); N(51,69,34); %A(14,39); R(14,39,"green"); %A(14,21); R(14,21,"green"); %A(14,12); R(14,12,"green"); %A(34,33); R(34,33,"green"); %A(51,74); R(51,74,"green"); %A(51,58); R(51,58,"green"); %A(51,13); R(51,13,"green"); %A(51,50); R(51,50,"green"); % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.81/0.00, 2/2.81/0.08, 3/2.25/0.90, 4/3.24/0.98, 5/3.81/0.16, 6/2.99/1.57, 7/1.95/0.99, 8/1.02/0.61, 9/1.15/1.60, 10/0.23/1.22, 11/2.08/1.98, 12/2.89/2.57, 13/3.81/2.18, 14/3.68/3.17, 15/1.03/1.81, 16/0.11/2.21, 17/0.92/2.81, 18/0.00/3.20, 19/1.96/2.20, 20/1.84/3.19, 21/2.76/2.79, 22/1.87/6.38, 23/2.84/6.62, 24/2.56/5.66, 25/3.53/5.90, 26/3.81/6.86, 27/3.02/4.77, 28/1.98/5.38, 29/1.06/5.78, 30/1.18/4.79, 31/0.26/5.19, 32/2.10/4.39, 33/2.89/3.78, 34/3.81/4.17, 35/1.05/4.58, 36/0.13/4.20, 37/0.92/3.59, 38/1.97/4.18, 39/2.77/3.57, 40/5.75/6.38, 41/4.78/6.62, 42/5.06/5.66, 43/4.08/5.90, 44/4.60/4.77, 45/5.64/5.38, 46/6.55/5.78, 47/6.44/4.79, 48/7.36/5.19, 49/5.52/4.39, 50/4.73/3.78, 51/3.94/3.17, 52/6.56/4.58, 53/7.49/4.20, 54/6.69/3.59, 55/7.62/3.20, 56/5.65/4.18, 57/5.78/3.19, 58/4.85/3.57, 59/5.80/0.00, 60/4.81/0.08, 61/5.37/0.90, 62/4.38/0.98, 63/4.63/1.57, 64/5.67/0.99, 65/6.60/0.61, 66/6.47/1.60, 67/7.39/1.22, 68/5.54/1.98, 69/4.73/2.57, 70/6.59/1.81, 71/7.50/2.21, 72/6.70/2.81, 73/5.66/2.20, 74/4.86/2.79} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/4.52/142.52/0.4/Blue} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 1/3, 2/5, 3/2, 3/4, 4/2, 4/5, 6/11, 6/3, 7/8, 7/1, 8/1, 9/8, 9/7, 10/8, 10/9, 11/9, 11/7, 12/11, 12/6, 13/69, 13/12, 14/33, 14/13, 14/39, 14/21, 14/12, 15/16, 15/10, 16/10, 17/16, 17/15, 18/16, 18/17, 19/20, 19/15, 20/37, 20/17, 21/20, 21/19, 22/29, 22/28, 23/22, 23/24, 24/22, 25/23, 25/24, 26/23, 26/25, 27/24, 27/32, 28/29, 28/30, 29/31, 29/30, 30/31, 31/36, 31/35, 32/28, 32/30, 33/27, 33/32, 34/14, 34/50, 34/33, 35/36, 35/37, 36/18, 36/37, 37/18, 38/35, 38/20, 39/38, 39/20, 40/41, 40/42, 41/26, 41/43, 42/41, 42/43, 43/26, 44/49, 44/42, 45/46, 45/40, 46/40, 47/46, 47/45, 48/46, 48/47, 49/47, 49/45, 50/49, 50/44, 51/69, 51/34, 51/74, 51/58, 51/13, 51/50, 52/53, 52/48, 53/48, 54/53, 54/52, 55/53, 55/54, 56/57, 56/52, 57/72, 57/54, 58/57, 58/56, 60/5, 60/59, 61/60, 61/59, 62/5, 62/60, 62/61, 63/61, 63/68, 64/59, 64/65, 64/66, 65/67, 65/59, 66/65, 66/67, 67/71, 67/70, 68/64, 68/66, 69/63, 69/68, 70/71, 70/72, 71/55, 71/72, 72/55, 73/70, 73/57, 74/73, 74/57} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,74} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/4.52/142.52/0.4/Blue} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/293, 2/335, 3/155, 4/35, 5/335, 6/306, 7/293, 8/293, 9/53, 10/173, 11/53, 12/187, 13/233, 14/67, 15/307, 16/127, 17/7, 18/233, 19/247, 20/127, 21/7, 22/164, 23/164, 24/284, 25/344, 26/136, 27/52, 28/307, 29/187, 30/307, 31/113, 32/307, 33/173, 34/127, 35/353, 36/173, 37/353, 38/113, 39/353, 40/113, 41/76, 42/256, 43/256, 44/128, 45/233, 46/53, 47/353, 48/353, 49/8, 50/248, 51/113, 52/187, 53/307, 54/187, 55/53, 56/67, 57/307, 58/187, 59/325, 60/325, 61/25, 62/145, 63/234, 64/127, 65/7, 66/127, 67/293, 68/127, 69/114, 70/173, 71/353, 72/113, 73/293, 74/173} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ [Ebenfalls Graph ins große Eingabefenster des Streichholzprogramms kopieren, dann Buttons "neu zeichnen", "Ausrichten", "Kanten" und Animationsknopf "Start_blauerWinkel" links neben dem Graph"] Dieses Ergebnis steht scheinbar im Widerspruch zu den Überlegungen mit der Ableitungsmatrix. Danach dürften es keine zwei Bewegungsmöglichkeiten geben. Wenn der Winkel in P5 vergrößert wird, dann darf der Winkel in P26 sich ebenfalls nur in einer Richtung verändern, entweder größer oder kleiner, und nicht in zwei Varianten. Bei dieser Berechnung eine Bewegungsmöglichkeit wegen Rundungsfehler übersehen geht auch nicht, weil das extra GAP-Programm mit exakter Berechnung bestätigt, dass der Graph (vom Anfang des Beitrages) nur einfach statisch unbestimmt ist. \showon GAP-Logfile \sourceon GAP gap> W60:=[[1/2,-1/2*Sqrt(3)],[1/2*Sqrt(3),1/2]]; [ [ 1/2, 1/2*E(12)^7-1/2*E(12)^11 ], [ -1/2*E(12)^7+1/2*E(12)^11, 1/2 ] ] gap> Wbl:=[[1/4,-1/4*Sqrt(15)],[1/4*Sqrt(15),1/4]]*W60^-1; #acos(1/4)_Graph [ [ 1/4*E(5)-1/2*E(5)^2-1/2*E(5)^3+1/4*E(5)^4, -1/4*E(60)^7+1/4*E(60)^23-1/4*E(60)^43+1/4*E(60)^47 ], [ 1/4*E(60)^7-1/4*E(60)^23+1/4*E(60)^43-1/4*E(60)^47, 1/4*E(5)-1/2*E(5)^2-1/2*E(5)^3+1/4*E(5)^4 ] ] gap> P:=[]; [ ] gap> P[1]:=[0,0]; [ 0, 0 ] gap> P[2]:=[1,0]; [ 1, 0 ] gap> P[3]:=P[1]+W60*(P[2]-P[1]);; gap> P[4]:=P[3]+W60*(P[2]-P[3]);; gap> P[5]:=P[2]-(P[1]-P[2]);; gap> P[6]:=P[3]-(P[1]-P[3]);; gap> P[7]:=P[1]+W60*Wbl^-2*(P[3]-P[1]);; gap> P[8]:=P[1]+W60*(P[7]-P[1]);; gap> P[9]:=P[8]+W60*(P[7]-P[8]);; gap> P[10]:=P[8]-(P[1]-P[8]);; gap> P[11]:=P[9]-(P[10]-P[9]);; gap> P[12]:=P[11]+W60*(P[6]-P[11]);; gap> P[13]:=P[12]+W60*(P[6]-P[12]);; gap> P[14]:=P[12]-(P[11]-P[12]);; gap> P[15]:=P[10]+Wbl*(P[9]-P[10]);; gap> P[16]:=P[10]+W60*(P[15]-P[10]);; gap> P[17]:=P[16]+W60*(P[15]-P[16]);; gap> P[18]:=P[16]-(P[10]-P[16]);; gap> P[19]:=P[15]+W60^3*Wbl^-1*(P[10]-P[15]);; gap> P[20]:=P[17]+W60^3*Wbl^-1*(P[16]-P[17]);; gap> P[21]:=P[20]+W60*(P[19]-P[20]);; gap> P[34]:=P[14]+W60^3*Wbl^-1*(P[13]-P[14]);; gap> P[36]:=P[18]+W60^3*Wbl^-1*(P[16]-P[18]);; gap> P[37]:=P[20]-(P[21]-P[20]);; gap> P[38]:=P[20]+W60^3*Wbl^-1*(P[19]-P[20]);; gap> P[39]:=P[20]-(P[17]-P[20]);; gap> P[50]:=P[34]+W60*Wbl*(P[14]-P[34]);; gap> P[51]:=P[50]+W60*(P[34]-P[50]);; gap> P[58]:=P[51]+W60^2*(P[13]-P[51]);; gap> P[69]:=P[51]+W60*(P[13]-P[51]);; gap> P[74]:=P[51]+Wbl*(P[69]-P[51]);; gap> P[31]:=P[36]-(P[18]-P[36]);; gap> P[33]:=P[14]+W60*(P[34]-P[14]);; gap> P[35]:=P[31]+W60*(P[36]-P[31]);; gap> P[49]:=P[50]-(P[51]-P[50]);; gap> P[57]:=P[58]+W60*W60*Wbl*(P[51]-P[58]);; gap> P[63]:=P[69]+W60*(P[13]-P[69]);; gap> P[68]:=P[69]-(P[51]-P[69]);; gap> P[72]:=P[57]-(P[58]-P[57]);; gap> P[73]:=P[57]+W60*(P[74]-P[57]);; gap> P[27]:=P[33]+W60*(P[34]-P[33]);; gap> P[29]:=P[31]+W60*Wbl*(P[35]-P[31]);; gap> P[30]:=P[29]+W60*(P[31]-P[29]);; gap> P[32]:=P[30]-(P[31]-P[30]);; gap> P[44]:=P[50]+W60*(P[49]-P[50]);; gap> P[47]:=P[49]+W60^3*Wbl^-1*(P[50]-P[49]);; gap> P[48]:=P[47]-(P[49]-P[47]);; gap> P[52]:=P[48]+Wbl*(P[47]-P[48]);; gap> P[53]:=P[48]+W60*(P[52]-P[48]);; gap> P[54]:=P[57]-(P[74]-P[57]);; gap> P[55]:=P[53]-(P[48]-P[53]);; gap> P[56]:=P[58]+W60*(P[57]-P[58]);; gap> P[64]:=P[68]+W60*Wbl*(P[63]-P[68]);; gap> P[66]:=P[68]+W60*(P[64]-P[68]);; gap> P[67]:=P[66]-(P[68]-P[66]);; gap> P[71]:=P[55]+W60*(P[72]-P[55]);; gap> P[22]:=P[29]-(P[31]-P[29]);; gap> P[24]:=P[22]+W60^2*Wbl^-2*(P[29]-P[22]);; gap> P[25]:=P[24]+W60*(P[27]-P[24]);; gap> P[28]:=P[22]+W60*(P[29]-P[22]);; gap> P[42]:=P[44]+W60*Wbl*(P[49]-P[44]);; gap> P[45]:=P[49]+W60*(P[47]-P[49]);; gap> P[46]:=P[45]+W60*(P[47]-P[45]);; gap> P[59]:=P[64]-(P[68]-P[64]);; gap> P[60]:=P[59]+W60^2*Wbl^-2*(P[64]-P[59]);; gap> P[61]:=P[60]+W60*(P[59]-P[60]);; gap> P[62]:=P[5]+W60*(P[60]-P[5]);; gap> P[65]:=P[64]+W60*(P[59]-P[64]);; gap> P[70]:=P[67]+W60*(P[71]-P[67]);; gap> P[23]:=P[22]+W60*(P[24]-P[22]);; gap> P[26]:=P[23]-(P[22]-P[23]);; gap> P[40]:=P[42]-(P[44]-P[42]);; gap> P[41]:=P[42]+W60*(P[40]-P[42]);; gap> P[43]:=P[41]+W60*(P[26]-P[41]);; gap> Kante:=[ [1,2],[1,3],[2,5],[2,3], [3,4],[2,4], [4,5],[6,11],[3,6], [7,8],[1,7], [1,8], [8,9], [7,9], [8,10], [9,10], [9,11], [7,11], [11,12], [6,12], [13,69],[12,13], [14,33],[13,14], [14,39],[14,21],[12,14], [15,16],[10,15], [10,16], [16,17], [15,17], [16,18], [17,18], [19,20],[15,19], [20,37],[17,20], [20,21], [19,21], [22,29],[22,28],[22,23], [23,24],[22,24], [23,25], [24,25], [23,26], [25,26], [24,27], [27,32],[28,29],[28,30],[29,31],[29,30],[30,31],[31,36],[31,35],[28,32], [30,32], [27,33], [32,33], [14,34], [34,50],[33,34], [35,36],[35,37],[18,36], [36,37],[18,37], [35,38], [20,38], [38,39], [20,39], [40,41],[40,42],[26,41], [41,43],[41,42], [42,43],[26,43], [44,49],[42,44], [45,46],[40,45], [40,46], [46,47], [45,47], [46,48], [47,48], [47,49], [45,49], [49,50], [44,50], [51,69],[34,51], [51,74],[51,58],[13,51], [50,51], [52,53],[48,52], [48,53], [53,54], [52,54], [53,55], [54,55], [56,57],[52,56], [57,72],[54,57], [57,58], [56,58], [5,60], [59,60], [60,61], [59,61], [5,62], [60,62], [61,62], [61,63], [63,68],[59,64], [64,65],[64,66],[65,67],[59,65], [65,66], [66,67],[67,71],[67,70],[64,68], [66,68], [63,69], [68,69], [70,71],[70,72],[55,71], [71,72],[55,72], [70,73], [57,73], [73,74], [57,74], ];; gap> Size(Kante); 144 gap> RESTKANTEN:=[[14,39],[14,21],[14,12],[34,33],[51,74],[51,58],[51,13],[51,50],];; gap> gap> for K in Kante do Print(" ",(P[K[1]]-P[K[2]])^2); od; 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 gap> gap> PUNKTEZAHL:=Size(P); KOORDINATENZAHL:=2*PUNKTEZAHL; KANTENZAHL:=Size(Kante); 74 148 144 gap> n:=Maximum(KOORDINATENZAHL,KANTENZAHL); A:=NullMat(n,n);; 148 gap> for i in [1..KANTENZAHL] do > A[2*Kante[i][1]-1][i]:=P[Kante[i][2]][1]-P[Kante[i][1]][1]; > A[2*Kante[i][1] ][i]:=P[Kante[i][2]][2]-P[Kante[i][1]][2]; > A[2*Kante[i][2]-1][i]:=P[Kante[i][1]][1]-P[Kante[i][2]][1]; > A[2*Kante[i][2] ][i]:=P[Kante[i][1]][2]-P[Kante[i][2]][2]; > od; gap> Nenner:=Lcm(List(Flat(A),i->DenominatorCyc(i))); 16 gap> A:=Nenner*A;;P:=Nenner*P;; gap> AlterNenner:=1; 1 gap> gap> RankA:=Rank(A); 144 gap> Print("gerechnet_mit_Button=\"",gerechnet_mit_Button,"\";"); gerechnet_mit_Button="acos(1/4)"; gap> Print("Beweglichkeit=",KOORDINATENZAHL-RankA-3); Beweglichkeit=1 gap> Print("Einsetzkanten=",KANTENZAHL-RankA); Einsetzkanten=0 gap> \sourceoff \showoff


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Slash
Aktiv Letzter Besuch: in der letzten Woche
Dabei seit: 23.03.2005
Mitteilungen: 8998
Wohnort: Westerburg
  Beitrag No.1903, vom Themenstarter, eingetragen 2020-02-15

Vielen Dank, Stefan, für die Neuerungen im Programm. :-) Hast du ein paar alte Graphen im Kopf, die wir auf Beweglichkeit noch mal untersuchen sollten?


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StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
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  Beitrag No.1904, eingetragen 2020-02-15

Graph #755 zum Beispiel. Weiterhin, wie die Beweglichkeit von Graphen aussieht, wenn man Kanten herausnimmt, \quoteon(2020-01-20 10:35 - haribo in Beitrag No. 1893) der graph aus #1881 ist also starr, dann kann man ja mal anfangen wieder kreativ zu werden... wenn man 9-19 herausnimmt wie beweglich verhält sich dann die strecke 15-11?, just playing around without target \quoteoff um sie an einer anderen Stelle wieder einzusetzen. Das sozusagen "with target" ausprobieren. Im Moment ist das aber alles nur Test von verschiedenen Programmfunktionen, ob dieses Ziel irgendwie erreichbar ist.


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StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
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Wohnort: Raun
  Beitrag No.1905, eingetragen 2020-02-15

\quoteon(2020-02-15 05:55 - StefanVogel in Beitrag No. 1902) Dieses Ergebnis steht scheinbar im Widerspruch zu den Überlegungen mit der Ableitungsmatrix. Danach dürften es keine zwei Bewegungsmöglichkeiten geben. Wenn der Winkel in P5 vergrößert wird, dann darf der Winkel in P26 sich ebenfalls nur in einer Richtung verändern, entweder größer oder kleiner, und nicht in zwei Varianten. \quoteoff Das ist auch der Fall. Wenn ich in Graph #1902-1+Button neue Eingabe "Rahmen zuerst" den Winkel blauerWinkel bei P1 in kleinsten Schritten von hundertstel, tausendstel, zehntausendstel Grad verringere von anfangs 148.9550° auf 147.4139° und dabei den Graph mit den übrigen Winkeln wieder zurechtziehe (Button "Feinjustieren(8,8)"), dann folgt fuenfterWinkel bei P22 ebenfalls von 88.9550° bis 87.4143°. Im Bild kaum erkennbar diese Veränderung $ %Eingabe war: % %#1905 = #1902 mit blauerWinkel=147.4139 % % % % % % % % % % % % %P[5]=[85.60885137359465,-18.74297846541552]; P[2]=[35.81828675525811,-14.171362231821632]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(8,1,2,blauerWinkel); N(7,8,1); N(9,8,7); N(10,8,9); M(16,10,8,gruenerWinkel); N(15,16,10); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(31,36,35); M(30,31,36,vierterWinkel); N(29,31,30); N(28,29,30); N(22,29,28); M(24,22,29,fuenfterWinkel); N(23,22,24); N(25,23,24); N(26,23,25); M(43,26,23,sechsterWinkel); N(41,26,43); N(42,41,43); N(40,41,42); M(46,40,41,siebenterWinkel); N(45,46,40); N(47,46,45); N(48,46,47); M(53,48,46,achterWinkel); N(52,53,48); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(67,71,70); Q(59,67,5,2*D,2*D); A(59,67); A(59,5); H(60,5,59,2); A(60,5); L(62,5,60); H(65,67,59,2); A(65,67); L(66,65,67); A(65,59); L(64,59,65); A(64,66); A(60,59); L(61,60,59); A(62,61); N(11,9,7); N(20,37,17); N(32,28,30); N(38,35,20); N(49,47,45); N(57,72,54); N(68,64,66); N(73,70,57); N(6,11,3); N(19,20,15); N(27,24,32); N(44,49,42); N(56,57,52); N(63,61,68); N(12,11,6); N(21,20,19); N(33,27,32); N(39,38,20); N(50,49,44); N(58,57,56); N(69,63,68); N(74,73,57); N(13,69,12); N(14,33,13); N(34,14,50); N(51,69,34); %A(14,39); R(14,39,"green"); %A(14,21); R(14,21,"green"); %A(14,12); R(14,12,"green"); %A(34,33); R(34,33,"green"); %A(51,74); R(51,74,"green"); %A(51,58); R(51,58,"green"); %A(51,13); R(51,13,"green"); %A(51,50); R(51,50,"green"); % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LightBlue}{rgb}{0.68,0.84,0.90} \definecolor{LightCoral}{rgb}{0.94,0.50,0.50} \definecolor{LightCyan}{rgb}{0.88,1.00,1.00} \definecolor{Lime}{rgb}{0.00,1.00,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.85/0.18, 2/2.85/0.09, 3/2.43/1.00, 4/3.43/0.91, 5/3.84/0.00, 6/3.05/1.78, 7/1.99/1.17, 8/1.06/0.80, 9/1.20/1.79, 10/0.27/1.41, 11/2.12/2.16, 12/2.92/2.78, 13/3.84/2.40, 14/3.70/3.39, 15/1.06/2.02, 16/0.14/2.40, 17/0.93/3.01, 18/0.00/3.39, 19/1.99/2.40, 20/1.85/3.39, 21/2.78/3.01, 22/1.85/6.60, 23/2.85/6.69, 24/2.43/5.78, 25/3.43/5.87, 26/3.84/6.78, 27/3.05/5.00, 28/1.99/5.61, 29/1.06/5.99, 30/1.20/4.99, 31/0.27/5.37, 32/2.12/4.62, 33/2.92/4.01, 34/3.84/4.38, 35/1.06/4.76, 36/0.14/4.38, 37/0.93/3.77, 38/1.99/4.38, 39/2.78/3.77, 40/5.84/6.60, 41/4.84/6.69, 42/5.26/5.78, 43/4.26/5.87, 44/4.64/5.00, 45/5.70/5.61, 46/6.63/5.99, 47/6.49/4.99, 48/7.42/5.37, 49/5.56/4.62, 50/4.77/4.01, 51/3.98/3.39, 52/6.63/4.76, 53/7.55/4.38, 54/6.76/3.77, 55/7.69/3.39, 56/5.70/4.38, 57/5.84/3.39, 58/4.91/3.77, 59/5.84/0.18, 60/4.84/0.09, 61/5.26/1.00, 62/4.26/0.91, 63/4.64/1.78, 64/5.70/1.17, 65/6.63/0.80, 66/6.49/1.79, 67/7.42/1.41, 68/5.56/2.16, 69/4.77/2.78, 70/6.63/2.02, 71/7.55/2.40, 72/6.76/3.01, 73/5.70/2.40, 74/4.91/3.01} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/354.75/502.17/0.4/Blue, 10/322.17/457.83/0.4/Green, 18/277.83/382.17/0.4/Orange, 31/262.17/337.83/0.4/Violet, 22/217.83/305.25/0.4/Teal, 26/185.25/294.75/0.4/Lime, 40/174.75/322.17/0.4/LightBlue, 48/142.17/277.83/0.4/LightCoral, 55/97.83/202.17/0.4/LightCyan} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 1/3, 2/5, 3/2, 3/4, 4/2, 4/5, 6/11, 6/3, 7/8, 7/1, 8/1, 9/8, 9/7, 10/8, 10/9, 11/9, 11/7, 12/11, 12/6, 13/69, 13/12, 14/33, 14/13, 14/39, 14/21, 14/12, 15/16, 15/10, 16/10, 17/16, 17/15, 18/16, 18/17, 19/20, 19/15, 20/37, 20/17, 21/20, 21/19, 22/29, 22/28, 23/22, 23/24, 24/22, 25/23, 25/24, 26/23, 26/25, 27/24, 27/32, 28/29, 28/30, 29/31, 29/30, 30/31, 31/36, 31/35, 32/28, 32/30, 33/27, 33/32, 34/14, 34/50, 34/33, 35/36, 35/37, 36/18, 36/37, 37/18, 38/35, 38/20, 39/38, 39/20, 40/41, 40/42, 41/26, 41/43, 42/41, 42/43, 43/26, 44/49, 44/42, 45/46, 45/40, 46/40, 47/46, 47/45, 48/46, 48/47, 49/47, 49/45, 50/49, 50/44, 51/69, 51/34, 51/74, 51/58, 51/13, 51/50, 52/53, 52/48, 53/48, 54/53, 54/52, 55/53, 55/54, 56/57, 56/52, 57/72, 57/54, 58/57, 58/56, 60/5, 60/59, 61/60, 61/59, 62/5, 62/60, 62/61, 63/61, 63/68, 64/59, 64/65, 64/66, 65/67, 65/59, 66/65, 66/67, 67/71, 67/70, 68/64, 68/66, 69/63, 69/68, 70/71, 70/72, 71/55, 71/72, 72/55, 73/70, 73/57, 74/73, 74/57} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,74} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-14) -- (p-39); \draw[Green,very thick] (p-14) -- (p-21); \draw[Green,very thick] (p-14) -- (p-12); \draw[Green,very thick] (p-34) -- (p-33); \draw[Green,very thick] (p-51) -- (p-74); \draw[Green,very thick] (p-51) -- (p-58); \draw[Green,very thick] (p-51) -- (p-13); \draw[Green,very thick] (p-51) -- (p-50); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/354.75/502.17/0.4/Blue, 10/322.17/457.83/0.4/Green, 18/277.83/382.17/0.4/Orange, 31/262.17/337.83/0.4/Violet, 22/217.83/305.25/0.4/Teal, 26/185.25/294.75/0.4/Lime, 40/174.75/322.17/0.4/LightBlue, 48/142.17/277.83/0.4/LightCoral, 55/97.83/202.17/0.4/LightCyan} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/205, 2/265, 3/85, 4/25, 5/215, 6/308, 7/292, 8/172, 9/112, 10/172, 11/188, 12/188, 13/232, 14/68, 15/8, 16/128, 17/8, 18/128, 19/248, 20/128, 21/8, 22/68, 23/95, 24/275, 25/335, 26/145, 27/52, 28/68, 29/68, 30/248, 31/188, 32/172, 33/172, 34/128, 35/352, 36/112, 37/292, 38/112, 39/352, 40/25, 41/25, 42/325, 43/205, 44/128, 45/172, 46/352, 47/232, 48/352, 49/232, 50/248, 51/112, 52/128, 53/8, 54/248, 55/52, 56/68, 57/52, 58/188, 59/335, 60/215, 61/35, 62/155, 63/232, 64/188, 65/308, 66/68, 67/8, 68/128, 69/112, 70/232, 71/52, 72/112, 73/292, 74/172} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Jetzt aber ergänzt Button "beweglich?" im Eingabefenster zwei unabhängige Winkel \sourceon gruenerWinkel=135.66530615863013+(-0.033776036047640026)*(fuenfterWinkel-(87.41434922655961))+(-0.0331132232416488)*(blauerWinkel-(147.4139)); orangerWinkel=104.33358940119679+(0.034172632982445765)*(fuenfterWinkel-(87.41434922655961))+(0.034164299479931014)*(blauerWinkel-(147.4139)); vierterWinkel=75.66530645296255+(-0.03312054920773207)*(fuenfterWinkel-(87.41434922655961))+(-0.03376868777536805)*(blauerWinkel-(147.4139)); sechsterWinkel=109.50712358893763+(-1.9137335482983882)*(fuenfterWinkel-(87.41434922655961))+(-0.020829460731078855)*(blauerWinkel-(147.4139)); siebenterWinkel=147.4143492265599+(1.0000094146143543)*(fuenfterWinkel-(87.41434922655961))+(0.0000040969209810061676)*(blauerWinkel-(147.4139)); achterWinkel=135.66530645296234+(-0.03312027244076022)*(fuenfterWinkel-(87.41434922655961))+(-0.03377047835281289)*(blauerWinkel-(147.4139)); neunterWinkel=104.33358940119686+(0.034165760083019706)*(fuenfterWinkel-(87.41434922655961))+(0.03416248513839332)*(blauerWinkel-(147.4139)); \sourceoff Das kann ich als Hinweis auffassen, dass in unmittelbarer Nähe ein Kreuzungspunkt zweier verschiedener Bewegungsmöglichkeiten liegt und die Überlegung mit der Ableitungsmatrix ist vorerst gerettet.


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  Beitrag No.1906, eingetragen 2020-02-19

\quoteon(2020-02-01 06:22 - StefanVogel in Beitrag No. 1900) Nach Button neue Eingabe "egal wie" 88 Knoten, 4×Grad 3, 80×Grad 4, 2×Grad 5, 2×Grad 7, 0 Überschneidungen 178 Kanten, minimal 0.99999999999960431651, maximal 1.00000000000029243274 $ %Eingabe war: % %Automatisch generierte Eingabe zu: #1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78); nach Button neue Eingabe "egal wie" % % % % % % %P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(38,5,4,blauerWinkel); N(36,5,38); N(8,4,36); N(37,8,36); N(40,37,38); N(43,37,40); N(44,40,38); N(46,43,44); N(72,46,44); N(74,8,43); N(75,8,74); N(7,3,8); N(71,46,72); N(73,7,8); N(76,73,75); N(77,73,76); N(6,1,7); N(9,1,6); N(10,9,6); N(11,9,10); N(69,71,72); M(84,74,8,gruenerWinkel); N(70,84,71); N(83,75,84); N(85,84,70); N(68,70,69); N(67,68,69); N(66,68,67); N(64,66,67); N(65,85,66); N(63,65,64); N(62,63,64); N(61,63,62); N(59,61,62); N(60,65,61); N(58,60,59); N(57,58,59); N(56,58,57); N(54,56,57); N(55,60,56); N(87,85,55); N(53,55,54); N(86,83,87); N(88,86,87); N(52,53,54); N(82,83,86); N(51,53,52); N(79,76,82); N(81,82,86); N(42,81,88); N(49,51,52); N(50,51,42); N(78,77,79); N(80,79,42); N(48,50,49); N(45,42,48); N(47,45,48); N(41,45,47); N(39,42,41); N(34,39,41); N(35,42,39); N(32,80,35); N(33,32,34); N(27,78,32); N(31,33,34); N(30,32,31); N(28,27,30); N(29,28,30); N(26,28,29); N(25,27,26); N(24,25,26); N(23,25,24); N(21,23,24); M(22,23,25,orangerWinkel); N(20,22,21); N(19,20,21); N(18,20,19); N(16,18,19); N(17,22,18); N(12,17,10); N(13,11,12); N(14,11,13); N(15,14,13); %A(50,88); R(50,88,"green"); %A(80,81); R(80,81,"green"); %A(47,49); R(47,49,"green"); %A(33,35); R(33,35,"green"); %A(29,31); R(29,31,"green"); %A(14,16); R(14,16,"green"); %A(15,16); R(15,16,"green"); %A(15,17); R(15,17,"green"); % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/3.23/1.87, 8/4.23/1.87, 9/1.87/0.50, 10/1.87/1.50, 11/1.00/1.00, 12/2.37/2.37, 13/1.50/1.87, 14/0.50/1.87, 15/1.00/2.73, 16/0.00/2.73, 17/1.87/3.23, 18/0.87/3.23, 19/0.00/3.73, 20/0.87/4.23, 21/0.00/4.73, 22/1.87/4.23, 23/1.00/4.73, 24/0.50/5.60, 25/1.50/5.60, 26/1.00/6.46, 27/2.37/5.10, 28/1.87/5.96, 29/1.87/6.96, 30/2.73/6.46, 31/2.73/7.46, 32/3.23/5.60, 33/3.23/6.60, 34/3.73/7.46, 35/4.10/6.10, 36/4.73/1.00, 37/5.23/1.87, 38/5.60/0.50, 39/4.60/6.96, 40/6.10/1.37, 41/4.60/7.96, 42/5.10/6.10, 43/6.10/2.37, 44/6.60/0.50, 45/5.10/7.10, 46/6.60/1.50, 47/5.60/7.96, 48/6.10/7.10, 49/6.60/7.96, 50/6.10/6.10, 51/6.60/6.96, 52/7.46/7.46, 53/7.46/6.46, 54/8.33/6.96, 55/6.96/5.60, 56/7.83/6.10, 57/8.83/6.10, 58/8.33/5.23, 59/9.33/5.23, 60/7.46/4.73, 61/8.46/4.73, 62/9.33/4.23, 63/8.46/3.73, 64/9.33/3.23, 65/7.46/3.73, 66/8.33/3.23, 67/8.83/2.37, 68/7.83/2.37, 69/8.33/1.50, 70/6.96/2.87, 71/7.46/2.00, 72/7.46/1.00, 73/3.73/2.73, 74/5.10/2.37, 75/4.23/2.87, 76/3.73/3.73, 77/2.87/3.23, 78/2.87/4.23, 79/3.73/4.73, 80/4.23/5.60, 81/5.10/5.10, 82/4.60/4.23, 83/5.10/3.37, 84/5.96/2.87, 85/6.46/3.73, 86/5.60/4.23, 87/6.46/4.73, 88/5.60/5.23} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 5/120.00/390.00/0.4/Blue, 74/210.00/390.00/0.4/Green, 23/60.00/330.00/0.4/Orange} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 6/7, 7/3, 7/8, 8/4, 8/36, 9/1, 9/6, 10/9, 10/6, 11/9, 11/10, 12/17, 12/10, 13/11, 13/12, 14/11, 14/13, 14/16, 15/14, 15/13, 15/16, 15/17, 16/18, 16/19, 17/22, 17/18, 18/20, 18/19, 19/20, 19/21, 20/22, 20/21, 21/23, 21/24, 22/23, 23/25, 23/24, 24/25, 24/26, 25/27, 25/26, 26/28, 26/29, 27/78, 27/32, 28/27, 28/30, 29/28, 29/30, 29/31, 30/32, 30/31, 31/33, 31/34, 32/80, 32/35, 33/32, 33/34, 33/35, 34/39, 34/41, 35/42, 35/39, 36/5, 36/38, 37/8, 37/36, 38/5, 39/42, 39/41, 40/37, 40/38, 41/45, 41/47, 42/81, 42/88, 43/37, 43/40, 44/40, 44/38, 45/42, 45/48, 46/43, 46/44, 47/45, 47/48, 47/49, 48/50, 48/49, 49/51, 49/52, 50/51, 50/42, 50/88, 51/53, 51/52, 52/53, 52/54, 53/55, 53/54, 54/56, 54/57, 55/60, 55/56, 56/58, 56/57, 57/58, 57/59, 58/60, 58/59, 59/61, 59/62, 60/65, 60/61, 61/63, 61/62, 62/63, 62/64, 63/65, 63/64, 64/66, 64/67, 65/85, 65/66, 66/68, 66/67, 67/68, 67/69, 68/70, 68/69, 69/71, 69/72, 70/84, 70/71, 71/46, 71/72, 72/46, 72/44, 73/7, 73/8, 74/8, 74/43, 75/8, 75/74, 76/73, 76/75, 77/73, 77/76, 78/77, 78/79, 79/76, 79/82, 80/79, 80/42, 80/81, 81/82, 81/86, 82/83, 82/86, 83/75, 83/84, 84/74, 85/84, 85/70, 86/83, 86/87, 87/85, 87/55, 88/86, 88/87} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,88} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-50) -- (p-88); \draw[Green,very thick] (p-80) -- (p-81); \draw[Green,very thick] (p-47) -- (p-49); \draw[Green,very thick] (p-33) -- (p-35); \draw[Green,very thick] (p-29) -- (p-31); \draw[Green,very thick] (p-14) -- (p-16); \draw[Green,very thick] (p-15) -- (p-16); \draw[Green,very thick] (p-15) -- (p-17); \draw[red,very thick] (p-34) -- (p-38); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 5/120.00/390.00/0.4/Blue, 74/210.00/390.00/0.4/Green, 23/60.00/330.00/0.4/Orange} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/210, 2/330, 3/150, 4/30, 5/330, 6/360, 7/210, 8/330, 9/180, 10/60, 11/180, 12/347, 13/30, 14/270, 15/30, 16/240, 17/77, 18/300, 19/120, 20/60, 21/120, 22/48, 23/330, 24/210, 25/30, 26/90, 27/167, 28/240, 29/180, 30/360, 31/60, 32/240, 33/270, 34/30, 35/210, 36/120, 37/30, 38/360, 39/300, 40/90, 41/60, 42/60, 43/60, 44/240, 45/270, 46/180, 47/30, 48/270, 49/120, 50/30, 51/240, 52/60, 53/240, 54/360, 55/93, 56/210, 57/330, 58/210, 59/60, 60/137, 61/120, 62/360, 63/180, 64/300, 65/227, 66/90, 67/270, 68/150, 69/360, 70/330, 71/60, 72/360, 73/300, 74/360, 75/120, 76/60, 77/180, 78/257, 79/62, 80/180, 81/90, 82/150, 83/270, 84/210, 85/90, 86/240, 87/360, 88/270} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ \quoteoff hallo stefan, mir ist es gelungen in deine zeichnung die rote linie von 34-38 einzufügen, darauf bin ich schonmal stolz ich hab mal wieder versucht mit deinem komplexen streichholzprogram herumzuspielen und obige zeichnung, bzw #1892-1 als grundlage genommen... und deinen oben beschriebenen weg bis zur eingabe "egal wie" nachzuvollziehen, erfolg diesmal gar nicht so schlecht, d.h. es zerknüllt meist erst nach mehreren minuten... ansich wollte ich dann folgende eingaben machen: [Z(82,86);A(34,38)] und irgendwie herausbekommen ob die beweglichkeit der rechten hälfte ausreicht um einen daraus gespiegelten 4/7er herzustellen... also ungefähr so wie hier im png händisch hergestellt, müsste man in der mitte auseinanderdrücken bis noch ein holz dazwischen passt... https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/35059_1892-test.png nun das bedeutet wohl das man neu eingeben muss??? oder hat man irgendwie eine chance mit "Z" sehr viel, also weitgehend all die inneren linken linien, herauszulöschen und wieder neue dazuzufügen? die zweite wichtige frage ist, was muss ich machen um irgendwie, also derzeit meist nur zufällig, hergestellte zwischenlösungen abzuspeichern, damit ich sie danach gesichert wieder aufrufen/herstellen kann reicht es wenn ich zum speichern alles zwischen .... als text in ein word dokument schreibe, oder brauch ich dann dazu weitere winkeleinstellungen oder ähnliches? lg haribo


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haribo
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 25.10.2012
Mitteilungen: 3872
  Beitrag No.1907, eingetragen 2020-02-19

händisch geht es wohl immer einfacher für mich, ist wohl auch noch ein falscher fünfer drin https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/35059_1892-test1.png aber es ging mir diesmal wirklich drum es mit dem program zu versuchen... zu nem etwas erstaunlich unsymetrischen 4/7er mit 177 hölzern konnte ich es noch retten, sofern ich nichts übersehen habe das dürfte immerhin mein persönlicher 4/7 rekord sein https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/35059_st4-7-177.png


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Slash
Aktiv Letzter Besuch: in der letzten Woche
Dabei seit: 23.03.2005
Mitteilungen: 8998
Wohnort: Westerburg
  Beitrag No.1908, vom Themenstarter, eingetragen 2020-02-19

\quoteon(2020-02-19 14:15 - haribo in Beitrag No. 1906) reicht es wenn ich zum speichern alles zwischen .... als text in ein word dokument schreibe, oder brauch ich dann dazu weitere winkeleinstellungen oder ähnliches? lg haribo \quoteoff Ja, das reicht. Texteditor reicht auch. :-)


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haribo
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 25.10.2012
Mitteilungen: 3872
  Beitrag No.1909, eingetragen 2020-02-19

bei den beweglichen klappt es bei mir eher nicht, scheints sind die eingestellten winkel nicht in dem angegebenen bereich abgespeichert? haribo


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StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
Mitteilungen: 4165
Wohnort: Raun
  Beitrag No.1910, eingetragen 2020-02-22

Hallo haribo, Eingabe Z(82,86) um Kante P82-P86 zu löschen ist richtig und Eingabe von beispielsweise Z(78) löscht Knoten P78 und alle von P78 ausgehenden Kanten auf einmal. Mit wenigen Eingaben kann man so den überflüssigen Anteil im Inneren der linken Hälfte entfernen: $ %Eingabe war: % %#1910-2 = #1892 Kanten entfernt % % % % % %P[1]=[-100,-50]; P[2]=[-50,-50]; D=ab(1,2); A(1,2); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,2,blauerWinkel); L(9,1,6); L(10,9,6); L(11,9,10); N(7,6,3); M(109,7,3,95.00000000000001); L(73,7,109); Q(8,7,4,ab(109,7,73,"gedreht"),D); M(110,8,4,35.000000000000014); L(37,8,110); M(111,5,2,-85.00000000000001); L(38,111,5); Q(36,8,5,ab(110,8,37,"gedreht"),ab(111,5,38,"gedreht")); M(112,37,8,154.99999999999997); L(43,37,112); M(113,38,5,-144.99999999999994); L(44,113,38); Q(40,37,38,ab(112,37,43,"gedreht"),ab(113,38,44,"gedreht")); M(114,44,38,-85.00000000000017); M(71,114,44,125.00000000000043); M(69,71,114,125.00000000000016); L(116,69,71); Q(115,71,114,ab(116,71,69,"gedreht"),D); Q(72,114,44,ab(115,114,69,71,"gedreht"),D); Q(46,43,44,D,ab(114,44,69,71,72,"gedreht")); M(117,8,4,125.00000000000001); L(75,8,117); Q(74,8,43,ab(117,8,75,"gedreht"),D); M(118,73,7,-144.99999999999994); L(77,73,118); Q(76,73,75,ab(118,73,77,"gedreht"),D); M(12,10,6,gruenerWinkel); M(119,11,9,95.00000000000006); L(14,11,119); L(15,14,119); L(16,14,15); Q(13,11,12,ab(119,11,14,15,16,"gedreht"),D); N(17,15,12); M(120,16,14,94.99999999999991); L(19,16,120); L(20,19,120); L(21,19,20); Q(18,16,17,ab(120,16,19,20,21,"gedreht"),D); N(22,20,17); M(121,21,19,95.00000000000006); L(24,21,121); L(25,24,121); L(26,24,25); Q(23,21,22,ab(121,21,24,25,26,"gedreht"),D); M(27,25,23,orangerWinkel); M(122,26,24,95.00000000000001); L(29,26,122); L(30,29,122); L(31,29,30); Q(28,26,27,ab(122,26,29,30,31,"gedreht"),D); N(32,30,27); M(123,31,29,95.00000000000009); L(34,31,123); M(124,32,27,-114.99999999999997); L(35,124,32); Q(33,31,32,ab(123,31,34,"gedreht"),ab(124,32,35,"gedreht")); M(125,34,31,154.99999999999991); L(41,34,125); M(126,35,32,-144.99999999999986); L(42,126,35); Q(39,34,35,ab(125,34,41,"gedreht"),ab(126,35,42,"gedreht")); M(127,41,34,95.00000000000006); L(47,41,127); L(48,47,127); L(49,47,48); Q(45,41,42,ab(127,41,47,48,49,"gedreht"),D); M(128,42,35,-174.99999999999991); L(88,128,42); Q(50,48,42,D,ab(128,42,88,"gedreht")); M(129,49,47,95.00000000000014); L(52,49,129); L(53,52,129); L(54,52,53); Q(51,49,50,ab(129,49,52,53,54,"gedreht"),D); N(78,27,77); N(79,78,76); N(80,32,79); M(130,42,35,34.999999999999915); L(81,42,130); A(80,42,ab(130,42,81,"gedreht")); M(131,81,42,155.0000000000003); M(83,131,81,-115.0000000000004); L(132,131,83); Q(86,81,131,D,ab(132,131,83,"gedreht")); Q(82,81,79,ab(131,81,83,86,"gedreht"),D); A(75,83); M(87,86,81,-84.99999999999967); L(133,86,87); A(88,86,ab(133,86,87,"gedreht")); N(84,83,74); M(134,84,74,155.00000000000026); L(85,84,134); Q(70,84,71,ab(134,84,85,"gedreht"),D); A(85,87); M(67,69,71,-85.00000000000058); M(64,67,69,185); L(66,67,64); L(136,67,66); Q(135,69,67,D,ab(136,67,64,66,"gedreht")); Q(68,70,69,D,ab(135,69,64,66,67,"gedreht")); M(56,54,52,94.99999999999955); L(57,54,56); L(58,57,56); L(137,57,58); M(62,64,66,-84.99999999999945); M(138,62,64,185); L(61,62,138); L(139,62,61); Q(63,64,62,D,ab(139,62,138,61,"gedreht")); Q(59,54,64,ab(137,54,56,57,58,"gedreht"),ab(138,64,61,62,63,"gedreht")); N(55,56,53); A(55,87); N(60,58,55); A(60,61); N(65,63,60); A(65,66); A(65,85); %R(42,80); // oder R(42,81); %R(75,83); %R(86,87); // oder R(86,88); %R(85,87); %R(55,87); %R(60,61); %R(65,66); %R(65,85); Z(78,27); Z(78); Z(77); Z(76); Z(73); Z(8,7); Z(75); Z(86,82); % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LimeGreen}{rgb}{0.20,0.80,0.20} \definecolor{Orange}{rgb}{1.00,0.64,0.00} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/3.23/1.87, 8/4.23/1.87, 9/1.87/0.50, 10/1.87/1.50, 11/1.00/1.00, 12/2.37/2.37, 13/1.50/1.87, 14/0.50/1.87, 15/1.00/2.73, 16/0.00/2.73, 17/1.87/3.23, 18/0.87/3.23, 19/0.00/3.73, 20/0.87/4.23, 21/0.00/4.73, 22/1.87/4.23, 23/1.00/4.73, 24/0.50/5.60, 25/1.50/5.60, 26/1.00/6.46, 27/2.37/5.10, 28/1.87/5.96, 29/1.87/6.96, 30/2.73/6.46, 31/2.73/7.46, 32/3.23/5.60, 33/3.23/6.60, 34/3.73/7.46, 35/4.10/6.10, 36/4.73/1.00, 37/5.23/1.87, 38/5.60/0.50, 39/4.60/6.96, 40/6.10/1.37, 41/4.60/7.96, 42/5.10/6.10, 43/6.10/2.37, 44/6.60/0.50, 45/5.10/7.10, 46/6.60/1.50, 47/5.60/7.96, 48/6.10/7.10, 49/6.60/7.96, 50/6.10/6.10, 51/6.60/6.96, 52/7.46/7.46, 53/7.46/6.46, 54/8.33/6.96, 55/6.96/5.60, 56/7.83/6.10, 57/8.83/6.10, 58/8.33/5.23, 59/9.33/5.23, 60/7.46/4.73, 61/8.46/4.73, 62/9.33/4.23, 63/8.46/3.73, 64/9.33/3.23, 65/7.46/3.73, 66/8.33/3.23, 67/8.83/2.37, 68/7.83/2.37, 69/8.33/1.50, 70/6.96/2.87, 71/7.46/2.00, 72/7.46/1.00, 74/5.10/2.37, 79/3.73/4.73, 80/4.23/5.60, 81/5.10/5.10, 82/4.60/4.23, 83/5.10/3.37, 84/5.96/2.87, 85/6.46/3.73, 86/5.60/4.23, 87/6.46/4.73, 88/5.60/5.23} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/0.00/90.00/0.4/Blue, 10/330.00/420.00/0.4/Green, 25/240.00/330.00/0.4/Orange} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 7/6, 7/3, 8/4, 9/1, 9/6, 10/9, 10/6, 11/9, 11/10, 12/10, 13/11, 13/12, 14/11, 14/13, 15/14, 15/13, 16/14, 16/15, 17/15, 17/12, 18/16, 18/17, 19/16, 19/18, 20/19, 20/18, 21/19, 21/20, 22/20, 22/17, 23/21, 23/22, 24/21, 24/23, 25/24, 25/23, 26/24, 26/25, 27/25, 28/26, 28/27, 29/26, 29/28, 30/29, 30/28, 31/29, 31/30, 32/30, 32/27, 33/31, 33/32, 34/31, 34/33, 35/33, 35/32, 36/8, 36/5, 37/8, 37/36, 38/36, 38/5, 39/34, 39/35, 40/37, 40/38, 41/34, 41/39, 42/39, 42/35, 43/37, 43/40, 44/40, 44/38, 45/41, 45/42, 46/43, 46/44, 47/41, 47/45, 48/47, 48/45, 49/47, 49/48, 50/48, 50/42, 51/49, 51/50, 52/49, 52/51, 53/52, 53/51, 54/52, 54/53, 55/56, 55/53, 55/87, 56/54, 57/54, 57/56, 58/57, 58/56, 59/57, 59/58, 59/62, 60/58, 60/55, 60/61, 61/62, 61/59, 62/64, 63/64, 63/61, 63/62, 64/67, 65/63, 65/60, 65/66, 65/85, 66/67, 66/64, 67/69, 68/70, 68/66, 68/67, 68/69, 69/71, 70/84, 70/71, 71/46, 72/69, 72/71, 72/46, 72/44, 74/8, 74/43, 80/32, 80/79, 80/42, 81/42, 81/80, 82/81, 82/79, 83/82, 84/83, 84/74, 85/84, 85/70, 85/87, 86/81, 86/83, 87/86, 88/50, 88/42, 88/86, 88/87} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,72,74,...,74,79,...,88} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/0.00/90.00/0.4/Blue, 10/330.00/420.00/0.4/Green, 25/240.00/330.00/0.4/Orange} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/210, 2/330, 3/150, 4/30, 5/330, 6/60, 7/258, 8/150, 9/240, 10/60, 11/270, 12/348, 13/330, 14/210, 15/30, 16/150, 17/78, 18/300, 19/240, 20/60, 21/210, 22/48, 23/270, 24/90, 25/30, 26/180, 27/258, 28/300, 29/120, 30/300, 31/150, 32/240, 33/120, 34/180, 35/360, 36/270, 37/180, 38/210, 39/90, 40/90, 41/150, 42/60, 43/60, 44/240, 45/270, 46/120, 47/150, 48/330, 49/120, 50/30, 51/180, 52/60, 53/240, 54/90, 55/92, 56/150, 57/30, 58/210, 59/330, 60/137, 61/180, 62/360, 63/180, 64/300, 65/318, 66/150, 67/330, 68/150, 69/360, 70/330, 71/120, 72/300, 74/108, 79/198, 80/180, 81/300, 82/288, 83/272, 84/210, 85/90, 86/240, 87/360, 88/120} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Anschließend Button neue Eingabe "Rahmen zuerst" erzeugt eine Eingabe ohne die Z(...) $ %Eingabe war: % %#1910-2 = #1892 Kanten entfernt % % % % % % % % % % % % % % % % %P[1]=[-100,-50]; P[9]=[-143.30127018922192,-25]; D=ab(1,9); A(9,1); N(6,9,1); N(10,9,6); N(11,9,10); M(14,11,9,blauerWinkel); N(13,14,11); N(15,14,13); N(16,14,15); M(19,16,14,gruenerWinkel); N(18,19,16); N(20,19,18); N(21,19,20); M(24,21,19,orangerWinkel); N(23,24,21); N(25,24,23); N(26,24,25); M(29,26,24,vierterWinkel); N(28,29,26); N(30,29,28); N(31,29,30); M(34,31,29,fuenfterWinkel); N(33,34,31); M(41,34,31,sechsterWinkel); N(39,41,34); M(47,41,34,siebenterWinkel); N(45,47,41); N(48,47,45); N(49,47,48); M(52,49,47,achterWinkel); N(51,52,49); N(53,52,51); N(54,52,53); M(57,54,52,neunterWinkel); N(56,57,54); N(58,57,56); N(59,57,58); M(62,59,57,zehnterWinkel); N(61,62,59); N(63,62,61); N(64,62,63); M(67,64,62,elfterWinkel); N(66,67,64); N(68,67,66); N(69,67,68); M(72,69,67,zwölfterWinkel); N(71,72,69); N(46,72,71); N(44,72,46); M(40,44,72,dreizehnterWinkel); N(38,44,40); Q(5,38,1,1*D,2*D); A(5,38); A(5,1); H(2,1,5,2); A(2,1); L(3,1,2); H(5,38,5,1); A(5,38); L(36,5,38); A(2,5); L(4,2,5); A(3,4); N(7,6,3); N(8,4,36); N(12,13,10); N(17,18,12); N(22,23,17); N(27,28,25); N(32,33,27); N(35,39,32); N(37,36,40); N(42,45,35); N(43,40,46); N(50,51,42); N(55,56,53); N(60,61,55); N(65,66,60); N(70,71,68); N(74,8,43); N(80,42,32); N(81,42,80); N(84,74,70); N(85,84,70); N(87,85,55); N(88,87,42); N(86,87,88); N(83,84,86); N(82,83,81); N(79,82,80); %A(17,15); R(17,15,"green"); %A(22,20); R(22,20,"green"); %A(32,30); R(32,30,"green"); %A(35,33); R(35,33,"green"); %A(37,8); R(37,8,"green"); %A(42,39); R(42,39,"green"); %A(43,37); R(43,37,"green"); %A(50,48); R(50,48,"green"); %A(60,58); R(60,58,"green"); %A(65,63); R(65,63,"green"); %A(85,65); R(85,65,"green"); %A(88,50); R(88,50,"green"); %A(86,81); R(86,81,"green"); % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LightBlue}{rgb}{0.68,0.84,0.90} \definecolor{LightCoral}{rgb}{0.94,0.50,0.50} \definecolor{LightCyan}{rgb}{0.88,1.00,1.00} \definecolor{LightGoldenrodYellow}{rgb}{0.98,0.98,0.82} \definecolor{LightGreen}{rgb}{0.56,0.93,0.56} \definecolor{LightGray}{rgb}{0.82,0.82,0.82} \definecolor{LightPink}{rgb}{1.00,0.71,0.75} \definecolor{Lime}{rgb}{0.00,1.00,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/3.23/1.87, 8/4.23/1.87, 9/1.87/0.50, 10/1.87/1.50, 11/1.00/1.00, 12/2.37/2.37, 13/1.50/1.87, 14/0.50/1.87, 15/1.00/2.73, 16/0.00/2.73, 17/1.87/3.23, 18/0.87/3.23, 19/0.00/3.73, 20/0.87/4.23, 21/0.00/4.73, 22/1.87/4.23, 23/1.00/4.73, 24/0.50/5.60, 25/1.50/5.60, 26/1.00/6.46, 27/2.37/5.10, 28/1.87/5.96, 29/1.87/6.96, 30/2.73/6.46, 31/2.73/7.46, 32/3.23/5.60, 33/3.23/6.60, 34/3.73/7.46, 35/4.10/6.10, 36/4.73/1.00, 37/5.23/1.87, 38/5.60/0.50, 39/4.60/6.96, 40/6.10/1.37, 41/4.60/7.96, 42/5.10/6.10, 43/6.10/2.37, 44/6.60/0.50, 45/5.10/7.10, 46/6.60/1.50, 47/5.60/7.96, 48/6.10/7.10, 49/6.60/7.96, 50/6.10/6.10, 51/6.60/6.96, 52/7.46/7.46, 53/7.46/6.46, 54/8.33/6.96, 55/6.96/5.60, 56/7.83/6.10, 57/8.83/6.10, 58/8.33/5.23, 59/9.33/5.23, 60/7.46/4.73, 61/8.46/4.73, 62/9.33/4.23, 63/8.46/3.73, 64/9.33/3.23, 65/7.46/3.73, 66/8.33/3.23, 67/8.83/2.37, 68/7.83/2.37, 69/8.33/1.50, 70/6.96/2.87, 71/7.46/2.00, 72/7.46/1.00, 74/5.10/2.37, 79/3.73/4.73, 80/4.23/5.60, 81/5.10/5.10, 82/4.60/4.23, 83/5.10/3.37, 84/5.96/2.87, 85/6.46/3.73, 86/5.60/4.23, 87/6.46/4.73, 88/5.60/5.23} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 11/330.00/480.00/0.4/Blue, 16/300.00/450.00/0.4/Green, 21/270.00/420.00/0.4/Orange, 26/240.00/390.00/0.4/Violet, 31/210.00/360.00/0.4/Teal, 34/180.00/390.00/0.4/Lime, 41/210.00/360.00/0.4/LightBlue, 49/180.00/330.00/0.4/LightCoral, 54/150.00/300.00/0.4/LightCyan, 59/120.00/270.00/0.4/LightGoldenrodYellow, 64/90.00/240.00/0.4/LightGreen, 69/60.00/210.00/0.4/LightGray, 44/30.00/120.00/0.4/LightPink} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 2/5, 3/1, 3/2, 3/4, 4/2, 4/5, 5/38, 6/9, 6/1, 7/6, 7/3, 8/4, 8/36, 9/1, 10/9, 10/6, 11/9, 11/10, 12/13, 12/10, 13/14, 13/11, 14/11, 15/14, 15/13, 16/14, 16/15, 17/18, 17/12, 17/15, 18/19, 18/16, 19/16, 20/19, 20/18, 21/19, 21/20, 22/23, 22/17, 22/20, 23/24, 23/21, 24/21, 25/24, 25/23, 26/24, 26/25, 27/28, 27/25, 28/29, 28/26, 29/26, 30/29, 30/28, 31/29, 31/30, 32/33, 32/27, 32/30, 33/34, 33/31, 34/31, 35/39, 35/32, 35/33, 36/5, 36/38, 37/36, 37/40, 37/8, 38/44, 38/40, 39/41, 39/34, 40/44, 41/34, 42/45, 42/35, 42/39, 43/40, 43/46, 43/37, 44/72, 44/46, 45/47, 45/41, 46/72, 46/71, 47/41, 48/47, 48/45, 49/47, 49/48, 50/51, 50/42, 50/48, 51/52, 51/49, 52/49, 53/52, 53/51, 54/52, 54/53, 55/56, 55/53, 56/57, 56/54, 57/54, 58/57, 58/56, 59/57, 59/58, 60/61, 60/55, 60/58, 61/62, 61/59, 62/59, 63/62, 63/61, 64/62, 64/63, 65/66, 65/60, 65/63, 66/67, 66/64, 67/64, 68/67, 68/66, 69/67, 69/68, 70/71, 70/68, 71/72, 71/69, 72/69, 74/8, 74/43, 79/82, 79/80, 80/42, 80/32, 81/42, 81/80, 82/83, 82/81, 83/84, 83/86, 84/74, 84/70, 85/84, 85/70, 85/65, 86/87, 86/88, 86/81, 87/85, 87/55, 88/87, 88/42, 88/50} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,72,74,...,74,79,...,88} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-17) -- (p-15); \draw[Green,very thick] (p-22) -- (p-20); \draw[Green,very thick] (p-32) -- (p-30); \draw[Green,very thick] (p-35) -- (p-33); \draw[Green,very thick] (p-37) -- (p-8); \draw[Green,very thick] (p-42) -- (p-39); \draw[Green,very thick] (p-43) -- (p-37); \draw[Green,very thick] (p-50) -- (p-48); \draw[Green,very thick] (p-60) -- (p-58); \draw[Green,very thick] (p-65) -- (p-63); \draw[Green,very thick] (p-85) -- (p-65); \draw[Green,very thick] (p-88) -- (p-50); \draw[Green,very thick] (p-86) -- (p-81); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 11/330.00/480.00/0.4/Blue, 16/300.00/450.00/0.4/Green, 21/270.00/420.00/0.4/Orange, 26/240.00/390.00/0.4/Violet, 31/210.00/360.00/0.4/Teal, 34/180.00/390.00/0.4/Lime, 41/210.00/360.00/0.4/LightBlue, 49/180.00/330.00/0.4/LightCoral, 54/150.00/300.00/0.4/LightCyan, 59/120.00/270.00/0.4/LightGoldenrodYellow, 64/90.00/240.00/0.4/LightGreen, 69/60.00/210.00/0.4/LightGray, 44/30.00/120.00/0.4/LightPink} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/210, 2/330, 3/90, 4/90, 5/330, 6/60, 7/257, 8/150, 9/180, 10/60, 11/180, 12/347, 13/30, 14/210, 15/30, 16/150, 17/77, 18/300, 19/120, 20/360, 21/120, 22/48, 23/330, 24/150, 25/330, 26/90, 27/257, 28/300, 29/120, 30/300, 31/60, 32/240, 33/120, 34/180, 35/360, 36/270, 37/30, 38/360, 39/90, 40/300, 41/60, 42/330, 43/60, 44/330, 45/210, 46/120, 47/90, 48/330, 49/30, 50/30, 51/180, 52/360, 53/300, 54/360, 55/92, 56/210, 57/30, 58/210, 59/330, 60/138, 61/120, 62/360, 63/180, 64/300, 65/318, 66/150, 67/30, 68/150, 69/360, 70/330, 71/60, 72/300, 74/107, 79/197, 80/180, 81/300, 82/287, 83/272, 84/210, 85/90, 86/240, 87/360, 88/270} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ und die fülle ich wie gewünscht mit neuen Kanten 89 Knoten, 2×Grad 3, 85×Grad 4, 2×Grad 7, 0 Überschneidungen 180 Kanten, minimal 0.99999999999995270450, maximal 1.00000000000001554312 $ %Eingabe war: % %#1910-3 = #1892 Kanten entfernt und neue eingesetzt % % % % % % % % % % % % % % % % %P[1]=[-100,-50]; P[9]=[-143.30127018922192,-25]; D=ab(1,9); A(9,1); N(6,9,1); N(10,9,6); N(11,9,10); M(14,11,9,blauerWinkel); N(13,14,11); N(15,14,13); N(16,14,15); M(19,16,14,gruenerWinkel); N(18,19,16); N(20,19,18); N(21,19,20); M(24,21,19,orangerWinkel); N(23,24,21); N(25,24,23); N(26,24,25); M(29,26,24,vierterWinkel); N(28,29,26); N(30,29,28); N(31,29,30); M(34,31,29,fuenfterWinkel); N(33,34,31); M(41,34,31,sechsterWinkel); N(39,41,34); M(47,41,34,siebenterWinkel); N(45,47,41); N(48,47,45); N(49,47,48); M(52,49,47,achterWinkel); N(51,52,49); N(53,52,51); N(54,52,53); M(57,54,52,neunterWinkel); N(56,57,54); N(58,57,56); N(59,57,58); M(62,59,57,zehnterWinkel); N(61,62,59); N(63,62,61); N(64,62,63); M(67,64,62,elfterWinkel); N(66,67,64); N(68,67,66); N(69,67,68); M(72,69,67,zwölfterWinkel); N(71,72,69); N(46,72,71); N(44,72,46); M(40,44,72,dreizehnterWinkel); N(38,44,40); Q(5,38,1,1*D,2*D); A(5,38); A(5,1); H(2,1,5,2); A(2,1); L(3,1,2); H(5,38,5,1); A(5,38); L(36,5,38); A(2,5); L(4,2,5); A(3,4); N(7,6,3); N(8,4,36); N(12,13,10); N(17,18,12); N(22,23,17); N(27,28,25); N(32,33,27); N(35,39,32); N(37,36,40); N(42,45,35); N(43,40,46); N(50,51,42); N(55,56,53); N(60,61,55); N(65,66,60); N(70,71,68); N(74,8,43); N(80,42,32); N(81,42,80); N(84,74,70); N(85,84,70); N(87,85,55); N(88,87,42); N(86,87,88); N(83,84,86); N(82,83,81); N(79,82,80); %A(17,15); R(17,15,"green"); %A(22,20); R(22,20,"green"); %A(32,30); R(32,30,"green"); %A(35,33); R(35,33,"green"); %A(37,8); R(37,8,"green"); %A(42,39); R(42,39,"green"); %A(43,37); R(43,37,"green"); %A(50,48); R(50,48,"green"); %A(60,58); R(60,58,"green"); %A(65,63); R(65,63,"green"); %A(85,65); R(85,65,"green"); %A(88,50); R(88,50,"green"); %A(86,81); R(86,81,"green"); L(73,32,27); N(75,79,73); N(76,82,75); N(77,73,22); A(77,75); N(78,77,12); A(7,78); N(89,74,76); A(78,89); A(89,7); A(79,32); % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LightBlue}{rgb}{0.68,0.84,0.90} \definecolor{LightCoral}{rgb}{0.94,0.50,0.50} \definecolor{LightCyan}{rgb}{0.88,1.00,1.00} \definecolor{LightGoldenrodYellow}{rgb}{0.98,0.98,0.82} \definecolor{LightGreen}{rgb}{0.56,0.93,0.56} \definecolor{LightGray}{rgb}{0.82,0.82,0.82} \definecolor{LightPink}{rgb}{1.00,0.71,0.75} \definecolor{Lime}{rgb}{0.00,1.00,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/3.23/1.87, 8/4.23/1.87, 9/1.87/0.50, 10/1.87/1.50, 11/1.00/1.00, 12/2.37/2.37, 13/1.50/1.87, 14/0.50/1.87, 15/1.00/2.73, 16/0.00/2.73, 17/1.87/3.23, 18/0.87/3.23, 19/0.00/3.73, 20/0.87/4.23, 21/0.00/4.73, 22/1.87/4.23, 23/1.00/4.73, 24/0.50/5.60, 25/1.50/5.60, 26/1.00/6.46, 27/2.37/5.10, 28/1.87/5.96, 29/1.87/6.96, 30/2.73/6.46, 31/2.73/7.46, 32/3.23/5.60, 33/3.23/6.60, 34/3.73/7.46, 35/4.10/6.10, 36/4.73/1.00, 37/5.23/1.87, 38/5.60/0.50, 39/4.60/6.96, 40/6.10/1.37, 41/4.60/7.96, 42/5.10/6.10, 43/6.10/2.37, 44/6.60/0.50, 45/5.10/7.10, 46/6.60/1.50, 47/5.60/7.96, 48/6.10/7.10, 49/6.60/7.96, 50/6.10/6.10, 51/6.60/6.96, 52/7.46/7.46, 53/7.46/6.46, 54/8.33/6.96, 55/6.96/5.60, 56/7.83/6.10, 57/8.83/6.10, 58/8.33/5.23, 59/9.33/5.23, 60/7.46/4.73, 61/8.46/4.73, 62/9.33/4.23, 63/8.46/3.73, 64/9.33/3.23, 65/7.46/3.73, 66/8.33/3.23, 67/8.83/2.37, 68/7.83/2.37, 69/8.33/1.50, 70/6.96/2.87, 71/7.46/2.00, 72/7.46/1.00, 73/3.23/4.60, 74/5.10/2.37, 75/3.73/3.73, 76/4.60/3.23, 77/2.73/3.73, 78/3.23/2.87, 79/3.73/4.73, 80/4.23/5.60, 81/5.10/5.10, 82/4.60/4.23, 83/5.10/3.37, 84/5.96/2.87, 85/6.46/3.73, 86/5.60/4.23, 87/6.46/4.73, 88/5.60/5.23, 89/4.10/2.37} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 11/330.00/480.00/0.4/Blue, 16/300.00/450.00/0.4/Green, 21/270.00/420.00/0.4/Orange, 26/240.00/390.00/0.4/Violet, 31/210.00/360.00/0.4/Teal, 34/180.00/390.00/0.4/Lime, 41/210.00/360.00/0.4/LightBlue, 49/180.00/330.00/0.4/LightCoral, 54/150.00/300.00/0.4/LightCyan, 59/120.00/270.00/0.4/LightGoldenrodYellow, 64/90.00/240.00/0.4/LightGreen, 69/60.00/210.00/0.4/LightGray, 44/30.00/120.00/0.4/LightPink} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 2/5, 3/1, 3/2, 3/4, 4/2, 4/5, 5/38, 6/9, 6/1, 7/6, 7/3, 7/78, 8/4, 8/36, 9/1, 10/9, 10/6, 11/9, 11/10, 12/13, 12/10, 13/14, 13/11, 14/11, 15/14, 15/13, 16/14, 16/15, 17/18, 17/12, 17/15, 18/19, 18/16, 19/16, 20/19, 20/18, 21/19, 21/20, 22/23, 22/17, 22/20, 23/24, 23/21, 24/21, 25/24, 25/23, 26/24, 26/25, 27/28, 27/25, 28/29, 28/26, 29/26, 30/29, 30/28, 31/29, 31/30, 32/33, 32/27, 32/30, 33/34, 33/31, 34/31, 35/39, 35/32, 35/33, 36/5, 36/38, 37/36, 37/40, 37/8, 38/44, 38/40, 39/41, 39/34, 40/44, 41/34, 42/45, 42/35, 42/39, 43/40, 43/46, 43/37, 44/72, 44/46, 45/47, 45/41, 46/72, 46/71, 47/41, 48/47, 48/45, 49/47, 49/48, 50/51, 50/42, 50/48, 51/52, 51/49, 52/49, 53/52, 53/51, 54/52, 54/53, 55/56, 55/53, 56/57, 56/54, 57/54, 58/57, 58/56, 59/57, 59/58, 60/61, 60/55, 60/58, 61/62, 61/59, 62/59, 63/62, 63/61, 64/62, 64/63, 65/66, 65/60, 65/63, 66/67, 66/64, 67/64, 68/67, 68/66, 69/67, 69/68, 70/71, 70/68, 71/72, 71/69, 72/69, 73/32, 73/27, 74/8, 74/43, 75/79, 75/73, 76/82, 76/75, 77/73, 77/22, 77/75, 78/77, 78/12, 78/89, 79/82, 79/80, 79/32, 80/42, 80/32, 81/42, 81/80, 82/83, 82/81, 83/84, 83/86, 84/74, 84/70, 85/84, 85/70, 85/65, 86/87, 86/88, 86/81, 87/85, 87/55, 88/87, 88/42, 88/50, 89/74, 89/76, 89/7} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,89} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-17) -- (p-15); \draw[Green,very thick] (p-22) -- (p-20); \draw[Green,very thick] (p-32) -- (p-30); \draw[Green,very thick] (p-35) -- (p-33); \draw[Green,very thick] (p-37) -- (p-8); \draw[Green,very thick] (p-42) -- (p-39); \draw[Green,very thick] (p-43) -- (p-37); \draw[Green,very thick] (p-50) -- (p-48); \draw[Green,very thick] (p-60) -- (p-58); \draw[Green,very thick] (p-65) -- (p-63); \draw[Green,very thick] (p-85) -- (p-65); \draw[Green,very thick] (p-88) -- (p-50); \draw[Green,very thick] (p-86) -- (p-81); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 11/330.00/480.00/0.4/Blue, 16/300.00/450.00/0.4/Green, 21/270.00/420.00/0.4/Orange, 26/240.00/390.00/0.4/Violet, 31/210.00/360.00/0.4/Teal, 34/180.00/390.00/0.4/Lime, 41/210.00/360.00/0.4/LightBlue, 49/180.00/330.00/0.4/LightCoral, 54/150.00/300.00/0.4/LightCyan, 59/120.00/270.00/0.4/LightGoldenrodYellow, 64/90.00/240.00/0.4/LightGreen, 69/60.00/210.00/0.4/LightGray, 44/30.00/120.00/0.4/LightPink} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/210, 2/330, 3/90, 4/90, 5/330, 6/60, 7/240, 8/150, 9/180, 10/60, 11/180, 12/347, 13/30, 14/210, 15/30, 16/150, 17/77, 18/300, 19/120, 20/360, 21/120, 22/122, 23/330, 24/150, 25/330, 26/90, 27/180, 28/300, 29/120, 30/300, 31/60, 32/60, 33/120, 34/180, 35/360, 36/270, 37/30, 38/360, 39/90, 40/300, 41/60, 42/330, 43/60, 44/330, 45/210, 46/120, 47/90, 48/330, 49/30, 50/30, 51/180, 52/360, 53/300, 54/360, 55/92, 56/210, 57/30, 58/210, 59/330, 60/138, 61/120, 62/360, 63/180, 64/300, 65/318, 66/150, 67/30, 68/150, 69/360, 70/330, 71/60, 72/300, 73/300, 74/107, 75/330, 76/303, 77/210, 78/120, 79/270, 80/30, 81/300, 82/287, 83/272, 84/210, 85/90, 86/240, 87/360, 88/270, 89/360} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Dann wieder Button neue Eingabe, diesmal "egal wie" (weil die anderen nicht funktionieren), um genau zwischen Anfüge- und Einsetzkanten zu unterscheiden $ %Eingabe war: % %Automatisch generierte Eingabe zu: #1910-3 = #1892 Kanten entfernt und neue eingesetzt % % % % % % % %P[1]=[-100,-50]; P[2]=[-50.000000000000014,-50.00000000000049]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(38,5,4,blauerWinkel); N(36,5,38); N(8,4,36); N(37,8,36); N(40,37,38); N(43,37,40); N(44,40,38); N(46,43,44); N(72,46,44); N(74,8,43); N(71,46,72); N(69,71,72); M(89,74,8,gruenerWinkel); N(7,3,89); N(78,7,89); N(6,1,7); N(9,1,6); N(10,9,6); N(11,9,10); N(12,10,78); N(13,11,12); N(14,11,13); N(15,14,13); N(16,14,15); N(17,15,12); N(18,16,17); N(19,16,18); N(20,19,18); N(21,19,20); N(22,20,17); N(23,21,22); N(24,21,23); N(25,24,23); N(26,24,25); N(77,22,78); M(84,74,8,orangerWinkel); N(70,84,71); N(85,84,70); N(68,70,69); N(67,68,69); N(66,68,67); N(64,66,67); N(65,85,66); N(63,65,64); N(62,63,64); N(61,63,62); N(59,61,62); N(60,65,61); N(58,60,59); N(57,58,59); N(56,58,57); N(54,56,57); N(55,60,56); N(87,85,55); N(53,55,54); N(52,53,54); N(51,53,52); N(49,51,52); M(88,87,85,vierterWinkel); N(50,51,88); N(86,87,88); N(42,88,50); N(48,50,49); N(81,86,42); N(83,84,86); N(45,42,48); N(47,45,48); N(80,81,42); N(82,83,81); N(41,45,47); N(76,82,89); N(79,82,80); N(32,79,80); N(35,32,42); N(39,41,35); N(73,32,77); N(75,79,73); N(27,32,25); N(28,26,27); N(29,26,28); N(30,29,28); N(31,29,30); N(33,31,32); N(34,31,33); %A(47,49); R(47,49,"green"); %A(39,42); R(39,42,"green"); %A(75,76); R(75,76,"green"); %A(75,77); R(75,77,"green"); %A(27,73); R(27,73,"green"); %A(30,32); R(30,32,"green"); %A(33,35); R(33,35,"green"); %A(34,39); R(34,39,"green"); %A(34,41); R(34,41,"green"); % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/3.23/1.87, 8/4.23/1.87, 9/1.87/0.50, 10/1.87/1.50, 11/1.00/1.00, 12/2.37/2.37, 13/1.50/1.87, 14/0.50/1.87, 15/1.00/2.73, 16/0.00/2.73, 17/1.87/3.23, 18/0.87/3.23, 19/0.00/3.73, 20/0.87/4.23, 21/0.00/4.73, 22/1.87/4.23, 23/1.00/4.73, 24/0.50/5.60, 25/1.50/5.60, 26/1.00/6.46, 27/2.37/5.10, 28/1.87/5.96, 29/1.87/6.96, 30/2.73/6.46, 31/2.73/7.46, 32/3.23/5.60, 33/3.23/6.60, 34/3.73/7.46, 35/4.10/6.10, 36/4.73/1.00, 37/5.23/1.87, 38/5.60/0.50, 39/4.60/6.96, 40/6.10/1.37, 41/4.60/7.96, 42/5.10/6.10, 43/6.10/2.37, 44/6.60/0.50, 45/5.10/7.10, 46/6.60/1.50, 47/5.60/7.96, 48/6.10/7.10, 49/6.60/7.96, 50/6.10/6.10, 51/6.60/6.96, 52/7.46/7.46, 53/7.46/6.46, 54/8.33/6.96, 55/6.96/5.60, 56/7.83/6.10, 57/8.83/6.10, 58/8.33/5.23, 59/9.33/5.23, 60/7.46/4.73, 61/8.46/4.73, 62/9.33/4.23, 63/8.46/3.73, 64/9.33/3.23, 65/7.46/3.73, 66/8.33/3.23, 67/8.83/2.37, 68/7.83/2.37, 69/8.33/1.50, 70/6.96/2.87, 71/7.46/2.00, 72/7.46/1.00, 73/3.23/4.60, 74/5.10/2.37, 75/3.73/3.73, 76/4.60/3.23, 77/2.73/3.73, 78/3.23/2.87, 79/3.73/4.73, 80/4.23/5.60, 81/5.10/5.10, 82/4.60/4.23, 83/5.10/3.37, 84/5.96/2.87, 85/6.46/3.73, 86/5.60/4.23, 87/6.46/4.73, 88/5.60/5.23, 89/4.10/2.37} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 5/120.00/390.00/0.4/Blue, 74/210.00/540.00/0.4/Green, 74/210.00/390.00/0.3/Orange, 87/270.00/510.00/0.4/Violet} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 6/7, 7/3, 7/89, 8/4, 8/36, 9/1, 9/6, 10/9, 10/6, 11/9, 11/10, 12/10, 12/78, 13/11, 13/12, 14/11, 14/13, 15/14, 15/13, 16/14, 16/15, 17/15, 17/12, 18/16, 18/17, 19/16, 19/18, 20/19, 20/18, 21/19, 21/20, 22/20, 22/17, 23/21, 23/22, 24/21, 24/23, 25/24, 25/23, 26/24, 26/25, 27/32, 27/25, 27/73, 28/26, 28/27, 29/26, 29/28, 30/29, 30/28, 30/32, 31/29, 31/30, 32/79, 32/80, 33/31, 33/32, 33/35, 34/31, 34/33, 34/39, 34/41, 35/32, 35/42, 36/5, 36/38, 37/8, 37/36, 38/5, 39/41, 39/35, 39/42, 40/37, 40/38, 41/45, 41/47, 42/88, 42/50, 43/37, 43/40, 44/40, 44/38, 45/42, 45/48, 46/43, 46/44, 47/45, 47/48, 47/49, 48/50, 48/49, 49/51, 49/52, 50/51, 50/88, 51/53, 51/52, 52/53, 52/54, 53/55, 53/54, 54/56, 54/57, 55/60, 55/56, 56/58, 56/57, 57/58, 57/59, 58/60, 58/59, 59/61, 59/62, 60/65, 60/61, 61/63, 61/62, 62/63, 62/64, 63/65, 63/64, 64/66, 64/67, 65/85, 65/66, 66/68, 66/67, 67/68, 67/69, 68/70, 68/69, 69/71, 69/72, 70/84, 70/71, 71/46, 71/72, 72/46, 72/44, 73/32, 73/77, 74/8, 74/43, 75/79, 75/73, 75/76, 75/77, 76/82, 76/89, 77/22, 77/78, 78/7, 78/89, 79/82, 79/80, 80/81, 80/42, 81/86, 81/42, 82/83, 82/81, 83/84, 83/86, 84/74, 85/84, 85/70, 86/87, 86/88, 87/85, 87/55, 88/87, 89/74} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,89} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-47) -- (p-49); \draw[Green,very thick] (p-39) -- (p-42); \draw[Green,very thick] (p-75) -- (p-76); \draw[Green,very thick] (p-75) -- (p-77); \draw[Green,very thick] (p-27) -- (p-73); \draw[Green,very thick] (p-30) -- (p-32); \draw[Green,very thick] (p-33) -- (p-35); \draw[Green,very thick] (p-34) -- (p-39); \draw[Green,very thick] (p-34) -- (p-41); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 5/120.00/390.00/0.4/Blue, 74/210.00/540.00/0.4/Green, 74/210.00/390.00/0.3/Orange, 87/270.00/510.00/0.4/Violet} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/300, 2/270, 3/90, 4/30, 5/330, 6/60, 7/240, 8/150, 9/300, 10/60, 11/180, 12/348, 13/330, 14/150, 15/30, 16/150, 17/78, 18/300, 19/120, 20/360, 21/210, 22/122, 23/270, 24/90, 25/330, 26/180, 27/180, 28/300, 29/60, 30/360, 31/60, 32/150, 33/120, 34/180, 35/360, 36/120, 37/30, 38/360, 39/90, 40/300, 41/60, 42/330, 43/60, 44/240, 45/210, 46/120, 47/90, 48/270, 49/120, 50/30, 51/240, 52/360, 53/240, 54/360, 55/92, 56/210, 57/30, 58/210, 59/60, 60/258, 61/180, 62/300, 63/180, 64/300, 65/317, 66/90, 67/330, 68/150, 69/360, 70/330, 71/60, 72/240, 73/300, 74/287, 75/330, 76/303, 77/210, 78/120, 79/270, 80/30, 81/300, 82/288, 83/272, 84/210, 85/90, 86/240, 87/360, 88/270, 89/360} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ und dann mit Button "beweglich?" die Beweglichkeit testen $ %Eingabe war: % %Automatisch generierte Eingabe zu: #1910-3 = #1892 Kanten entfernt und neue eingesetzt % % % % %blauerWinkel=269.99999999999966+(-0.9999993761706794)*(gruenerWinkel-(329.999999999998)); %orangerWinkel=179.99999999999835+(8.63294614215187e-12)*(gruenerWinkel-(329.999999999998)); %vierterWinkel=239.99999999999784+(7.52931877907356e-7)*(gruenerWinkel-(329.999999999998)); %P[1]=[-100,-50]; P[2]=[-50.000000000000014,-50.00000000000049]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(38,5,4,blauerWinkel); N(36,5,38); N(8,4,36); N(37,8,36); N(40,37,38); N(43,37,40); N(44,40,38); N(46,43,44); N(72,46,44); N(74,8,43); N(71,46,72); N(69,71,72); M(89,74,8,gruenerWinkel); N(7,3,89); N(78,7,89); N(6,1,7); N(9,1,6); N(10,9,6); N(11,9,10); N(12,10,78); N(13,11,12); N(14,11,13); N(15,14,13); N(16,14,15); N(17,15,12); N(18,16,17); N(19,16,18); N(20,19,18); N(21,19,20); N(22,20,17); N(23,21,22); N(24,21,23); N(25,24,23); N(26,24,25); N(77,22,78); M(84,74,8,orangerWinkel); N(70,84,71); N(85,84,70); N(68,70,69); N(67,68,69); N(66,68,67); N(64,66,67); N(65,85,66); N(63,65,64); N(62,63,64); N(61,63,62); N(59,61,62); N(60,65,61); N(58,60,59); N(57,58,59); N(56,58,57); N(54,56,57); N(55,60,56); N(87,85,55); N(53,55,54); N(52,53,54); N(51,53,52); N(49,51,52); M(88,87,85,vierterWinkel); N(50,51,88); N(86,87,88); N(42,88,50); N(48,50,49); N(81,86,42); N(83,84,86); N(45,42,48); N(47,45,48); N(80,81,42); N(82,83,81); N(41,45,47); N(76,82,89); N(79,82,80); N(32,79,80); N(35,32,42); N(39,41,35); N(73,32,77); N(75,79,73); N(27,32,25); N(28,26,27); N(29,26,28); N(30,29,28); N(31,29,30); N(33,31,32); N(34,31,33); %A(47,49); R(47,49,"green"); %A(39,42); R(39,42,"green"); %A(75,76); R(75,76,"green"); %A(75,77); R(75,77,"green"); %A(27,73); R(27,73,"green"); %A(30,32); R(30,32,"green"); %A(33,35); R(33,35,"green"); %A(34,39); R(34,39,"green"); %A(34,41); R(34,41,"green"); % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Green}{rgb}{0.00,0.50,0.00} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.73/0.00, 2/3.73/0.00, 3/3.23/0.87, 4/4.23/0.87, 5/4.73/0.00, 6/2.73/1.00, 7/3.23/1.87, 8/4.23/1.87, 9/1.87/0.50, 10/1.87/1.50, 11/1.00/1.00, 12/2.37/2.37, 13/1.50/1.87, 14/0.50/1.87, 15/1.00/2.73, 16/0.00/2.73, 17/1.87/3.23, 18/0.87/3.23, 19/0.00/3.73, 20/0.87/4.23, 21/0.00/4.73, 22/1.87/4.23, 23/1.00/4.73, 24/0.50/5.60, 25/1.50/5.60, 26/1.00/6.46, 27/2.37/5.10, 28/1.87/5.96, 29/1.87/6.96, 30/2.73/6.46, 31/2.73/7.46, 32/3.23/5.60, 33/3.23/6.60, 34/3.73/7.46, 35/4.10/6.10, 36/4.73/1.00, 37/5.23/1.87, 38/5.60/0.50, 39/4.60/6.96, 40/6.10/1.37, 41/4.60/7.96, 42/5.10/6.10, 43/6.10/2.37, 44/6.60/0.50, 45/5.10/7.10, 46/6.60/1.50, 47/5.60/7.96, 48/6.10/7.10, 49/6.60/7.96, 50/6.10/6.10, 51/6.60/6.96, 52/7.46/7.46, 53/7.46/6.46, 54/8.33/6.96, 55/6.96/5.60, 56/7.83/6.10, 57/8.83/6.10, 58/8.33/5.23, 59/9.33/5.23, 60/7.46/4.73, 61/8.46/4.73, 62/9.33/4.23, 63/8.46/3.73, 64/9.33/3.23, 65/7.46/3.73, 66/8.33/3.23, 67/8.83/2.37, 68/7.83/2.37, 69/8.33/1.50, 70/6.96/2.87, 71/7.46/2.00, 72/7.46/1.00, 73/3.23/4.60, 74/5.10/2.37, 75/3.73/3.73, 76/4.60/3.23, 77/2.73/3.73, 78/3.23/2.87, 79/3.73/4.73, 80/4.23/5.60, 81/5.10/5.10, 82/4.60/4.23, 83/5.10/3.37, 84/5.96/2.87, 85/6.46/3.73, 86/5.60/4.23, 87/6.46/4.73, 88/5.60/5.23, 89/4.10/2.37} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 74/210.00/540.00/0.4/Green} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 6/7, 7/3, 7/89, 8/4, 8/36, 9/1, 9/6, 10/9, 10/6, 11/9, 11/10, 12/10, 12/78, 13/11, 13/12, 14/11, 14/13, 15/14, 15/13, 16/14, 16/15, 17/15, 17/12, 18/16, 18/17, 19/16, 19/18, 20/19, 20/18, 21/19, 21/20, 22/20, 22/17, 23/21, 23/22, 24/21, 24/23, 25/24, 25/23, 26/24, 26/25, 27/32, 27/25, 27/73, 28/26, 28/27, 29/26, 29/28, 30/29, 30/28, 30/32, 31/29, 31/30, 32/79, 32/80, 33/31, 33/32, 33/35, 34/31, 34/33, 34/39, 34/41, 35/32, 35/42, 36/5, 36/38, 37/8, 37/36, 38/5, 39/41, 39/35, 39/42, 40/37, 40/38, 41/45, 41/47, 42/88, 42/50, 43/37, 43/40, 44/40, 44/38, 45/42, 45/48, 46/43, 46/44, 47/45, 47/48, 47/49, 48/50, 48/49, 49/51, 49/52, 50/51, 50/88, 51/53, 51/52, 52/53, 52/54, 53/55, 53/54, 54/56, 54/57, 55/60, 55/56, 56/58, 56/57, 57/58, 57/59, 58/60, 58/59, 59/61, 59/62, 60/65, 60/61, 61/63, 61/62, 62/63, 62/64, 63/65, 63/64, 64/66, 64/67, 65/85, 65/66, 66/68, 66/67, 67/68, 67/69, 68/70, 68/69, 69/71, 69/72, 70/84, 70/71, 71/46, 71/72, 72/46, 72/44, 73/32, 73/77, 74/8, 74/43, 75/79, 75/73, 75/76, 75/77, 76/82, 76/89, 77/22, 77/78, 78/7, 78/89, 79/82, 79/80, 80/81, 80/42, 81/86, 81/42, 82/83, 82/81, 83/84, 83/86, 84/74, 85/84, 85/70, 86/87, 86/88, 87/85, 87/55, 88/87, 89/74} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,89} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-47) -- (p-49); \draw[Green,very thick] (p-39) -- (p-42); \draw[Green,very thick] (p-75) -- (p-76); \draw[Green,very thick] (p-75) -- (p-77); \draw[Green,very thick] (p-27) -- (p-73); \draw[Green,very thick] (p-30) -- (p-32); \draw[Green,very thick] (p-33) -- (p-35); \draw[Green,very thick] (p-34) -- (p-39); \draw[Green,very thick] (p-34) -- (p-41); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 74/210.00/540.00/0.4/Green} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/300, 2/270, 3/90, 4/30, 5/330, 6/60, 7/240, 8/150, 9/300, 10/60, 11/180, 12/348, 13/330, 14/150, 15/30, 16/150, 17/78, 18/300, 19/120, 20/360, 21/210, 22/122, 23/270, 24/90, 25/330, 26/180, 27/180, 28/300, 29/60, 30/360, 31/60, 32/150, 33/120, 34/180, 35/360, 36/120, 37/30, 38/360, 39/90, 40/300, 41/60, 42/330, 43/60, 44/240, 45/210, 46/120, 47/90, 48/270, 49/120, 50/30, 51/240, 52/360, 53/240, 54/360, 55/92, 56/210, 57/30, 58/210, 59/60, 60/258, 61/180, 62/300, 63/180, 64/300, 65/317, 66/90, 67/330, 68/150, 69/360, 70/330, 71/60, 72/240, 73/300, 74/287, 75/330, 76/303, 77/210, 78/120, 79/270, 80/30, 81/300, 82/288, 83/272, 84/210, 85/90, 86/240, 87/360, 88/270, 89/360} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Der Graph ist mit einem Winkel beweglich und wenn ich diesen Winkel mit Buttons "+1" oder "+10" variiere, 89 Knoten, 87×Grad 4, 2×Grad 7, 0 Überschneidungen 181 Kanten, minimal 0.89239598372476003352, maximal 1.00000477840259138773 nicht passende Kanten: |P76-P83|=0.89239598372476003352 $ %Eingabe war: % %Automatisch generierte Eingabe zu: #1910-3 = #1892 Kanten entfernt und neue eingesetzt % % % % %blauerWinkel=269.99999999999966+(-0.9999993761706794)*(gruenerWinkel-(329.999999999998)); %orangerWinkel=179.99999999999835+(8.63294614215187e-12)*(gruenerWinkel-(329.999999999998)); %vierterWinkel=239.99999999999784+(7.52931877907356e-7)*(gruenerWinkel-(329.999999999998)); %P[1]=[-100,-50]; P[2]=[-50.000000000000014,-50.00000000000049]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(38,5,4,blauerWinkel); N(36,5,38); N(8,4,36); N(37,8,36); N(40,37,38); N(43,37,40); N(44,40,38); N(46,43,44); N(72,46,44); N(74,8,43); N(71,46,72); N(69,71,72); M(89,74,8,gruenerWinkel); N(7,3,89); N(78,7,89); N(6,1,7); N(9,1,6); N(10,9,6); N(11,9,10); N(12,10,78); N(13,11,12); N(14,11,13); N(15,14,13); N(16,14,15); N(17,15,12); N(18,16,17); N(19,16,18); N(20,19,18); N(21,19,20); N(22,20,17); N(23,21,22); N(24,21,23); N(25,24,23); N(26,24,25); N(77,22,78); M(84,74,8,orangerWinkel); N(70,84,71); N(85,84,70); N(68,70,69); N(67,68,69); N(66,68,67); N(64,66,67); N(65,85,66); N(63,65,64); N(62,63,64); N(61,63,62); N(59,61,62); N(60,65,61); N(58,60,59); N(57,58,59); N(56,58,57); N(54,56,57); N(55,60,56); N(87,85,55); N(53,55,54); N(52,53,54); N(51,53,52); N(49,51,52); M(88,87,85,vierterWinkel); N(50,51,88); N(86,87,88); N(42,88,50); N(48,50,49); N(81,86,42); N(83,84,86); N(45,42,48); N(47,45,48); N(80,81,42); N(82,83,81); N(41,45,47); N(76,82,89); N(79,82,80); N(32,79,80); N(35,32,42); N(39,41,35); N(73,32,77); N(75,79,73); N(27,32,25); N(28,26,27); N(29,26,28); N(30,29,28); N(31,29,30); N(33,31,32); N(34,31,33); %A(47,49); R(47,49,"green"); %A(39,42); R(39,42,"green"); %A(75,76); R(75,76,"green"); %A(75,77); R(75,77,"green"); %A(27,73); R(27,73,"green"); %A(30,32); R(30,32,"green"); %A(33,35); R(33,35,"green"); %A(34,39); R(34,39,"green"); %A(34,41); R(34,41,"green"); RA(76,83); % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LimeGreen}{rgb}{0.20,0.80,0.20} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.20/0.00, 2/3.20/0.00, 3/2.70/0.87, 4/3.70/0.87, 5/4.20/0.00, 6/2.59/0.92, 7/3.09/1.79, 8/4.09/1.79, 9/1.60/0.80, 10/1.99/1.72, 11/1.00/1.60, 12/2.49/2.59, 13/1.50/2.46, 14/0.50/2.46, 15/1.00/3.33, 16/0.00/3.33, 17/1.99/3.45, 18/0.99/3.45, 19/0.39/4.25, 20/1.38/4.37, 21/0.78/5.17, 22/2.38/4.37, 23/1.78/5.17, 24/1.28/6.04, 25/2.28/6.04, 26/1.78/6.90, 27/2.88/5.24, 28/2.38/6.10, 29/2.77/7.02, 30/3.38/6.23, 31/3.77/7.15, 32/3.88/5.36, 33/4.27/6.28, 34/4.77/7.15, 35/4.87/5.48, 36/4.59/0.92, 37/5.09/1.79, 38/5.20/0.12, 39/5.37/6.35, 40/5.70/0.99, 41/5.76/7.27, 42/5.87/5.48, 43/6.09/1.91, 44/6.20/0.12, 45/6.26/6.40, 46/6.59/1.04, 47/6.76/7.27, 48/7.26/6.40, 49/7.76/7.27, 50/6.87/5.48, 51/7.37/6.35, 52/8.36/6.47, 53/7.97/5.55, 54/8.96/5.67, 55/7.47/4.68, 56/8.46/4.80, 57/9.46/4.80, 58/8.96/3.94, 59/9.96/3.94, 60/7.97/3.82, 61/8.97/3.82, 62/9.57/3.02, 63/8.58/2.90, 64/9.18/2.10, 65/7.58/2.90, 66/8.18/2.10, 67/8.68/1.23, 68/7.68/1.23, 69/8.18/0.37, 70/7.08/2.03, 71/7.58/1.16, 72/7.19/0.24, 73/3.49/4.44, 74/5.09/1.91, 75/3.99/3.57, 76/4.59/2.77, 77/2.99/3.57, 78/3.49/2.71, 79/4.38/4.49, 80/4.88/5.36, 81/5.48/4.56, 82/4.98/3.69, 83/5.48/2.83, 84/6.08/2.03, 85/6.58/2.90, 86/5.98/3.69, 87/6.97/3.82, 88/6.37/4.62, 89/4.09/1.91} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 74/187.00/540.00/0.4/Green} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 6/7, 7/3, 7/89, 8/4, 8/36, 9/1, 9/6, 10/9, 10/6, 11/9, 11/10, 12/10, 12/78, 13/11, 13/12, 14/11, 14/13, 15/14, 15/13, 16/14, 16/15, 17/15, 17/12, 18/16, 18/17, 19/16, 19/18, 20/19, 20/18, 21/19, 21/20, 22/20, 22/17, 23/21, 23/22, 24/21, 24/23, 25/24, 25/23, 26/24, 26/25, 27/32, 27/25, 27/73, 28/26, 28/27, 29/26, 29/28, 30/29, 30/28, 30/32, 31/29, 31/30, 32/79, 32/80, 33/31, 33/32, 33/35, 34/31, 34/33, 34/39, 34/41, 35/32, 35/42, 36/5, 36/38, 37/8, 37/36, 38/5, 39/41, 39/35, 39/42, 40/37, 40/38, 41/45, 41/47, 42/88, 42/50, 43/37, 43/40, 44/40, 44/38, 45/42, 45/48, 46/43, 46/44, 47/45, 47/48, 47/49, 48/50, 48/49, 49/51, 49/52, 50/51, 50/88, 51/53, 51/52, 52/53, 52/54, 53/55, 53/54, 54/56, 54/57, 55/60, 55/56, 56/58, 56/57, 57/58, 57/59, 58/60, 58/59, 59/61, 59/62, 60/65, 60/61, 61/63, 61/62, 62/63, 62/64, 63/65, 63/64, 64/66, 64/67, 65/85, 65/66, 66/68, 66/67, 67/68, 67/69, 68/70, 68/69, 69/71, 69/72, 70/84, 70/71, 71/46, 71/72, 72/46, 72/44, 73/32, 73/77, 74/8, 74/43, 75/79, 75/73, 75/76, 75/77, 76/82, 76/89, 76/83, 77/22, 77/78, 78/7, 78/89, 79/82, 79/80, 80/81, 80/42, 81/86, 81/42, 82/83, 82/81, 83/84, 83/86, 84/74, 85/84, 85/70, 86/87, 86/88, 87/85, 87/55, 88/87, 89/74} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,89} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-47) -- (p-49); \draw[Green,very thick] (p-39) -- (p-42); \draw[Green,very thick] (p-75) -- (p-76); \draw[Green,very thick] (p-75) -- (p-77); \draw[Green,very thick] (p-27) -- (p-73); \draw[Green,very thick] (p-30) -- (p-32); \draw[Green,very thick] (p-33) -- (p-35); \draw[Green,very thick] (p-34) -- (p-39); \draw[Green,very thick] (p-34) -- (p-41); \draw[LimeGreen,very thick] (p-76) -- (p-83); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); \draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-76) -- (p-83); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 74/187.00/540.00/0.4/Green} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/210, 2/270, 3/90, 4/30, 5/330, 6/37, 7/217, 8/150, 9/277, 10/37, 11/270, 12/336, 13/330, 14/150, 15/30, 16/150, 17/66, 18/337, 19/217, 20/337, 21/210, 22/100, 23/330, 24/150, 25/30, 26/90, 27/157, 28/217, 29/97, 30/337, 31/37, 32/217, 33/270, 34/157, 35/210, 36/97, 37/30, 38/337, 39/277, 40/90, 41/150, 42/37, 43/37, 44/217, 45/210, 46/157, 47/30, 48/270, 49/97, 50/30, 51/217, 52/37, 53/217, 54/337, 55/93, 56/210, 57/90, 58/270, 59/330, 60/246, 61/157, 62/337, 63/217, 64/30, 65/216, 66/90, 67/270, 68/210, 69/270, 70/330, 71/97, 72/337, 73/277, 74/276, 75/330, 76/215, 77/210, 78/97, 79/270, 80/30, 81/277, 82/276, 83/332, 84/210, 85/90, 86/217, 87/337, 88/270, 89/337} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ dann stellt sich heraus, dass Kante P76-P83 erst 1 wird, wenn etliche Knoten zusammenfallen.


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haribo
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 25.10.2012
Mitteilungen: 3872
  Beitrag No.1911, eingetragen 2020-02-22

danke stefan, -genau in die rautenförmige richtung ähnlich deinem letzten bild hatte ich es auch verzogen und eben vergeblich versucht abzuspeichern, hast du zu dem speichern einen tip? kann gut sein dass ich zu früh gespeichert hatte, aber ich hatte eine aufgebaute version gespeichert und wenn ich sie jetzt wieder hochlade zerfällt sie sofort drum vermute ich dass einige winkel nicht mitgespeichert wurden - zweitens gibt es eine abrufbare version von slash´s alten rekordgraph 4/7, der müsste sehr ähnlich aufgebaut sein und evtl auch beweglich sein können, also auch in diese rautenform geschoben werden können, bevor er dann mit eben den gleichen überschneidungen zusammenfällt, meine suche gilt seinem grundsätzlichem aufbau um ihn ggfls zu reduzieren haribo


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haribo
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 25.10.2012
Mitteilungen: 3872
  Beitrag No.1912, eingetragen 2020-02-22

nochmals versucht dein #1910 schrittweise nachzukonstruieren Z(j) klappt einwandfrei, "eingabe : rahmen zuerst" klappt auch, dann einige linien dazugefügt(aber noch nicht alle), dann wieder "eingabe:egal wie" dann sieht es als bild so aus: https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/35059_streichholztest1.png und ich schaff es nicht die "nichtpassenden kanten" auf 1 zu bekommen, bei weiteren eingaben zerknüllt es, ??? wie ich dir jetzt meine eingaben am besten zur verfügung stellen kann weiss ich nicht, ich versuchs mal mit show: \showon Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: #1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78); P[1]=[-36.489648590837135,-1.7967881657507974]; P[2]=[13.517130825300598,-11.798144048978344]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(38,5,4,blauerWinkel); N(36,5,38); N(8,4,36); N(37,8,36); N(40,37,38); N(43,37,40); N(44,40,38); N(46,43,44); N(72,46,44); N(74,8,43); N(71,46,72); N(69,71,72); M(100,74,8,gruenerWinkel); N(7,3,100); N(101,7,100); N(6,1,7); N(9,1,6); M(104,9,1,orangerWinkel); N(11,9,104); M(84,74,8,vierterWinkel); N(70,84,71); N(85,84,70); N(68,70,69); N(67,68,69); N(66,68,67); N(64,66,67); N(65,85,66); N(63,65,64); N(62,63,64); N(61,63,62); N(59,61,62); N(60,65,61); N(58,60,59); N(57,58,59); N(56,58,57); N(54,56,57); N(55,60,56); N(87,85,55); N(53,55,54); N(52,53,54); N(51,53,52); N(49,51,52); M(88,87,85,fuenfterWinkel); N(50,88,51); N(86,87,88); N(42,88,50); N(48,50,49); N(81,86,42); N(82,86,81); N(83,84,82); N(45,42,48); N(47,45,48); N(80,81,42); N(41,45,47); N(79,82,80); N(102,82,79); N(32,79,80); Q(34,38,41,jam(7.209768520107519)*D,D); N(35,32,42); N(39,41,35); N(103,102,32); N(27,103,32); N(33,32,34); N(31,33,34); N(30,32,31); N(28,27,30); N(29,28,30); N(26,28,29); N(25,27,26); N(24,25,26); N(23,25,24); N(21,23,24); M(22,23,25,sechsterWinkel); N(20,22,21); N(19,20,21); N(18,20,19); N(16,18,19); N(17,22,18); N(14,16,11); N(15,14,17); N(13,14,11); N(12,17,13); A(83,86); R(83,86,"green"); A(47,49); R(47,49,"green"); A(39,34); R(39,34,"green"); A(39,42); R(39,42,"green"); A(33,35); R(33,35,"green"); A(29,31); R(29,31,"green"); A(15,16); R(15,16,"green"); A(13,15); R(13,15,"green"); \showoff haribo


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StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
Mitteilungen: 4165
Wohnort: Raun
  Beitrag No.1913, eingetragen 2020-02-23

Der Graph ist angekommen, geht so zu machen. Button "TikZ" in der letzten/vorletzten Zeile des Streichholzprogramms erzeugt darunter den Code, um den Graph als TikZ-Zeichnung in den eigenen Beitrag zu kopieren. Über dem Button befinden sich einige Checkboxen, um die Darstellung (Linienstärken, Punktnummern...) vorher noch etwas zu variieren und man kann auch nachträglich noch den Code ändern und ergänzen: 87 Knoten, 3×Grad 2, 6×Grad 3, 72×Grad 4, 4×Grad 5, 2×Grad 7, 10? Überschneidungen 173 Kanten, minimal 0.99986961525115092275, maximal 7.20976852010751922961 einzustellende Kanten, Abstände und Winkel: |P83-P86|=1.00000000967858837519 |P47-P49|=0.99999999516070392502 |P39-P34|=1.00000000838191871466 |P39-P42|=0.99999999516070270378 |P33-P35|=0.99999997485425307087 |P29-P31|=1.00000002514574704016 |P15-P16|=0.99986961525115092275 |P13-P15|=1.00039131148478310784 nicht passende Kanten: |P13-P15|=1.00039131148478310784 |P15-P16|=0.99986961525115092275 |P34-P38|=7.20976852010751922961 $ %Eingabe war: % %Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: #1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78); % % % % % % % % % %P[1]=[-36.489648590837135,-1.7967881657507974]; P[2]=[13.517130825300598,-11.798144048978344]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(38,5,4,blauerWinkel); N(36,5,38); N(8,4,36); N(37,8,36); N(40,37,38); N(43,37,40); N(44,40,38); N(46,43,44); N(72,46,44); N(74,8,43); N(71,46,72); N(69,71,72); M(100,74,8,gruenerWinkel); N(7,3,100); N(101,7,100); N(6,1,7); N(9,1,6); M(104,9,1,orangerWinkel); N(11,9,104); M(84,74,8,vierterWinkel); N(70,84,71); N(85,84,70); N(68,70,69); N(67,68,69); N(66,68,67); N(64,66,67); N(65,85,66); N(63,65,64); N(62,63,64); N(61,63,62); N(59,61,62); N(60,65,61); N(58,60,59); N(57,58,59); N(56,58,57); N(54,56,57); N(55,60,56); N(87,85,55); N(53,55,54); N(52,53,54); N(51,53,52); N(49,51,52); M(88,87,85,fuenfterWinkel); N(50,88,51); N(86,87,88); N(42,88,50); N(48,50,49); N(81,86,42); N(82,86,81); N(83,84,82); N(45,42,48); N(47,45,48); N(80,81,42); N(41,45,47); N(79,82,80); N(102,82,79); N(32,79,80); Q(34,38,41,jam(7.209768520107519)*D,D); N(35,32,42); N(39,41,35); N(103,102,32); N(27,103,32); N(33,32,34); N(31,33,34); N(30,32,31); N(28,27,30); N(29,28,30); N(26,28,29); N(25,27,26); N(24,25,26); N(23,25,24); N(21,23,24); M(22,23,25,sechsterWinkel); N(20,22,21); N(19,20,21); N(18,20,19); N(16,18,19); N(17,22,18); N(14,16,11); N(15,14,17); N(13,14,11); N(12,17,13); %A(83,86); R(83,86,"green"); %A(47,49); R(47,49,"green"); %A(39,34); R(39,34,"green"); %A(39,42); R(39,42,"green"); %A(33,35); R(33,35,"green"); %A(29,31); R(29,31,"green"); %A(15,16); R(15,16,"green"); %A(13,15); R(13,15,"green"); % % % % % % % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{Lime}{rgb}{0.00,1.00,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.14319692163537300900/0.39223227027636820008, 2/3.12377759732629289857/0.19611613513818415555, 3/2.80332881460252236749/1.14338197831572307983, 4/3.78390949029344314525/0.94726584317753892428, 5/4.10435827301721367633/0.00000000000000000000, 6/2.33894652488346377339/1.37288618110740912037, 7/2.99907841785061268780/2.12403588914676433319, 8/3.98002562543162685671/1.92784651886845925794, 9/1.39180052415917709929/1.05208335488546000924, 11/0.64089767443553680160/1.71249603668140815138, 12/2.24836671419524991578/2.78411867718268490890, 13/1.30114268390953480292/2.46354631959506242822, 14/0.32059155464982147521/2.65981012906461478096, 15/0.98049711433392772175/3.41115868486146123217, 16/0.00000000000000000000/3.60702766220428916455, 17/1.92784651574202037239/3.73136035826703293949, 18/0.94726583511961204298/3.92747646874777389669, 19/0.19611611048074373276/4.58760834282669716089, 20/1.14338194560035599778/4.90805714937018144894, 21/0.39223222096148802063/5.56818902344910515723, 22/2.12396262622276488230/4.71194103888944137992, 23/1.37281290158389657208/5.37207291296836597638, 24/1.05236409504040850926/6.31933874808797657607, 25/2.03294477566281717174/6.12322263760723650705, 26/1.71249596911932955301/7.07048847272684710674, 27/2.78409449009132314856/5.46309075191016280115, 28/2.46364568354783397552/6.41035658702977340084, 29/2.65976180919537386060/7.39093726461882205570, 30/3.41091152362387850516/6.73080537892174746162, 31/3.60702767774337118567/7.71138605081640449157, 32/3.73136033016736723411/5.78353954380213508557, 33/3.92747648428685902644/6.76412021569679389188, 34/4.58760835836578007019/7.51526994033566442255, 35/4.67862617024341176375/6.10398833569410914635, 36/4.30047440815539783188/0.98058067569092011162, 37/4.96060630112254674629/1.73173038373027510239, 38/5.05162411619475193447/0.32044878272377019801, 39/5.33875806950662923356/6.85513803820029821168, 40/5.71175600916190173706/1.07159849076312529981, 41/5.53487420464481516547/7.83571871389121898943, 42/5.65920684538638951722/5.90787219781621253389, 43/5.90787214430008678079/2.05217916645404541143, 44/6.03220479188567271223/0.12433264758558643104, 45/5.85532299001521749915/6.88845287160900365819, 46/6.22832092702385686778/1.10491332327650648715, 47/6.51545488088367719115/7.63960258149274729078, 48/6.83590366625407952483/6.69233673921053373590, 49/7.49603555292516166020/7.44348645278305287576, 50/6.63978752162525243108/5.71175606541774172342, 51/7.29991941778697839283/6.46290577709213298618, 52/8.24718526096451576279/6.78335455981590396135, 53/8.05106912582633249542/5.80277388412498495995, 54/8.99833496900387075357/6.12322266684875593512, 55/7.39093723285918535737/5.05162417608562996918, 56/8.33820307603672361552/5.37207295880940183253, 57/9.31878375172764350509/5.17595682367121767697, 58/8.65865185876049459068/4.42480711563186268620, 59/9.63923253445141625662/4.22869098049367853065, 60/7.71138601558295633254/4.10435833290808993468, 61/8.69196669127387622211/3.90824219776990533504, 62/9.44311639931323298924/3.24811030480275775290, 63/8.49585055613569295474/2.92766152207898500137, 64/9.24700026417505149823/2.26752962911183697514, 65/7.51526988044477395334/3.12377765721716960101, 66/8.26641958848412983230/2.46364576425002113069, 67/8.58686837120789903111/1.51637992107248265050, 68/7.60628769551697914153/1.71249605621066591787, 69/7.92673647824075100488/0.76523021303312743768, 70/6.85513798747762503893/2.37262794917781638659, 71/7.17558677020139601410/1.42536210600027724027, 72/6.97947063506321185855/0.44478143030935718416, 74/4.92729146860916600303/2.24829530159222912289, 79/4.05180911024450729485/4.83627369972927301234, 80/4.71194100531034543167/5.58742340592423936130, 81/5.46309071973885007623/4.92729152022716387904, 82/4.80295882467301193941/4.17614181403219753008, 83/5.12340759416362878653/3.22887596637804064059, 84/5.87455731178670603754/2.56874408431599920988, 85/6.53468920475385406377/3.31989379235535420065, 86/5.78353949981598969288/3.98002567615430091763, 87/6.73080533989203377843/4.30047446804627586658, 88/5.97965562546352735751/4.96060635374334957248, 100/3.94658383845218052599/2.44377559254727527716, 101/3.19592842240805241616/3.10446950531143617269, 102/3.85569298459696652159/3.85569302214022346931, 103/3.53524420451982734903/4.80295886621308643072, 104/1.58828325871405695580/2.03259063941823514554} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 5/108.69/378.69/0.4/Blue, 74/198.69/528.73/0.4/Green, 9/318.71/438.67/0.4/Orange, 74/198.69/378.69/0.3/Violet, 87/258.69/498.69/0.4/Teal, 23/48.69/318.69/0.4/Lime} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 6/7, 7/3, 7/100, 8/4, 8/36, 9/1, 9/6, 11/9, 11/104, 12/17, 12/13, 13/14, 13/11, 13/15, 14/16, 14/11, 15/14, 15/17, 15/16, 16/18, 16/19, 17/22, 17/18, 18/20, 18/19, 19/20, 19/21, 20/22, 20/21, 21/23, 21/24, 22/23, 23/25, 23/24, 24/25, 24/26, 25/27, 25/26, 26/28, 26/29, 27/103, 27/32, 28/27, 28/30, 29/28, 29/30, 29/31, 30/32, 30/31, 31/33, 31/34, 32/79, 32/80, 33/32, 33/34, 33/35, 34/38, 34/41, 35/32, 35/42, 36/5, 36/38, 37/8, 37/36, 38/5, 39/41, 39/35, 39/34, 39/42, 40/37, 40/38, 41/45, 41/47, 42/88, 42/50, 43/37, 43/40, 44/40, 44/38, 45/42, 45/48, 46/43, 46/44, 47/45, 47/48, 47/49, 48/50, 48/49, 49/51, 49/52, 50/88, 50/51, 51/53, 51/52, 52/53, 52/54, 53/55, 53/54, 54/56, 54/57, 55/60, 55/56, 56/58, 56/57, 57/58, 57/59, 58/60, 58/59, 59/61, 59/62, 60/65, 60/61, 61/63, 61/62, 62/63, 62/64, 63/65, 63/64, 64/66, 64/67, 65/85, 65/66, 66/68, 66/67, 67/68, 67/69, 68/70, 68/69, 69/71, 69/72, 70/84, 70/71, 71/46, 71/72, 72/46, 72/44, 74/8, 74/43, 79/82, 79/80, 80/81, 80/42, 81/86, 81/42, 82/86, 82/81, 83/84, 83/82, 83/86, 84/74, 85/84, 85/70, 86/87, 86/88, 87/85, 87/55, 88/87, 100/74, 101/7, 101/100, 102/82, 102/79, 103/102, 103/32, 104/9} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,9,11,...,72,74,...,74,79,...,88,100,...,104} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-83) -- (p-86); \draw[Green,very thick] (p-47) -- (p-49); \draw[Green,very thick] (p-39) -- (p-34); \draw[Green,very thick] (p-39) -- (p-42); \draw[Green,very thick] (p-33) -- (p-35); \draw[Green,very thick] (p-29) -- (p-31); \draw[Green,very thick] (p-15) -- (p-16); \draw[Green,very thick] (p-13) -- (p-15); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-13) -- (p-15); \draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-15) -- (p-16); \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-34) -- (p-38); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 5/108.69/378.69/0.4/Blue, 74/198.69/528.73/0.4/Green, 9/318.71/438.67/0.4/Orange, 74/198.69/378.69/0.3/Violet, 87/258.69/498.69/0.4/Teal, 23/48.69/318.69/0.4/Lime} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/289, 2/259, 3/139, 4/19, 5/319, 6/49, 7/229, 8/139, 9/169, 11/169, 12/336, 13/319, 14/259, 15/79, 16/229, 17/306, 18/349, 19/229, 20/349, 21/109, 22/36, 23/319, 24/199, 25/19, 26/79, 27/169, 28/229, 29/169, 30/349, 31/49, 32/229, 33/259, 34/169, 35/199, 36/109, 37/169, 38/199, 39/289, 40/289, 41/139, 42/49, 43/49, 44/229, 45/199, 46/109, 47/19, 48/259, 49/109, 50/19, 51/229, 52/49, 53/229, 54/349, 55/81, 56/139, 57/319, 58/259, 59/49, 60/126, 61/169, 62/49, 63/229, 64/19, 65/306, 66/139, 67/19, 68/199, 69/349, 70/319, 71/49, 72/229, 74/96, 79/109, 80/169, 81/289, 82/349, 83/259, 84/199, 85/79, 86/19, 87/349, 88/259, 100/349, 101/109, 102/229, 103/289, 104/49} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Die Linie P34-P38 ist als Symmetrielinie gedacht. Eingabe A(34,38) erzeugt aber eine neue Kante des Graphen. P34 und P38 werden dadurch zu Knoten vom Grad 5 und auf die Bestimmung der Beweglichkeit wirkt sich diese Eingabe ebenfalls als starre Kante aus. Deshalb muss man davor diese Eingabe wieder entfernen. Ich verwende für den Zweck eher Eingabe R(34,38) als zu messender Abstand, aber auch das kann unerwünschte Wirkungen beim Zurechtziehen des Graphen haben. Für dauerhafte Eingabe solcher Hilfslinien wäre eine neue Funktion H(34,38) denkbar. Da wird es vielleicht so sein, dass man spätestens beim fertigen (Rekord-)Graph diese Hilfslinien wieder entfernt, so dass die Eingabevariante als A, R oder H eigentlich egal ist. Ich habe jetzt mit zusätzlicher Eingabe Z(34,38) gefolgt von Button neue Eingabe "egal wie" diese Linie entfernt und dafür im TikZ-Code ergänzt als \draw[red!30,very thick] (p-34) -- (p-38); Außerdem habe ich die Winkel auf die Werte wie in der Vorlage zurückgestellt, ohne das mit Zurechtziehen zu versuchen. Allein fuenfterWinkel von 240.0000005545425° auf 240° ändern macht schon die Kanten passend. 87 Knoten, 3×Grad 2, 6×Grad 3, 74×Grad 4, 2×Grad 5, 2×Grad 7, 0 Überschneidungen 172 Kanten, minimal 0.99999999999998090416, maximal 1.00000000000002309264 einzustellende Kanten, Abstände und Winkel: |P83-P86|=0.99999999999998900879 |P47-P49|=0.99999999999999822364 |P39-P42|=0.99999999999999111822 |P34-P39|=1.00000000000000621725 |P29-P31|=1.00000000000000421885 |P15-P16|=0.99999999999998090416 |P13-P15|=1.00000000000002309264 $ %Eingabe war: % %Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: #1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78); % % % % % % % % % %P[1]=[-36.489648590837135,-1.7967881657507974]; P[2]=[13.517130825300598,-11.798144048978344]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(38,5,4,blauerWinkel); N(36,5,38); N(8,4,36); N(37,8,36); N(40,37,38); N(43,37,40); N(44,40,38); N(46,43,44); N(72,46,44); N(74,8,43); N(71,46,72); N(69,71,72); M(100,74,8,gruenerWinkel); N(7,3,100); N(101,7,100); N(6,1,7); N(9,1,6); M(104,9,1,orangerWinkel); N(11,9,104); M(84,74,8,vierterWinkel); N(70,84,71); N(85,84,70); N(68,70,69); N(67,68,69); N(66,68,67); N(64,66,67); N(65,85,66); N(63,65,64); N(62,63,64); N(61,63,62); N(59,61,62); N(60,65,61); N(58,60,59); N(57,58,59); N(56,58,57); N(54,56,57); N(55,60,56); N(87,85,55); N(53,55,54); N(52,53,54); N(51,53,52); N(49,51,52); M(88,87,85,fuenfterWinkel); N(50,88,51); N(86,87,88); N(42,88,50); N(48,50,49); N(81,86,42); N(82,86,81); N(83,84,82); N(45,42,48); N(47,45,48); N(80,81,42); N(41,45,47); N(79,82,80); N(102,82,79); N(32,79,80); N(35,32,42); N(39,41,35); N(103,102,32); N(27,103,32); N(33,32,35); N(34,33,41); N(31,33,34); N(30,32,31); N(28,27,30); N(29,28,30); N(26,28,29); N(25,27,26); N(24,25,26); N(23,25,24); N(21,23,24); M(22,23,25,sechsterWinkel); N(20,22,21); N(19,20,21); N(18,20,19); N(16,18,19); N(17,22,18); N(14,16,11); N(15,14,17); N(13,14,11); N(12,17,13); %A(83,86); R(83,86,"green"); %A(47,49); R(47,49,"green"); %A(39,42); R(39,42,"green"); %A(34,39); R(34,39,"green"); %A(29,31); R(29,31,"green"); %A(15,16); R(15,16,"green"); %A(13,15); R(13,15,"green"); % % % % % % % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{Lime}{rgb}{0.00,1.00,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.14319698152628790311/0.39223227027636820008, 2/3.12377765721720823677/0.19611613513818415555, 3/2.80332887449343726161/1.14338197831572307983, 4/3.78390955018435803936/0.94726584317753892428, 5/4.10435833290812812635/0.00000000000000000000, 6/2.33931311666447339093/1.37281294596728820068, 7/2.99944500963162230533/2.12396265400664274736, 8/3.98002568532254219491/1.92784651886845925794, 9/1.39204727348693380051/1.05236416324351855778, 11/0.64089756544757969792/1.71249605621066880445, 12/2.24829530159226109731/2.78409454697378100363, 13/1.30102945841471329125/2.46364576425003800608, 14/0.32044878272378984896/2.65976189938820573033, 15/0.98058067569090678894/3.41091160742758869873, 16/0.00000000000000000000/3.60702774256574176803, 17/1.92784651886846236657/3.73136039015130993590, 18/0.94726584317754325415/3.92747652528949986461, 19/0.19611613513819683985/4.58760841825665899307, 20/1.14338197831573951113/4.90805720098041753374, 21/0.39223227027639367970/5.56818909394757710629, 22/2.12396265400665873457/4.71194106584222804912, 23/1.37281294596731218149/5.37207295880938673349, 24/1.05236416324354853380/6.31933880198692765617, 25/2.03294483893446686906/6.12322266684873639520, 26/1.71249605621070455364/7.07048851002627731788, 27/2.78409454697382940935/5.46309077388159458621, 28/2.46364576425006642779/6.41035661705913550890, 29/2.65976189938823948111/7.39093729275005806301, 30/3.41091160742760202140/6.73080539978291625403, 31/3.60702774256578040379/7.71138607547383703178, 32/3.73136039015136500296/5.78353955660537444317, 33/3.92747652528954249718/6.76412023229629522092, 34/4.58760841825669896110/7.51526994033564310627, 35/4.67862623332890148475/6.10398833932915163558, 36/4.30047446804631317008/0.98058067569092011162, 37/4.96060636101346208449/1.73173038373027510239, 38/5.05162417608566727267/0.32044878272377019801, 39/5.33875812629606372184/6.85513804736849596821, 40/5.71175606905281707526/1.07159849076312529981, 41/5.53487426143423633107/7.83571872305941852233, 42/5.65920690901982048615/5.90787220419096215096, 43/5.90787220419100211899/2.05217916645404541143, 44/6.03220485177658805043/0.12433264758558643104, 45/5.85532304415800730624/6.88845287988188026418, 46/6.22832098691477131780/1.10491332327650648715, 47/6.51545493712515710882/7.63960258792123614313, 48/6.83590371984892808399/6.69233674474369699681, 49/7.49603561281607522204/7.44348645278305287576, 50/6.63978758471074126390/5.71175606905277710723, 51/7.29991947767789195467/6.46290577709213209801, 52/8.24718532085543110099/6.78335455981590396135, 53/8.05106918571724960998/5.80277388412498318360, 54/8.99833502889478609177/6.12322266684875593512, 55/7.39093729275010069557/5.05162417608562819282, 56/8.33820313592763717736/5.37207295880940005617, 57/9.31878381161855884329/5.17595682367121678880, 58/8.65865191865140992888/4.42480711563186179802, 59/9.63923259434232981846/4.22869098049367853065, 60/7.71138607547387167074/4.10435833290808904650, 61/8.69196675116479156031/3.90824219776990533504, 62/9.44311645920414832744/3.24811030480275775290, 63/8.49585061602660829294/2.92766152207898455728, 64/9.24700032406596683643/2.26752962911183697514, 65/7.51526994033568840337/3.12377765721716871283, 66/8.26641964837504517050/2.46364576425002113069, 67/8.58686843109881436931/1.51637992107248265050, 68/7.60628775540789447973/1.71249605621066591787, 69/7.92673653813166634308/0.76523021303312743768, 70/6.85513804736854037714/2.37262794917781638659, 71/7.17558683009231135230/1.42536210600027724027, 72/6.97947069495412630857/0.44478143030935718416, 74/4.92729152850008134124/2.24829530159222912289, 79/4.05180917287513064906/4.83627371342783263231, 80/4.71194106584228400436/5.58742342146718407037, 81/5.46309077388164254785/4.92729152850003959685, 82/4.80295888091449008073/4.17614182046068815879, 83/5.12340766363826904950/3.22887597728315212109, 84/5.87455737167762048756/2.56874408431599920988, 85/6.53468926464476940197/3.31989379235535508883, 86/5.78353955660540997030/3.98002568532249956235, 87/6.73080539978294734027/4.30047446804627675476, 88/5.97965569174358790860/4.96060636101342122828, 100/3.94671085280916145166/2.44441143673041416662, 101/3.19556114476980601680/3.10454332969756263694, 102/3.85569303773695315485/3.85569303773691141046, 103/3.53524425501318972920/4.80295888091445277723, 104/1.58816340862511906629/2.03294483893443844735} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 5/108.69/378.69/0.4/Blue, 74/198.69/528.69/0.4/Green, 9/318.69/438.69/0.4/Orange, 74/198.69/378.69/0.3/Violet, 87/258.69/498.69/0.4/Teal, 23/48.69/318.69/0.4/Lime} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 6/7, 7/3, 7/100, 8/4, 8/36, 9/1, 9/6, 11/9, 11/104, 12/17, 12/13, 13/14, 13/11, 13/15, 14/16, 14/11, 15/14, 15/17, 15/16, 16/18, 16/19, 17/22, 17/18, 18/20, 18/19, 19/20, 19/21, 20/22, 20/21, 21/23, 21/24, 22/23, 23/25, 23/24, 24/25, 24/26, 25/27, 25/26, 26/28, 26/29, 27/103, 27/32, 28/27, 28/30, 29/28, 29/30, 29/31, 30/32, 30/31, 31/33, 31/34, 32/79, 32/80, 33/32, 33/35, 34/33, 34/41, 34/39, 35/32, 35/42, 36/5, 36/38, 37/8, 37/36, 38/5, 39/41, 39/35, 39/42, 40/37, 40/38, 41/45, 41/47, 42/88, 42/50, 43/37, 43/40, 44/40, 44/38, 45/42, 45/48, 46/43, 46/44, 47/45, 47/48, 47/49, 48/50, 48/49, 49/51, 49/52, 50/88, 50/51, 51/53, 51/52, 52/53, 52/54, 53/55, 53/54, 54/56, 54/57, 55/60, 55/56, 56/58, 56/57, 57/58, 57/59, 58/60, 58/59, 59/61, 59/62, 60/65, 60/61, 61/63, 61/62, 62/63, 62/64, 63/65, 63/64, 64/66, 64/67, 65/85, 65/66, 66/68, 66/67, 67/68, 67/69, 68/70, 68/69, 69/71, 69/72, 70/84, 70/71, 71/46, 71/72, 72/46, 72/44, 74/8, 74/43, 79/82, 79/80, 80/81, 80/42, 81/86, 81/42, 82/86, 82/81, 83/84, 83/82, 83/86, 84/74, 85/84, 85/70, 86/87, 86/88, 87/85, 87/55, 88/87, 100/74, 101/7, 101/100, 102/82, 102/79, 103/102, 103/32, 104/9} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,9,11,...,72,74,...,74,79,...,88,100,...,104} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-83) -- (p-86); \draw[Green,very thick] (p-47) -- (p-49); \draw[Green,very thick] (p-39) -- (p-42); \draw[Green,very thick] (p-34) -- (p-39); \draw[Green,very thick] (p-29) -- (p-31); \draw[Green,very thick] (p-15) -- (p-16); \draw[Green,very thick] (p-13) -- (p-15); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 5/108.69/378.69/0.4/Blue, 74/198.69/528.69/0.4/Green, 9/318.69/438.69/0.4/Orange, 74/198.69/378.69/0.3/Violet, 87/258.69/498.69/0.4/Teal, 23/48.69/318.69/0.4/Lime} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/199, 2/259, 3/139, 4/19, 5/319, 6/49, 7/229, 8/139, 9/169, 11/259, 12/336, 13/319, 14/259, 15/79, 16/229, 17/306, 18/289, 19/229, 20/49, 21/109, 22/36, 23/259, 24/199, 25/19, 26/79, 27/169, 28/289, 29/169, 30/349, 31/49, 32/139, 33/259, 34/169, 35/199, 36/109, 37/169, 38/199, 39/289, 40/289, 41/139, 42/49, 43/49, 44/229, 45/259, 46/109, 47/19, 48/259, 49/109, 50/19, 51/229, 52/109, 53/289, 54/349, 55/81, 56/139, 57/319, 58/199, 59/49, 60/246, 61/169, 62/49, 63/229, 64/19, 65/306, 66/139, 67/19, 68/199, 69/349, 70/319, 71/49, 72/229, 74/276, 79/109, 80/19, 81/289, 82/139, 83/259, 84/199, 85/79, 86/229, 87/349, 88/259, 100/349, 101/109, 102/229, 103/289, 104/49} \node[anchor=\a] (P\i) at (p-\i) {\i}; %nachträglich Hilfslinie ergänzt: \draw[red!30,very thick] (p-34) -- (p-38); \end{tikzpicture} $ Jetzt sind nur noch P82 und P86 Knoten vom Grad 5. Dann habe ich den Graph symmetrisch ergänzt 89 Knoten, 2×Grad 3, 82×Grad 4, 2×Grad 5, 1×Grad 6, 2×Grad 7, 0 Überschneidungen 182 Kanten, minimal 0.99999999999998090416, maximal 1.00000000000002309264 einzustellende Kanten, Abstände und Winkel: |P83-P86|=0.99999999999998900879 |P47-P49|=0.99999999999999822364 |P39-P42|=0.99999999999999111822 |P34-P39|=1.00000000000000621725 |P29-P31|=1.00000000000000421885 |P15-P16|=0.99999999999998090416 |P13-P15|=1.00000000000002309264 $ %Eingabe war: % %Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: #1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78); % % % % % % % % % %P[1]=[-36.489648590837135,-1.7967881657507974]; P[2]=[13.517130825300598,-11.798144048978344]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(38,5,4,blauerWinkel); N(36,5,38); N(8,4,36); N(37,8,36); N(40,37,38); N(43,37,40); N(44,40,38); N(46,43,44); N(72,46,44); N(74,8,43); N(71,46,72); N(69,71,72); M(100,74,8,gruenerWinkel); N(7,3,100); N(101,7,100); N(6,1,7); N(9,1,6); M(104,9,1,orangerWinkel); N(11,9,104); M(84,74,8,vierterWinkel); N(70,84,71); N(85,84,70); N(68,70,69); N(67,68,69); N(66,68,67); N(64,66,67); N(65,85,66); N(63,65,64); N(62,63,64); N(61,63,62); N(59,61,62); N(60,65,61); N(58,60,59); N(57,58,59); N(56,58,57); N(54,56,57); N(55,60,56); N(87,85,55); N(53,55,54); N(52,53,54); N(51,53,52); N(49,51,52); M(88,87,85,fuenfterWinkel); N(50,88,51); N(86,87,88); N(42,88,50); N(48,50,49); N(81,86,42); N(82,86,81); N(83,84,82); N(45,42,48); N(47,45,48); N(80,81,42); N(41,45,47); N(79,82,80); N(102,82,79); N(32,79,80); N(35,32,42); N(39,41,35); N(103,102,32); N(27,103,32); N(33,32,35); N(34,33,41); N(31,33,34); N(30,32,31); N(28,27,30); N(29,28,30); N(26,28,29); N(25,27,26); N(24,25,26); N(23,25,24); N(21,23,24); M(22,23,25,sechsterWinkel); N(20,22,21); N(19,20,21); N(18,20,19); N(16,18,19); N(17,22,18); N(14,16,11); N(15,14,17); N(13,14,11); N(12,17,13); %A(83,86); R(83,86,"green"); %A(47,49); R(47,49,"green"); %A(39,42); R(39,42,"green"); %A(34,39); R(34,39,"green"); %A(29,31); R(29,31,"green"); %A(15,16); R(15,16,"green"); %A(13,15); R(13,15,"green"); A(6,104); A(104,12); A(12,101); L(10,82,102); A(100,10); N(73,101,102); A(73,22); A(73,103); % % % % % % % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{Lime}{rgb}{0.00,1.00,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.14319698152628790311/0.39223227027636820008, 2/3.12377765721720823677/0.19611613513818415555, 3/2.80332887449343726161/1.14338197831572307983, 4/3.78390955018435803936/0.94726584317753892428, 5/4.10435833290812812635/0.00000000000000000000, 6/2.33931311666447339093/1.37281294596728820068, 7/2.99944500963162230533/2.12396265400664274736, 8/3.98002568532254219491/1.92784651886845925794, 9/1.39204727348693380051/1.05236416324351855778, 10/4.60684274577631214243/3.19556114476976693695, 11/0.64089756544757969792/1.71249605621066880445, 12/2.24829530159226109731/2.78409454697378100363, 13/1.30102945841471329125/2.46364576425003800608, 14/0.32044878272378984896/2.65976189938820573033, 15/0.98058067569090678894/3.41091160742758869873, 16/0.00000000000000000000/3.60702774256574176803, 17/1.92784651886846236657/3.73136039015130993590, 18/0.94726584317754325415/3.92747652528949986461, 19/0.19611613513819683985/4.58760841825665899307, 20/1.14338197831573951113/4.90805720098041753374, 21/0.39223227027639367970/5.56818909394757710629, 22/2.12396265400665873457/4.71194106584222804912, 23/1.37281294596731218149/5.37207295880938673349, 24/1.05236416324354853380/6.31933880198692765617, 25/2.03294483893446686906/6.12322266684873639520, 26/1.71249605621070455364/7.07048851002627731788, 27/2.78409454697382940935/5.46309077388159458621, 28/2.46364576425006642779/6.41035661705913550890, 29/2.65976189938823948111/7.39093729275005806301, 30/3.41091160742760202140/6.73080539978291625403, 31/3.60702774256578040379/7.71138607547383703178, 32/3.73136039015136500296/5.78353955660537444317, 33/3.92747652528954249718/6.76412023229629522092, 34/4.58760841825669896110/7.51526994033564310627, 35/4.67862623332890148475/6.10398833932915163558, 36/4.30047446804631317008/0.98058067569092011162, 37/4.96060636101346208449/1.73173038373027510239, 38/5.05162417608566727267/0.32044878272377019801, 39/5.33875812629606372184/6.85513804736849596821, 40/5.71175606905281707526/1.07159849076312529981, 41/5.53487426143423633107/7.83571872305941852233, 42/5.65920690901982048615/5.90787220419096215096, 43/5.90787220419100211899/2.05217916645404541143, 44/6.03220485177658805043/0.12433264758558643104, 45/5.85532304415800730624/6.88845287988188026418, 46/6.22832098691477131780/1.10491332327650648715, 47/6.51545493712515710882/7.63960258792123614313, 48/6.83590371984892808399/6.69233674474369699681, 49/7.49603561281607522204/7.44348645278305287576, 50/6.63978758471074126390/5.71175606905277710723, 51/7.29991947767789195467/6.46290577709213209801, 52/8.24718532085543110099/6.78335455981590396135, 53/8.05106918571724960998/5.80277388412498318360, 54/8.99833502889478609177/6.12322266684875593512, 55/7.39093729275010069557/5.05162417608562819282, 56/8.33820313592763717736/5.37207295880940005617, 57/9.31878381161855884329/5.17595682367121678880, 58/8.65865191865140992888/4.42480711563186179802, 59/9.63923259434232981846/4.22869098049367853065, 60/7.71138607547387167074/4.10435833290808904650, 61/8.69196675116479156031/3.90824219776990533504, 62/9.44311645920414832744/3.24811030480275775290, 63/8.49585061602660829294/2.92766152207898455728, 64/9.24700032406596683643/2.26752962911183697514, 65/7.51526994033568840337/3.12377765721716871283, 66/8.26641964837504517050/2.46364576425002113069, 67/8.58686843109881436931/1.51637992107248265050, 68/7.60628775540789447973/1.71249605621066591787, 69/7.92673653813166634308/0.76523021303312743768, 70/6.85513804736854037714/2.37262794917781638659, 71/7.17558683009231135230/1.42536210600027724027, 72/6.97947069495412630857/0.44478143030935718416, 73/2.87511236204603459754/4.05180917287510133917, 74/4.92729152850008134124/2.24829530159222912289, 79/4.05180917287513064906/4.83627371342783263231, 80/4.71194106584228400436/5.58742342146718407037, 81/5.46309077388164254785/4.92729152850003959685, 82/4.80295888091449008073/4.17614182046068815879, 83/5.12340766363826904950/3.22887597728315212109, 84/5.87455737167762048756/2.56874408431599920988, 85/6.53468926464476940197/3.31989379235535508883, 86/5.78353955660540997030/3.98002568532249956235, 87/6.73080539978294734027/4.30047446804627675476, 88/5.97965569174358790860/4.96060636101342122828, 100/3.94671085280916145166/2.44441143673041416662, 101/3.19556114476980601680/3.10454332969756263694, 102/3.85569303773695315485/3.85569303773691141046, 103/3.53524425501318972920/4.80295888091445277723, 104/1.58816340862511906629/2.03294483893443844735} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 5/108.69/378.69/0.4/Blue, 74/198.69/528.69/0.4/Green, 9/318.69/438.69/0.4/Orange, 74/198.69/378.69/0.3/Violet, 87/258.69/498.69/0.4/Teal, 23/48.69/318.69/0.4/Lime} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 6/7, 6/104, 7/3, 7/100, 8/4, 8/36, 9/1, 9/6, 10/82, 10/102, 11/9, 11/104, 12/17, 12/13, 12/101, 13/14, 13/11, 13/15, 14/16, 14/11, 15/14, 15/17, 15/16, 16/18, 16/19, 17/22, 17/18, 18/20, 18/19, 19/20, 19/21, 20/22, 20/21, 21/23, 21/24, 22/23, 23/25, 23/24, 24/25, 24/26, 25/27, 25/26, 26/28, 26/29, 27/103, 27/32, 28/27, 28/30, 29/28, 29/30, 29/31, 30/32, 30/31, 31/33, 31/34, 32/79, 32/80, 33/32, 33/35, 34/33, 34/41, 34/39, 35/32, 35/42, 36/5, 36/38, 37/8, 37/36, 38/5, 39/41, 39/35, 39/42, 40/37, 40/38, 41/45, 41/47, 42/88, 42/50, 43/37, 43/40, 44/40, 44/38, 45/42, 45/48, 46/43, 46/44, 47/45, 47/48, 47/49, 48/50, 48/49, 49/51, 49/52, 50/88, 50/51, 51/53, 51/52, 52/53, 52/54, 53/55, 53/54, 54/56, 54/57, 55/60, 55/56, 56/58, 56/57, 57/58, 57/59, 58/60, 58/59, 59/61, 59/62, 60/65, 60/61, 61/63, 61/62, 62/63, 62/64, 63/65, 63/64, 64/66, 64/67, 65/85, 65/66, 66/68, 66/67, 67/68, 67/69, 68/70, 68/69, 69/71, 69/72, 70/84, 70/71, 71/46, 71/72, 72/46, 72/44, 73/101, 73/102, 73/22, 73/103, 74/8, 74/43, 79/82, 79/80, 80/81, 80/42, 81/86, 81/42, 82/86, 82/81, 83/84, 83/82, 83/86, 84/74, 85/84, 85/70, 86/87, 86/88, 87/85, 87/55, 88/87, 100/74, 100/10, 101/7, 101/100, 102/82, 102/79, 103/102, 103/32, 104/9, 104/12} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,74,79,...,88,100,...,104} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-83) -- (p-86); \draw[Green,very thick] (p-47) -- (p-49); \draw[Green,very thick] (p-39) -- (p-42); \draw[Green,very thick] (p-34) -- (p-39); \draw[Green,very thick] (p-29) -- (p-31); \draw[Green,very thick] (p-15) -- (p-16); \draw[Green,very thick] (p-13) -- (p-15); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 5/108.69/378.69/0.4/Blue, 74/198.69/528.69/0.4/Green, 9/318.69/438.69/0.4/Orange, 74/198.69/378.69/0.3/Violet, 87/258.69/498.69/0.4/Teal, 23/48.69/318.69/0.4/Lime} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/199, 2/259, 3/139, 4/19, 5/319, 6/349, 7/229, 8/139, 9/169, 10/289, 11/259, 12/336, 13/319, 14/259, 15/79, 16/229, 17/306, 18/289, 19/229, 20/49, 21/109, 22/111, 23/259, 24/199, 25/19, 26/79, 27/169, 28/289, 29/169, 30/349, 31/49, 32/139, 33/259, 34/169, 35/199, 36/109, 37/169, 38/199, 39/289, 40/289, 41/139, 42/49, 43/49, 44/229, 45/259, 46/109, 47/19, 48/259, 49/109, 50/19, 51/229, 52/109, 53/289, 54/349, 55/81, 56/139, 57/319, 58/199, 59/49, 60/246, 61/169, 62/49, 63/229, 64/19, 65/306, 66/139, 67/19, 68/199, 69/349, 70/319, 71/49, 72/229, 73/199, 74/276, 79/109, 80/19, 81/289, 82/139, 83/259, 84/199, 85/79, 86/229, 87/349, 88/259, 100/349, 101/109, 102/229, 103/79, 104/49} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ doch nach Button neueEingabe "egal wie" und Button "beweglich?" wird keine Beweglichkeit ausgegeben. In der Ableitungsmatrix müsste theoretisch erste Spalte die Summe der zweiten und dritten Spalten sein, doch ist das nur in sehr grober Näherung der Fall \sourceon nameDerSprache Ableitungsmatrix=[ [-0.00020518752155596065,-0.00019200642046779404,-0.00007235821178419588], [-0.00020518050403905974,-0.00019200027561239175,-0.00007235733909483066], [-0.00035543821498229544,-0.00033260384594824277,-0.00012533213008014688], [ 0.00010265381224616732, 0.00009605693310166252, 0.00003618543300720756], [-0.00010259927480993358,-0.0000960084189659538, -0.000036179412317483006], [-0.00041427791714809814,-0.00038764095470056326,-0.00014585726667082355], [-0.00047462727693481366,-0.0004441365001471853, -0.00016751482371002435], [ 0.0006161028637529098, 0.0005766861652777289, 0.00021850824323588203], [ 0.0008300157668484909, 0.0007768310904954223, 0.00029378737916463393], [-0.0010951731045960589, -0.0010250026502605092, -0.00038765391139761185] ]; \sourceoff So grob, dass eine daraus abgeleitete näherungsweise Abhängigkeit der Winkel den Graph bei der Animation verziehen würde. Button "egal wie" ist also nicht geeignet, war bei Graph #1900-8 auch schon mal so. Statt "egal wie" Button "Rahmen zuerst" verwenden funktioniert auch nicht $ %Eingabe war: % %Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: #1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78); % % % % % % % % % % % % % % % % %P[5]=[63.52391024143834,-21.799499932205897]; P[2]=[13.517130825300598,-11.798144048978344]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(9,1,2,blauerWinkel); N(6,9,1); N(104,9,6); N(11,9,104); M(14,11,9,gruenerWinkel); N(13,14,11); N(15,14,13); N(16,14,15); M(19,16,14,orangerWinkel); N(18,19,16); N(20,19,18); N(21,19,20); M(24,21,19,vierterWinkel); N(23,24,21); N(25,24,23); N(26,24,25); M(29,26,24,fuenfterWinkel); N(28,29,26); N(30,29,28); N(31,29,30); M(34,31,29,sechsterWinkel); N(33,34,31); M(41,34,31,siebenterWinkel); N(39,41,34); M(47,41,34,achterWinkel); N(45,47,41); N(48,47,45); N(49,47,48); M(52,49,47,neunterWinkel); N(51,52,49); N(53,52,51); N(54,52,53); M(57,54,52,zehnterWinkel); N(56,57,54); N(58,57,56); N(59,57,58); M(62,59,57,elfterWinkel); N(61,62,59); N(63,62,61); N(64,62,63); M(67,64,62,zwölfterWinkel); N(66,67,64); N(68,67,66); N(69,67,68); M(72,69,67,dreizehnterWinkel); N(71,72,69); N(46,72,71); N(44,72,46); Q(38,44,5,1*D,1*D); A(38,44); A(38,5); H(38,5,38,1); A(38,5); L(36,5,38); H(38,44,38,1); A(38,44); L(40,38,44); N(7,6,3); N(8,4,36); N(12,13,104); N(17,18,15); N(22,23,20); N(27,28,25); N(32,33,30); N(35,39,32); N(37,36,40); N(42,45,39); N(43,40,46); N(50,51,48); N(55,56,53); N(60,61,58); N(65,66,63); N(70,71,68); N(74,8,43); N(80,42,32); N(81,42,80); N(84,74,70); N(85,84,70); N(87,85,55); N(88,87,50); N(100,7,74); N(101,7,100); N(103,32,27); N(73,103,22); N(79,80,32); N(82,81,79); N(83,84,82); N(86,87,88); N(102,79,103); N(10,102,100); %A(17,12); R(17,12,"green"); %A(22,17); R(22,17,"green"); %A(32,27); R(32,27,"green"); %A(35,33); R(35,33,"green"); %A(37,8); R(37,8,"green"); %A(42,35); R(42,35,"green"); %A(43,37); R(43,37,"green"); %A(50,42); R(50,42,"green"); %A(60,55); R(60,55,"green"); %A(65,60); R(65,60,"green"); %A(85,65); R(85,65,"green"); %A(88,42); R(88,42,"green"); %A(101,12); R(101,12,"green"); %A(73,101); R(73,101,"green"); %A(86,81); R(86,81,"green"); %A(86,82); R(86,82,"green"); %A(86,83); R(86,83,"green"); %A(102,73); R(102,73,"green"); %A(102,82); R(102,82,"green"); %A(10,82); R(10,82,"green"); % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LightBlue}{rgb}{0.68,0.84,0.90} \definecolor{LightCoral}{rgb}{0.94,0.50,0.50} \definecolor{LightCyan}{rgb}{0.88,1.00,1.00} \definecolor{LightGoldenrodYellow}{rgb}{0.98,0.98,0.82} \definecolor{LightGreen}{rgb}{0.56,0.93,0.56} \definecolor{LightGray}{rgb}{0.82,0.82,0.82} \definecolor{LightPink}{rgb}{1.00,0.71,0.75} \definecolor{Lime}{rgb}{0.00,1.00,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.14319698152628612675/0.58834840541445643236, 2/3.12377765721720601633/0.39223227027627233232, 3/2.80332887449343548525/1.33949811345381131211, 4/3.78390955018435537482/1.14338197831562715656, 5/4.10435833290812634999/0.19611613513808820453, 6/2.33931311666447072639/1.56892908110537643296, 7/2.99944500963162052898/2.32007878914473142373, 8/4.44404144315143145860/1.89453168635504676232, 9/1.39204727348693180211/1.24848029838160634597, 10/4.63549016707257255376/3.42577687572095745949, 11/0.64089756544757736645/1.90861219134875614856, 12/2.24829530159225132735/2.98021068211189366082, 13/1.30102945841471262511/2.65976189938812357383, 14/0.32044878272378868322/2.85587803452628863354, 15/0.98058067569092388638/3.60702774256565561473, 16/0.00000000000000000000/3.80314387770382111853, 17/1.92784651886846680746/3.92747652528941371131, 18/0.94726584317754314313/4.12359266042757965920, 19/0.19611613513819681209/4.78372455339473834357, 20/1.14338197831573973318/5.10417333611849777242, 21/0.39223227027639334663/5.76430522908565645679, 22/2.12396265400665829048/4.90805720098030562326, 23/1.37281294596731262558/5.56818909394746519581, 24/1.05236416324354786767/6.51545493712500700667, 25/2.03294483893446686906/6.31933880198681574569, 26/1.71249605621070277728/7.26660464516435755655, 27/2.78409454697383118571/5.65920690901967660125, 28/2.46364576425006553961/6.60647275219721752393, 29/2.65976189938823770476/7.58705342788813918986, 30/3.41091160742760113322/6.92692153492099915724, 31/3.60702774256577285428/7.90750221061192259953, 32/3.73136039015136944386/5.97965569174346001091, 33/3.92747652528954072082/6.96023636743438256502, 34/4.58760841825669185567/7.71138607547373577944, 35/4.67862623332890592565/6.30010447446724075604, 36/4.76449022587520243377/0.94726584317750806008, 37/4.96060636101347451898/1.92784651886841040813, 38/5.08493900859906666767/0.00000000000000000000, 39/5.33875812629605395188/7.05125418250659485864, 40/5.28105514373733608835/0.98058067569090268112, 41/5.53487426143422744929/8.03183485819751830093, 42/5.65920690901983380883/6.10398833932905837685, 43/5.47717127887551402665/1.96116135138182445807, 44/6.03220485177663334753/0.32044878272368765293, 45/5.85532304415800641806/7.08456901501998093096, 46/6.22832098691481128583/1.30102945841460915233, 47/6.51545493712514911522/7.83571872305934213898, 48/6.83590371984892719581/6.88845287988180476901, 49/7.49603561281607078115/7.63960258792116508886, 50/6.63978758471075103387/5.90787220419088310308, 51/7.29991947767789284285/6.65902191223024342293, 52/8.24718532085543110099/6.97947069495402061534, 53/8.05106918571725316269/5.99889001926310072577, 54/8.99833502889478964448/6.31933880198687703000, 55/7.39093729275010868918/5.24774031122374129410, 56/8.33820313592764605914/5.56818909394751582198, 57/9.31878381161856772508/5.37207295880934054821, 58/8.65865191865142413974/4.62092325076997934019, 59/9.63923259434234580567/4.42480711563180406642, 60/7.71138607547388676977/4.30047446804620125960, 61/8.69196675116480932388/4.10435833290802509765, 62/9.44311645920416964373/3.44422643994088240049, 63/8.49585061602663493829/3.12377765721710343172, 64/9.24700032406599525814/2.46364576424996073456, 65/7.51526994033571238418/3.31989379235528048184, 66/8.26641964837507359221/2.65976189938813734059, 67/8.58686843109884989644/1.71249605621060108085, 68/7.60628775540792911869/1.90861219134877813097, 69/7.92673653813170631111/0.96134634817124176021, 70/6.85513804736856968702/2.56874408431592238244, 71/7.17558683009234687944/1.62147824113838634474, 72/6.97947069495417071749/0.64089756544746501188, 73/2.87511236204604037070/4.24792530801318690692, 74/4.90554055252159226796/2.78167235843053406441, 79/4.05180917287515729441/5.03238984856592619366, 80/4.71194106584229377432/5.78353955660529361893, 81/5.46309077388164432421/5.12340766363813937545, 82/4.80295888091450873247/4.37225795559877283836, 83/5.05670531104646059362/3.40498718213598960958, 84/5.90162384978413090408/2.87009218038573887810, 85/6.63935605515488447281/3.54518565032809007675, 86/5.73286360248155624220/4.22390528715468605014, 87/6.68012944565909361216/4.54435406987846324256, 88/5.92897973761973418050/5.20448596284560860425, 100/3.90635136856714959563/2.74141102873992270617, 101/3.08801376617655742862/3.31614885463414399425, 102/3.85569303773698246474/4.05180917287500363955, 103/3.53524425501319505827/4.99907501605253745680, 104/1.58816340862511640175/2.22906097407252667963} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/348.69/498.69/0.4/Blue, 11/318.69/468.69/0.4/Green, 16/288.69/438.69/0.4/Orange, 21/258.69/408.69/0.4/Violet, 26/228.69/378.69/0.4/Teal, 31/198.69/348.69/0.4/Lime, 34/168.69/378.69/0.4/LightBlue, 41/198.69/348.69/0.4/LightCoral, 49/168.69/318.69/0.4/LightCyan, 54/138.69/288.69/0.4/LightGoldenrodYellow, 59/108.69/258.69/0.4/LightGreen, 64/78.69/228.69/0.4/LightGray, 69/48.69/198.69/0.4/LightPink} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 1/3, 2/5, 3/2, 3/4, 4/2, 4/5, 6/9, 6/1, 7/6, 7/3, 8/4, 8/36, 9/1, 10/102, 10/100, 10/82, 11/9, 11/104, 12/13, 12/104, 13/14, 13/11, 14/11, 15/14, 15/13, 16/14, 16/15, 17/18, 17/15, 17/12, 18/19, 18/16, 19/16, 20/19, 20/18, 21/19, 21/20, 22/23, 22/20, 22/17, 23/24, 23/21, 24/21, 25/24, 25/23, 26/24, 26/25, 27/28, 27/25, 28/29, 28/26, 29/26, 30/29, 30/28, 31/29, 31/30, 32/33, 32/30, 32/27, 33/34, 33/31, 34/31, 35/39, 35/32, 35/33, 36/5, 36/38, 37/36, 37/40, 37/8, 38/5, 38/44, 39/41, 39/34, 40/38, 40/44, 41/34, 42/45, 42/39, 42/35, 43/40, 43/46, 43/37, 44/72, 44/46, 45/47, 45/41, 46/72, 46/71, 47/41, 48/47, 48/45, 49/47, 49/48, 50/51, 50/48, 50/42, 51/52, 51/49, 52/49, 53/52, 53/51, 54/52, 54/53, 55/56, 55/53, 56/57, 56/54, 57/54, 58/57, 58/56, 59/57, 59/58, 60/61, 60/58, 60/55, 61/62, 61/59, 62/59, 63/62, 63/61, 64/62, 64/63, 65/66, 65/63, 65/60, 66/67, 66/64, 67/64, 68/67, 68/66, 69/67, 69/68, 70/71, 70/68, 71/72, 71/69, 72/69, 73/103, 73/22, 73/101, 74/8, 74/43, 79/80, 79/32, 80/42, 80/32, 81/42, 81/80, 82/81, 82/79, 83/84, 83/82, 84/74, 84/70, 85/84, 85/70, 85/65, 86/87, 86/88, 86/81, 86/82, 86/83, 87/85, 87/55, 88/87, 88/50, 88/42, 100/7, 100/74, 101/7, 101/100, 101/12, 102/79, 102/103, 102/73, 102/82, 103/32, 103/27, 104/9, 104/6} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,74,79,...,88,100,...,104} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-17) -- (p-12); \draw[Green,very thick] (p-22) -- (p-17); \draw[Green,very thick] (p-32) -- (p-27); \draw[Green,very thick] (p-35) -- (p-33); \draw[Green,very thick] (p-37) -- (p-8); \draw[Green,very thick] (p-42) -- (p-35); \draw[Green,very thick] (p-43) -- (p-37); \draw[Green,very thick] (p-50) -- (p-42); \draw[Green,very thick] (p-60) -- (p-55); \draw[Green,very thick] (p-65) -- (p-60); \draw[Green,very thick] (p-85) -- (p-65); \draw[Green,very thick] (p-88) -- (p-42); \draw[Green,very thick] (p-101) -- (p-12); \draw[Green,very thick] (p-73) -- (p-101); \draw[Green,very thick] (p-86) -- (p-81); \draw[Green,very thick] (p-86) -- (p-82); \draw[Green,very thick] (p-86) -- (p-83); \draw[Green,very thick] (p-102) -- (p-73); \draw[Green,very thick] (p-102) -- (p-82); \draw[Green,very thick] (p-10) -- (p-82); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); \draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-10) -- (p-82); \draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-37) -- (p-8); \draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-43) -- (p-37); \draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-73) -- (p-101); \draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-85) -- (p-65); \draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-86) -- (p-81); \draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-86) -- (p-82); \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-86) -- (p-83); \draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-88) -- (p-42); \draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-101) -- (p-12); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/348.69/498.69/0.4/Blue, 11/318.69/468.69/0.4/Green, 16/288.69/438.69/0.4/Orange, 21/258.69/408.69/0.4/Violet, 26/228.69/378.69/0.4/Teal, 31/198.69/348.69/0.4/Lime, 34/168.69/378.69/0.4/LightBlue, 41/198.69/348.69/0.4/LightCoral, 49/168.69/318.69/0.4/LightCyan, 54/138.69/288.69/0.4/LightGoldenrodYellow, 59/108.69/258.69/0.4/LightGreen, 64/78.69/228.69/0.4/LightGray, 69/48.69/198.69/0.4/LightPink} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/289, 2/319, 3/139, 4/19, 5/319, 6/49, 7/235, 8/216, 9/289, 10/291, 11/169, 12/248, 13/19, 14/199, 15/19, 16/139, 17/306, 18/289, 19/109, 20/349, 21/199, 22/111, 23/319, 24/139, 25/319, 26/169, 27/169, 28/229, 29/49, 30/349, 31/49, 32/49, 33/109, 34/19, 35/199, 36/79, 37/41, 38/229, 39/289, 40/109, 41/49, 42/319, 43/337, 44/229, 45/259, 46/169, 47/79, 48/259, 49/109, 50/306, 51/169, 52/49, 53/229, 54/349, 55/79, 56/199, 57/19, 58/199, 59/49, 60/126, 61/109, 62/349, 63/169, 64/289, 65/305, 66/139, 67/19, 68/199, 69/349, 70/312, 71/49, 72/349, 73/199, 74/157, 79/109, 80/169, 81/289, 82/349, 83/192, 84/192, 85/72, 86/21, 87/349, 88/109, 100/355, 101/115, 102/319, 103/289, 104/49} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ doch da fällt mir ein, dass das ein schonmal erkannter Fehler ist. Button "Rahmen zuerst" beginnt beim untersten Punkt des Graphen, hier P5 und baut dann im Uhrzeigersinn den Rahmen auf mit Winkeln in P1, P11, P16 ... bis P69 und schließt dann den Rahmen ohne weitere Winkel zurück nach P5. Wenn dort der Rahmen zufällig nach innen gedrückt ist, wird er nach außen geschlossen und das ist der Fehler. Als Notbehelf habe ich dann immer den Graph etwas gedreht, so dass ein anderer Punkt der unterste ist, hier mit Button "Ausrichten von P11 nach P5" 89 Knoten, 2×Grad 3, 82×Grad 4, 2×Grad 5, 1×Grad 6, 2×Grad 7, 0 Überschneidungen 182 Kanten, minimal 0.99999999999993116617, maximal 1.00000000000009969803 einzustellende Kanten, Abstände und Winkel: |P83-P86|=0.99999999999997657429 |P47-P49|=0.99999999999999344968 |P39-P42|=0.99999999999999167333 |P34-P39|=0.99999999999998245848 |P29-P31|=1.00000000000000399680 |P15-P16|=0.99999999999993116617 |P13-P15|=1.00000000000009969803 $ %Eingabe war: % %Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: #1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78); % % % % % % % % % %P[1]=[-14.583726446083169,39.134801773829274]; P[2]=[34.67569802050004,52.33382477927216]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(38,5,4,blauerWinkel); N(36,5,38); N(8,4,36); N(37,8,36); N(40,37,38); N(43,37,40); N(44,40,38); N(46,43,44); N(72,46,44); N(74,8,43); N(71,46,72); N(69,71,72); M(100,74,8,gruenerWinkel); N(7,3,100); N(101,7,100); N(6,1,7); N(9,1,6); M(104,9,1,orangerWinkel); N(11,9,104); M(84,74,8,vierterWinkel); N(70,84,71); N(85,84,70); N(68,70,69); N(67,68,69); N(66,68,67); N(64,66,67); N(65,85,66); N(63,65,64); N(62,63,64); N(61,63,62); N(59,61,62); N(60,65,61); N(58,60,59); N(57,58,59); N(56,58,57); N(54,56,57); N(55,60,56); N(87,85,55); N(53,55,54); N(52,53,54); N(51,53,52); N(49,51,52); M(88,87,85,fuenfterWinkel); N(50,88,51); N(86,87,88); N(42,88,50); N(48,50,49); N(81,86,42); N(82,86,81); N(83,84,82); N(45,42,48); N(47,45,48); N(80,81,42); N(41,45,47); N(79,82,80); N(102,82,79); N(32,79,80); N(35,32,42); N(39,41,35); N(103,102,32); N(27,103,32); N(33,32,35); N(34,33,41); N(31,33,34); N(30,32,31); N(28,27,30); N(29,28,30); N(26,28,29); N(25,27,26); N(24,25,26); N(23,25,24); N(21,23,24); M(22,23,25,sechsterWinkel); N(20,22,21); N(19,20,21); N(18,20,19); N(16,18,19); N(17,22,18); N(14,16,11); N(15,14,17); N(13,14,11); N(12,17,13); %A(83,86); R(83,86,"green"); %A(47,49); R(47,49,"green"); %A(39,42); R(39,42,"green"); %A(34,39); R(34,39,"green"); %A(29,31); R(29,31,"green"); %A(15,16); R(15,16,"green"); %A(13,15); R(13,15,"green"); A(6,104); A(104,12); A(12,101); L(10,82,102); A(100,10); N(73,101,102); A(73,22); A(73,103); % % % % % % % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{Lime}{rgb}{0.00,1.00,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/3.86370330515631721369/0.00000000000000000000, 2/4.82962913144538585897/0.25881904510252129459, 3/4.12252235025883706498/0.96592582628906853426, 4/5.08844817654790571027/1.22474487139158982885, 5/5.79555495773445361607/0.51763809020504247815, 6/3.60488426005379691830/0.96592582628906853426, 7/3.86370330515631765778/1.93185165257813684647, 8/4.82962913144538497079/2.19067069768065803004, 9/2.89777747886724945658/0.25881904510252157214, 10/4.82962913144539740529/3.60488426005374806849, 11/1.93185165257818103335/0.51763809020504336633, 12/2.89777747886723213711/2.19067069768062250290, 13/2.19067069768062783197/1.48356391649413144052, 14/1.22474487139157006688/1.22474487139157073301, 15/1.48356391649393959398/2.19067069768067934632, 16/0.51763809020495876734/1.93185165257809776662, 17/2.19067069768061495338/2.89777747886709979852, 18/1.22474487139153653814/2.63895843376461547436, 19/0.25881904510247938367/2.89777747886717751413, 20/0.96592582628905720998/3.60488426005369433369, 21/0.00000000000000000000/3.86370330515625681755, 22/1.93185165257813507012/3.86370330515617954603, 23/0.96592582628907786013/4.12252235025874114172, 24/0.25881904510255682172/4.82962913144531480469, 25/1.22474487139163468186/5.08844817654779912885, 26/0.51763809020511364345/5.79555495773437279183, 27/2.19067069768070954439/4.82962913144530237020, 28/1.48356391649418828393/5.53673591263187514500, 29/1.22474487139164467386/6.50266173892093668485, 30/2.19067069768071975844/6.24384269381843903801, 31/1.93185165257817992313/7.20976852010750235422, 32/2.89777747886724101889/5.53673591263186626321, 33/2.63895843376470118358/6.50266173892092957942, 34/2.89777747886725833837/7.46858756520998667838, 35/3.60488426005377471384/6.24384269381842660351, 36/5.53673591263193287659/1.48356391649411079037, 37/5.79555495773445272789/2.44948974278317921360, 38/6.50266173892100152187/1.22474487139158982885, 39/3.86370330515631410506/7.20976852010749080790, 40/6.76148078402352048499/2.19067069768065803004, 41/3.60488426005378492789/8.17569434639655590047, 42/4.57081008634284557957/6.50266173892093846121, 43/6.50266173892100063370/3.15659652396972623123, 44/7.46858756521006927898/1.48356391649411123446, 45/4.31199104124033194552/7.46858756521000799466, 46/7.20976852010754853950/2.44948974278317921360, 47/4.57081008634285357317/8.43451339149907575177, 48/5.27791686752940059080/7.72740661031252873414, 49/5.53673591263191511302/8.69333243660159915578, 50/5.53673591263191422485/6.76148078402345831250, 51/5.79555495773444206975/7.72740661031253139868, 52/6.50266173892098464648/8.43451339149908463355, 53/6.76148078402351160321/7.46858756521001687645, 54/7.46858756521005506812/8.17569434639657011132, 55/6.50266173892099264009/6.50266173892094823117, 56/7.20976852010753432864/7.20976852010750146604, 57/8.17569434639660208575/7.46858756521002309370, 58/7.91687530129408134627/6.50266173892095533660, 59/8.88280112758314821519/6.76148078402347518789, 60/7.20976852010753965772/5.79555495773440032536, 61/8.17569434639660919117/6.05437400283691928848, 62/9.14162017268567872463/5.79555495773440831897, 63/8.43451339149913792426/5.08844817654785330774, 64/9.40043921778820923407/4.82962913144534233822, 65/7.46858756521007105533/4.82962913144533523280, 66/8.43451339149914147697/4.57081008634282337511, 67/9.14162017268568760642/3.86370330515627458112, 68/8.17569434639661807296/3.60488426005375561800, 69/8.88280112758316420241/2.89777747886720682402, 70/7.20976852010754942768/3.86370330515627458112, 71/7.91687530129409466895/3.15659652396972711941, 72/8.17569434639661629660/2.19067069768065891822, 73/2.89777747886724812432/3.60488426005375206529, 74/5.53673591263193287659/2.89777747886720504766, 79/3.60488426005378093109/4.82962913144531125198, 80/3.86370330515631277279/5.79555495773437545637, 81/4.82962913144538585897/5.53673591263187603317, 82/4.57081008634285534953/4.57081008634281182879, 83/5.27791686752941391347/3.86370330515627413703, 84/6.24384269381848078240/3.60488426005375206529, 85/6.50266173892099974552/4.57081008634282071057, 86/5.53673591263192577117/4.82962913144532013376, 87/6.24384269381845946612/5.53673591263188225042, 88/5.27791686752938637994/5.79555495773438344997, 100/4.57081008634286423131/2.63895843376468519637, 101/3.60488426005379603012/2.89777747886720460357, 102/3.86370330515632254276/3.86370330515624793577, 103/3.15659652396978307465/4.57081008634280205882, 104/2.63895843376472916120/1.22474487139159027294} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 5/135.00/405.00/0.4/Blue, 74/225.00/555.00/0.4/Green, 9/345.00/465.00/0.4/Orange, 74/225.00/405.00/0.3/Violet, 87/285.00/525.00/0.4/Teal, 23/75.00/345.00/0.4/Lime} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 6/7, 6/104, 7/3, 7/100, 8/4, 8/36, 9/1, 9/6, 10/82, 10/102, 11/9, 11/104, 12/17, 12/13, 12/101, 13/14, 13/11, 13/15, 14/16, 14/11, 15/14, 15/17, 15/16, 16/18, 16/19, 17/22, 17/18, 18/20, 18/19, 19/20, 19/21, 20/22, 20/21, 21/23, 21/24, 22/23, 23/25, 23/24, 24/25, 24/26, 25/27, 25/26, 26/28, 26/29, 27/103, 27/32, 28/27, 28/30, 29/28, 29/30, 29/31, 30/32, 30/31, 31/33, 31/34, 32/79, 32/80, 33/32, 33/35, 34/33, 34/41, 34/39, 35/32, 35/42, 36/5, 36/38, 37/8, 37/36, 38/5, 39/41, 39/35, 39/42, 40/37, 40/38, 41/45, 41/47, 42/88, 42/50, 43/37, 43/40, 44/40, 44/38, 45/42, 45/48, 46/43, 46/44, 47/45, 47/48, 47/49, 48/50, 48/49, 49/51, 49/52, 50/88, 50/51, 51/53, 51/52, 52/53, 52/54, 53/55, 53/54, 54/56, 54/57, 55/60, 55/56, 56/58, 56/57, 57/58, 57/59, 58/60, 58/59, 59/61, 59/62, 60/65, 60/61, 61/63, 61/62, 62/63, 62/64, 63/65, 63/64, 64/66, 64/67, 65/85, 65/66, 66/68, 66/67, 67/68, 67/69, 68/70, 68/69, 69/71, 69/72, 70/84, 70/71, 71/46, 71/72, 72/46, 72/44, 73/101, 73/102, 73/22, 73/103, 74/8, 74/43, 79/82, 79/80, 80/81, 80/42, 81/86, 81/42, 82/86, 82/81, 83/84, 83/82, 83/86, 84/74, 85/84, 85/70, 86/87, 86/88, 87/85, 87/55, 88/87, 100/74, 100/10, 101/7, 101/100, 102/82, 102/79, 103/102, 103/32, 104/9, 104/12} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,74,79,...,88,100,...,104} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-83) -- (p-86); \draw[Green,very thick] (p-47) -- (p-49); \draw[Green,very thick] (p-39) -- (p-42); \draw[Green,very thick] (p-34) -- (p-39); \draw[Green,very thick] (p-29) -- (p-31); \draw[Green,very thick] (p-15) -- (p-16); \draw[Green,very thick] (p-13) -- (p-15); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 5/135.00/405.00/0.4/Blue, 74/225.00/555.00/0.4/Green, 9/345.00/465.00/0.4/Orange, 74/225.00/405.00/0.3/Violet, 87/285.00/525.00/0.4/Teal, 23/75.00/345.00/0.4/Lime} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/315, 2/225, 3/105, 4/45, 5/345, 6/15, 7/255, 8/165, 9/255, 10/315, 11/285, 12/3, 13/345, 14/285, 15/105, 16/255, 17/332, 18/15, 19/195, 20/15, 21/135, 22/138, 23/345, 24/165, 25/345, 26/195, 27/195, 28/315, 29/195, 30/15, 31/75, 32/165, 33/135, 34/45, 35/225, 36/135, 37/45, 38/15, 39/105, 40/315, 41/75, 42/75, 43/75, 44/345, 45/225, 46/195, 47/45, 48/285, 49/135, 50/45, 51/195, 52/75, 53/315, 54/15, 55/107, 56/225, 57/345, 58/225, 59/75, 60/153, 61/135, 62/15, 63/195, 64/45, 65/333, 66/165, 67/45, 68/225, 69/285, 70/345, 71/135, 72/315, 73/225, 74/302, 79/135, 80/195, 81/105, 82/165, 83/285, 84/225, 85/105, 86/345, 87/15, 88/285, 100/15, 101/135, 102/345, 103/315, 104/135} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Dann funktioniert Button neue Eingabe "Rahmen zuerst" richtig. 89 Knoten, 2×Grad 3, 82×Grad 4, 2×Grad 5, 1×Grad 6, 2×Grad 7, 0 Überschneidungen 182 Kanten, minimal 0.99999999999989475086, maximal 1.00000000000012945200 einzustellende Kanten, Abstände und Winkel: |P17-P12|=0.99999999999995725641 |P22-P17|=0.99999999999990274446 |P32-P27|=1.00000000000000310862 |P35-P33|=0.99999999999998911981 |P37-P8|=1.00000000000000976996 |P42-P35|=1.00000000000004130030 |P43-P37|=0.99999999999995259348 |P50-P42|=0.99999999999997335465 |P60-P55|=1.00000000000000288658 |P65-P60|=0.99999999999999777955 |P85-P65|=0.99999999999993571809 |P88-P42|=0.99999999999989830357 |P101-P12|=1.00000000000009325873 |P73-P101|=0.99999999999998367972 |P86-P81|=0.99999999999992505995 |P86-P82|=0.99999999999989475086 |P86-P83|=1.00000000000012945200 |P102-P73|=1.00000000000007593925 |P102-P82|=0.99999999999994426680 und mehr $ %Eingabe war: % %Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: Automatisch generierte Eingabe zu: #1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78); % % % % % % % % % % % % % % % % %P[1]=[-14.583726446083169,39.134801773829274]; P[9]=[-63.843150912666374,52.33382477927218]; D=ab(1,9); A(9,1); N(6,9,1); N(104,9,6); N(11,9,104); M(14,11,9,blauerWinkel); N(13,14,11); N(15,14,13); N(16,14,15); M(19,16,14,gruenerWinkel); N(18,19,16); N(20,19,18); N(21,19,20); M(24,21,19,orangerWinkel); N(23,24,21); N(25,24,23); N(26,24,25); M(29,26,24,vierterWinkel); N(28,29,26); N(30,29,28); N(31,29,30); M(34,31,29,fuenfterWinkel); N(33,34,31); M(41,34,31,sechsterWinkel); N(39,41,34); M(47,41,34,siebenterWinkel); N(45,47,41); N(48,47,45); N(49,47,48); M(52,49,47,achterWinkel); N(51,52,49); N(53,52,51); N(54,52,53); M(57,54,52,neunterWinkel); N(56,57,54); N(58,57,56); N(59,57,58); M(62,59,57,zehnterWinkel); N(61,62,59); N(63,62,61); N(64,62,63); M(67,64,62,elfterWinkel); N(66,67,64); N(68,67,66); N(69,67,68); M(72,69,67,zwölfterWinkel); N(71,72,69); N(46,72,71); N(44,72,46); M(40,44,72,dreizehnterWinkel); N(38,44,40); Q(5,38,1,1*D,2*D); A(5,38); A(5,1); H(2,1,5,2); A(2,1); L(3,1,2); H(5,38,5,1); A(5,38); L(36,5,38); A(2,5); L(4,2,5); A(3,4); N(7,6,3); N(8,4,36); N(12,13,104); N(17,18,15); N(22,23,20); N(27,28,25); N(32,33,30); N(35,39,32); N(37,36,40); N(42,45,39); N(43,40,46); N(50,51,48); N(55,56,53); N(60,61,58); N(65,66,63); N(70,71,68); N(74,8,43); N(80,42,32); N(81,42,80); N(84,74,70); N(85,84,70); N(87,85,55); N(88,87,50); N(100,7,74); N(101,7,100); N(103,32,27); N(73,103,22); N(79,80,32); N(82,81,79); N(83,84,82); N(86,87,88); N(102,79,103); N(10,102,100); %A(17,12); R(17,12,"green"); %A(22,17); R(22,17,"green"); %A(32,27); R(32,27,"green"); %A(35,33); R(35,33,"green"); %A(37,8); R(37,8,"green"); %A(42,35); R(42,35,"green"); %A(43,37); R(43,37,"green"); %A(50,42); R(50,42,"green"); %A(60,55); R(60,55,"green"); %A(65,60); R(65,60,"green"); %A(85,65); R(85,65,"green"); %A(88,42); R(88,42,"green"); %A(101,12); R(101,12,"green"); %A(73,101); R(73,101,"green"); %A(86,81); R(86,81,"green"); %A(86,82); R(86,82,"green"); %A(86,83); R(86,83,"green"); %A(102,73); R(102,73,"green"); %A(102,82); R(102,82,"green"); %A(10,82); R(10,82,"green"); % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LightBlue}{rgb}{0.68,0.84,0.90} \definecolor{LightCoral}{rgb}{0.94,0.50,0.50} \definecolor{LightCyan}{rgb}{0.88,1.00,1.00} \definecolor{LightGoldenrodYellow}{rgb}{0.98,0.98,0.82} \definecolor{LightGreen}{rgb}{0.56,0.93,0.56} \definecolor{LightGray}{rgb}{0.82,0.82,0.82} \definecolor{LightPink}{rgb}{1.00,0.71,0.75} \definecolor{Lime}{rgb}{0.00,1.00,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/3.86370330515627236068/0.00000000000000000000, 2/4.82962913144533878551/0.25881904510252912166, 3/4.12252235025878555064/0.96592582628907086573, 4/5.08844817654785153138/1.22474487139159959881, 5/5.79555495773440565443/0.51763809020505813230, 6/3.60488426005375295347/0.96592582628906864528, 7/3.86370330515626481116/1.93185165257813928896, 8/4.82962913144538408261/2.19067069768068289903, 9/2.89777747886720460357/0.25881904510252162765, 10/4.82962913144542493882/3.60488426005368900462, 11/1.93185165257813618034/0.51763809020504336633, 12/2.89777747886714776016/2.19067069768067401725, 13/2.19067069768059985435/1.48356391649412722167, 14/1.22474487139154675219/1.22474487139154919468, 15/1.48356391649401064825/2.19067069768063271695, 16/0.51763809020495765711/1.93185165257805513406, 17/2.19067069768058919621/2.89777747886714998060, 18/1.22474487139153564996/2.63895843376457195362, 19/0.25881904510247882856/2.89777747886713488157, 20/0.96592582628905743203/3.60488426005365170113, 21/0.00000000000000000000/3.86370330515621462908, 22/1.93185165257813551420/3.86370330515613558120, 23/0.96592582628907852627/4.12252235025869939733, 24/0.25881904510255743235/4.82962913144527306031, 25/1.22474487139163534799/5.08844817654775738447, 26/0.51763809020511430958/5.79555495773433193563, 27/2.19067069768071043256/4.82962913144526329035, 28/1.48356391649418850598/5.53673591263183517697, 29/1.22474487139164489591/6.50266173892089671682, 30/2.19067069768071975844/6.24384269381839995816, 31/1.93185165257817503814/7.20976852010746238619, 32/2.89777747886724412751/5.53673591263182895972, 33/2.63895843376469851904/6.50266173892089138775, 34/2.89777747886725167703/7.46858756520995026307, 35/3.60488426005376449979/6.24384269381840439905, 36/5.53673591263193820566/1.48356391649414098843, 37/5.79555495773446160968/2.44948974278320852349, 38/6.50266173892099264009/1.22474487139156629212, 39/3.86370330515632876001/7.20976852010746060984, 40/6.76148078402351515592/2.19067069768063360513, 41/3.60488426005377649020/8.17569434639652037333, 42/4.57081008634287933035/6.50266173892091448039, 43/6.50266173892099619280/3.15659652396970180632, 44/7.46858756521006039719/1.48356391649408481115, 45/4.31199104124032572827/7.46858756520997513206, 46/7.20976852010754143407/2.44948974278315345643, 47/4.57081008634284469139/8.43451339149904377734, 48/5.27791686752939348537/7.72740661031249853608, 49/5.53673591263191156031/8.69333243660156718136, 50/5.53673591263192044210/6.76148078402343166715, 51/5.79555495773443940521/7.72740661031250031243, 52/6.50266173892098109377/8.43451339149905265913, 53/6.76148078402350805050/7.46858756520998579020, 54/7.46858756521005151541/8.17569434639653813690, 55/6.50266173892098908738/6.50266173892091714492, 56/7.20976852010753166411/7.20976852010747037980, 57/8.17569434639660030939/7.46858756520999023110, 58/7.91687530129407868174/6.50266173892092158582, 59/8.88280112758314821519/6.76148078402344232529, 60/7.20976852010753788136/5.79555495773436657458, 61/8.17569434639660563846/6.05437400283688820224, 62/9.14162017268567694828/5.79555495773437634455, 63/8.43451339149913614790/5.08844817654782222149, 64/9.40043921778820745772/4.82962913144531125198, 65/7.46858756521006750262/4.82962913144530325837, 66/8.43451339149913792426/4.57081008634279406522, 67/9.14162017268568405370/3.86370330515624349488, 68/8.17569434639661452024/3.60488426005372719629, 69/8.88280112758315887334/2.89777747886717662595, 70/7.20976852010754676314/3.86370330515625015622, 71/7.91687530129409200441/3.15659652396969914179, 72/8.17569434639661096753/2.19067069768063049651, 73/2.89777747886722858439/3.60488426005370765637, 74/5.53673591263190889578/2.89777747886725345339, 79/3.60488426005382756045/4.82962913144531746923, 80/3.86370330515629856194/5.79555495773439854901, 81/4.82962913144535566090/5.53673591263183517697, 82/4.57081008634288465942/4.57081008634275409719, 83/5.27791686752933753013/3.86370330515611248856, 84/6.24384269381846124247/3.60488426005379647421, 85/6.50266173892104948351/4.57081008634284646774, 86/5.53673591263183073607/4.82962913144532191012, 87/6.24384269381837420099/5.53673591263187425682, 88/5.27791686752930377935/5.79555495773438877904, 100/4.57081008634286867220/2.63895843376463057339, 101/3.60488426005382089912/2.89777747886722814030, 102/3.86370330515636828395/3.86370330515625415302, 103/3.15659652396978529509/4.57081008634276653169, 104/2.63895843376468519637/1.22474487139159027294} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 11/345.00/495.00/0.4/Blue, 16/315.00/465.00/0.4/Green, 21/285.00/435.00/0.4/Orange, 26/255.00/405.00/0.4/Violet, 31/225.00/375.00/0.4/Teal, 34/195.00/405.00/0.4/Lime, 41/225.00/375.00/0.4/LightBlue, 49/195.00/345.00/0.4/LightCoral, 54/165.00/315.00/0.4/LightCyan, 59/135.00/285.00/0.4/LightGoldenrodYellow, 64/105.00/255.00/0.4/LightGreen, 69/75.00/225.00/0.4/LightGray, 44/45.00/135.00/0.4/LightPink} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 2/5, 3/1, 3/2, 3/4, 4/2, 4/5, 5/38, 6/9, 6/1, 7/6, 7/3, 8/4, 8/36, 9/1, 10/102, 10/100, 10/82, 11/9, 11/104, 12/13, 12/104, 13/14, 13/11, 14/11, 15/14, 15/13, 16/14, 16/15, 17/18, 17/15, 17/12, 18/19, 18/16, 19/16, 20/19, 20/18, 21/19, 21/20, 22/23, 22/20, 22/17, 23/24, 23/21, 24/21, 25/24, 25/23, 26/24, 26/25, 27/28, 27/25, 28/29, 28/26, 29/26, 30/29, 30/28, 31/29, 31/30, 32/33, 32/30, 32/27, 33/34, 33/31, 34/31, 35/39, 35/32, 35/33, 36/5, 36/38, 37/36, 37/40, 37/8, 38/44, 38/40, 39/41, 39/34, 40/44, 41/34, 42/45, 42/39, 42/35, 43/40, 43/46, 43/37, 44/72, 44/46, 45/47, 45/41, 46/72, 46/71, 47/41, 48/47, 48/45, 49/47, 49/48, 50/51, 50/48, 50/42, 51/52, 51/49, 52/49, 53/52, 53/51, 54/52, 54/53, 55/56, 55/53, 56/57, 56/54, 57/54, 58/57, 58/56, 59/57, 59/58, 60/61, 60/58, 60/55, 61/62, 61/59, 62/59, 63/62, 63/61, 64/62, 64/63, 65/66, 65/63, 65/60, 66/67, 66/64, 67/64, 68/67, 68/66, 69/67, 69/68, 70/71, 70/68, 71/72, 71/69, 72/69, 73/103, 73/22, 73/101, 74/8, 74/43, 79/80, 79/32, 80/42, 80/32, 81/42, 81/80, 82/81, 82/79, 83/84, 83/82, 84/74, 84/70, 85/84, 85/70, 85/65, 86/87, 86/88, 86/81, 86/82, 86/83, 87/85, 87/55, 88/87, 88/50, 88/42, 100/7, 100/74, 101/7, 101/100, 101/12, 102/79, 102/103, 102/73, 102/82, 103/32, 103/27, 104/9, 104/6} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,74,79,...,88,100,...,104} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-17) -- (p-12); \draw[Green,very thick] (p-22) -- (p-17); \draw[Green,very thick] (p-32) -- (p-27); \draw[Green,very thick] (p-35) -- (p-33); \draw[Green,very thick] (p-37) -- (p-8); \draw[Green,very thick] (p-42) -- (p-35); \draw[Green,very thick] (p-43) -- (p-37); \draw[Green,very thick] (p-50) -- (p-42); \draw[Green,very thick] (p-60) -- (p-55); \draw[Green,very thick] (p-65) -- (p-60); \draw[Green,very thick] (p-85) -- (p-65); \draw[Green,very thick] (p-88) -- (p-42); \draw[Green,very thick] (p-101) -- (p-12); \draw[Green,very thick] (p-73) -- (p-101); \draw[Green,very thick] (p-86) -- (p-81); \draw[Green,very thick] (p-86) -- (p-82); \draw[Green,very thick] (p-86) -- (p-83); \draw[Green,very thick] (p-102) -- (p-73); \draw[Green,very thick] (p-102) -- (p-82); \draw[Green,very thick] (p-10) -- (p-82); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 11/345.00/495.00/0.4/Blue, 16/315.00/465.00/0.4/Green, 21/285.00/435.00/0.4/Orange, 26/255.00/405.00/0.4/Violet, 31/225.00/375.00/0.4/Teal, 34/195.00/405.00/0.4/Lime, 41/225.00/375.00/0.4/LightBlue, 49/195.00/345.00/0.4/LightCoral, 54/165.00/315.00/0.4/LightCyan, 59/135.00/285.00/0.4/LightGoldenrodYellow, 64/105.00/255.00/0.4/LightGreen, 69/75.00/225.00/0.4/LightGray, 44/45.00/135.00/0.4/LightPink} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/315, 2/285, 3/105, 4/105, 5/345, 6/15, 7/255, 8/165, 9/315, 10/315, 11/285, 12/3, 13/345, 14/225, 15/105, 16/165, 17/93, 18/15, 19/135, 20/15, 21/135, 22/138, 23/345, 24/165, 25/45, 26/195, 27/195, 28/255, 29/75, 30/15, 31/75, 32/255, 33/285, 34/45, 35/225, 36/135, 37/45, 38/225, 39/315, 40/315, 41/165, 42/345, 43/75, 44/345, 45/225, 46/135, 47/45, 48/345, 49/45, 50/45, 51/195, 52/75, 53/315, 54/105, 55/107, 56/225, 57/45, 58/285, 59/75, 60/273, 61/135, 62/315, 63/195, 64/315, 65/332, 66/165, 67/345, 68/165, 69/15, 70/345, 71/135, 72/15, 73/225, 74/122, 79/135, 80/195, 81/105, 82/225, 83/285, 84/225, 85/105, 86/45, 87/15, 88/135, 100/15, 101/135, 102/345, 103/315, 104/135} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Anschließender Button "beweglich?" ergibt immer noch einen starren Graph, doch da muss ich den Grund noch suchen, warum die erwartete Beweglichkeit übersehen wird. Bei diesen Versuchen sind mir dann noch weitere Fehler aufgefallen: Wenn man P1 oder P2 mit Z(.) entfernt, funktioniert neue Eingabe auch nicht und bei der Ableitungsmatrix hat beim Versuch, die Berechnung ganzzahlig zu halten, einmal der Zahlenbereich nicht ausgereicht. Das muss ich auch ausbessern. Insgesamt doch etliche Fehler und Mängel. Sonst versuche ich immer, die Testbeispiele so auszuwählen, dass nur ein oder wenige Mängel zum Vorschein kommen. Zum Speichern der verschiedenen Graphen verwende ich auch nur Eingabe kopieren in irgendeinen Texteditor hinein und wieder zurück. Versuche mit Undo/Redo waren nicht überzeugend und Filezugriff vom Browser aus habe ich gar nicht erst versucht.


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haribo
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 25.10.2012
Mitteilungen: 3872
  Beitrag No.1914, eingetragen 2020-02-23

oh haua haa! da werd ich noch einige zeit dran knabbern müssen um etwas davon zu verstehen, wie ein eichhörnchen schönes wochenende noch haribo


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Slash
Aktiv Letzter Besuch: in der letzten Woche
Dabei seit: 23.03.2005
Mitteilungen: 8998
Wohnort: Westerburg
  Beitrag No.1915, vom Themenstarter, eingetragen 2020-02-24

Am 17.02 hatte unser Thread 4. Geburtstag. Hurra! 8-) ...und bald feiern wir den 2000. Beitrag. :-) Aber statt Konfetti werfen wir natürlich Streichhölzer in die Luft.


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StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
Mitteilungen: 4165
Wohnort: Raun
  Beitrag No.1916, eingetragen 2020-02-29

Die zuletzt festgestellten Fehler und Mängel habe ich in Streichholzgraph-1898.htm versucht zu beseitigt. Konkret, Button neue Eingabe "wenig Winkel" funktioniert, da hatte ich javascript if (Variablenname=1) drin statt richtig if (Variablenname==1) in einem selten verwendeten Programmabschnitt. Button neue Eingabe "Rahmen zuerst" bei nach innen gestülpten Rahmen geht jetzt auch und der andere Fehler lag vermutlich mit an Überschreitung des Zahlenbereiches, ist auch geändert. Dann Umlaut in Variablenbezeichnung zwölfterWinkel hatte funtioniert, nach Kopieren aber nicht mehr, deshalb ab jetzt zwoelfterWinkel wie bisher bereits bei fuenfterWinkel und anderen auch. Beide Buttons funktionieren jetzt auch, wenn P1 ode P2 gelöscht sind, Beispiel folgt. Dann noch weitere Änderungen, die sich so nebenbei mit ergeben. Alle Buttons für neue Eingabe behalten die Punkte Pi und Pj für die Ausrichtung des Graphen bei. Bisher wurden diese neu durch P1 und P2 ersetzt. Z(j) entfernt auch alle zu messenden Abstände R(i,j), welche Pj enthalten. Bisher war dann eine Ausgabe "nicht mehr vohanden". Das führt zu einem Mißverständnis, wenn man später Pj an anderer Stelle wieder hinzufügt. Button "beweglich?" listet mehrere Winkel auf, wenn eine mehrfache Beweglichkeit gefunden wird. Bisher hatte ich nur einen Winkel angegeben, was aber nicht ausgereicht hat, um eine Bewegung zu starten. Neu, die Z(j) lassen sich mit Mauszeiger eingeben, wenn man bei gedrückter linker Alt-Taste den Mauszeuger ohne Klick auf eine Punktbezeichnung bewegt. Es ist schon mühsam genug, den Graph aufzubauen, beim Entfernen von Punkten muss das nicht mehr sein. Einzelne Kanten lassen sich ebenso entfernen, bei gedrückter linker Alt-Taste den Mauszeiger ohne Klick auf den Mittelkreis der betreffenden Kante bewegen. Jetzt gehe ich nochmal die letzten Eingaben durch. Es wiederholt sich etwas, doch diesmal soll alles funktionieren. Ich beginne mit Graph #1913-3 89 Knoten, 2×Grad 3, 82×Grad 4, 2×Grad 5, 1×Grad 6, 2×Grad 7, 0 Überschneidungen 182 Kanten, minimal 0.99999999999998090416, maximal 1.00000000000002309264 $ %Eingabe war: % %#1913-3 % % % % % % % % % %P[1]=[-36.489648590837135,-1.7967881657507974]; P[2]=[13.517130825300598,-11.798144048978344]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(38,5,4,blauerWinkel); N(36,5,38); N(8,4,36); N(37,8,36); N(40,37,38); N(43,37,40); N(44,40,38); N(46,43,44); N(72,46,44); N(74,8,43); N(71,46,72); N(69,71,72); M(100,74,8,gruenerWinkel); N(7,3,100); N(101,7,100); N(6,1,7); N(9,1,6); M(104,9,1,orangerWinkel); N(11,9,104); M(84,74,8,vierterWinkel); N(70,84,71); N(85,84,70); N(68,70,69); N(67,68,69); N(66,68,67); N(64,66,67); N(65,85,66); N(63,65,64); N(62,63,64); N(61,63,62); N(59,61,62); N(60,65,61); N(58,60,59); N(57,58,59); N(56,58,57); N(54,56,57); N(55,60,56); N(87,85,55); N(53,55,54); N(52,53,54); N(51,53,52); N(49,51,52); M(88,87,85,fuenfterWinkel); N(50,88,51); N(86,87,88); N(42,88,50); N(48,50,49); N(81,86,42); N(82,86,81); N(83,84,82); N(45,42,48); N(47,45,48); N(80,81,42); N(41,45,47); N(79,82,80); N(102,82,79); N(32,79,80); N(35,32,42); N(39,41,35); N(103,102,32); N(27,103,32); N(33,32,35); N(34,33,41); N(31,33,34); N(30,32,31); N(28,27,30); N(29,28,30); N(26,28,29); N(25,27,26); N(24,25,26); N(23,25,24); N(21,23,24); M(22,23,25,sechsterWinkel); N(20,22,21); N(19,20,21); N(18,20,19); N(16,18,19); N(17,22,18); N(14,16,11); N(15,14,17); N(13,14,11); N(12,17,13); %A(83,86); R(83,86,"green"); %A(47,49); R(47,49,"green"); %A(39,42); R(39,42,"green"); %A(34,39); R(34,39,"green"); %A(29,31); R(29,31,"green"); %A(15,16); R(15,16,"green"); %A(13,15); R(13,15,"green"); A(6,104); A(104,12); A(12,101); L(10,82,102); A(100,10); N(73,101,102); A(73,22); A(73,103); % % % % % % % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{Lime}{rgb}{0.00,1.00,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.14/0.39, 2/3.12/0.20, 3/2.80/1.14, 4/3.78/0.95, 5/4.10/0.00, 6/2.34/1.37, 7/3.00/2.12, 8/3.98/1.93, 9/1.39/1.05, 10/4.61/3.20, 11/0.64/1.71, 12/2.25/2.78, 13/1.30/2.46, 14/0.32/2.66, 15/0.98/3.41, 16/0.00/3.61, 17/1.93/3.73, 18/0.95/3.93, 19/0.20/4.59, 20/1.14/4.91, 21/0.39/5.57, 22/2.12/4.71, 23/1.37/5.37, 24/1.05/6.32, 25/2.03/6.12, 26/1.71/7.07, 27/2.78/5.46, 28/2.46/6.41, 29/2.66/7.39, 30/3.41/6.73, 31/3.61/7.71, 32/3.73/5.78, 33/3.93/6.76, 34/4.59/7.52, 35/4.68/6.10, 36/4.30/0.98, 37/4.96/1.73, 38/5.05/0.32, 39/5.34/6.86, 40/5.71/1.07, 41/5.53/7.84, 42/5.66/5.91, 43/5.91/2.05, 44/6.03/0.12, 45/5.86/6.89, 46/6.23/1.10, 47/6.52/7.64, 48/6.84/6.69, 49/7.50/7.44, 50/6.64/5.71, 51/7.30/6.46, 52/8.25/6.78, 53/8.05/5.80, 54/9.00/6.12, 55/7.39/5.05, 56/8.34/5.37, 57/9.32/5.18, 58/8.66/4.42, 59/9.64/4.23, 60/7.71/4.10, 61/8.69/3.91, 62/9.44/3.25, 63/8.50/2.93, 64/9.25/2.27, 65/7.52/3.12, 66/8.27/2.46, 67/8.59/1.52, 68/7.61/1.71, 69/7.93/0.77, 70/6.86/2.37, 71/7.18/1.43, 72/6.98/0.44, 73/2.88/4.05, 74/4.93/2.25, 79/4.05/4.84, 80/4.71/5.59, 81/5.46/4.93, 82/4.80/4.18, 83/5.12/3.23, 84/5.87/2.57, 85/6.53/3.32, 86/5.78/3.98, 87/6.73/4.30, 88/5.98/4.96, 100/3.95/2.44, 101/3.20/3.10, 102/3.86/3.86, 103/3.54/4.80, 104/1.59/2.03} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 5/108.69/378.69/0.4/Blue, 74/198.69/528.69/0.4/Green, 9/318.69/438.69/0.4/Orange, 74/198.69/378.69/0.3/Violet, 87/258.69/498.69/0.4/Teal, 23/48.69/318.69/0.4/Lime} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 6/7, 6/104, 7/3, 7/100, 8/4, 8/36, 9/1, 9/6, 10/82, 10/102, 11/9, 11/104, 12/17, 12/13, 12/101, 13/14, 13/11, 13/15, 14/16, 14/11, 15/14, 15/17, 15/16, 16/18, 16/19, 17/22, 17/18, 18/20, 18/19, 19/20, 19/21, 20/22, 20/21, 21/23, 21/24, 22/23, 23/25, 23/24, 24/25, 24/26, 25/27, 25/26, 26/28, 26/29, 27/103, 27/32, 28/27, 28/30, 29/28, 29/30, 29/31, 30/32, 30/31, 31/33, 31/34, 32/79, 32/80, 33/32, 33/35, 34/33, 34/41, 34/39, 35/32, 35/42, 36/5, 36/38, 37/8, 37/36, 38/5, 39/41, 39/35, 39/42, 40/37, 40/38, 41/45, 41/47, 42/88, 42/50, 43/37, 43/40, 44/40, 44/38, 45/42, 45/48, 46/43, 46/44, 47/45, 47/48, 47/49, 48/50, 48/49, 49/51, 49/52, 50/88, 50/51, 51/53, 51/52, 52/53, 52/54, 53/55, 53/54, 54/56, 54/57, 55/60, 55/56, 56/58, 56/57, 57/58, 57/59, 58/60, 58/59, 59/61, 59/62, 60/65, 60/61, 61/63, 61/62, 62/63, 62/64, 63/65, 63/64, 64/66, 64/67, 65/85, 65/66, 66/68, 66/67, 67/68, 67/69, 68/70, 68/69, 69/71, 69/72, 70/84, 70/71, 71/46, 71/72, 72/46, 72/44, 73/101, 73/102, 73/22, 73/103, 74/8, 74/43, 79/82, 79/80, 80/81, 80/42, 81/86, 81/42, 82/86, 82/81, 83/84, 83/82, 83/86, 84/74, 85/84, 85/70, 86/87, 86/88, 87/85, 87/55, 88/87, 100/74, 100/10, 101/7, 101/100, 102/82, 102/79, 103/102, 103/32, 104/9, 104/12} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,74,79,...,88,100,...,104} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-83) -- (p-86); \draw[Green,very thick] (p-47) -- (p-49); \draw[Green,very thick] (p-39) -- (p-42); \draw[Green,very thick] (p-34) -- (p-39); \draw[Green,very thick] (p-29) -- (p-31); \draw[Green,very thick] (p-15) -- (p-16); \draw[Green,very thick] (p-13) -- (p-15); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 5/108.69/378.69/0.4/Blue, 74/198.69/528.69/0.4/Green, 9/318.69/438.69/0.4/Orange, 74/198.69/378.69/0.3/Violet, 87/258.69/498.69/0.4/Teal, 23/48.69/318.69/0.4/Lime} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/199, 2/259, 3/139, 4/19, 5/319, 6/349, 7/229, 8/139, 9/169, 10/289, 11/259, 12/336, 13/319, 14/259, 15/79, 16/229, 17/306, 18/289, 19/229, 20/49, 21/109, 22/111, 23/259, 24/199, 25/19, 26/79, 27/169, 28/289, 29/169, 30/349, 31/49, 32/139, 33/259, 34/169, 35/199, 36/109, 37/169, 38/199, 39/289, 40/289, 41/139, 42/49, 43/49, 44/229, 45/259, 46/109, 47/19, 48/259, 49/109, 50/19, 51/229, 52/109, 53/289, 54/349, 55/81, 56/139, 57/319, 58/199, 59/49, 60/246, 61/169, 62/49, 63/229, 64/19, 65/306, 66/139, 67/19, 68/199, 69/349, 70/319, 71/49, 72/229, 73/199, 74/276, 79/109, 80/19, 81/289, 82/139, 83/259, 84/199, 85/79, 86/229, 87/349, 88/259, 100/349, 101/109, 102/229, 103/79, 104/49} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Dann Button neue Eingabe "wenig Winkel" $ %Eingabe war: % %#1913-3 % % % % % % % %P[1]=[-36.489648590837135,-1.7967881657507974]; P[2]=[13.517130825300598,-11.798144048978344]; D=ab(1,2); A(2,1); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,2,blauerWinkel); L(9,1,6); L(104,9,6); L(11,9,104); N(7,6,3); M(100,7,3,gruenerWinkel); L(101,7,100); N(12,104,101); M(125,11,9,95.00000000000128); L(14,11,125); L(15,14,125); L(16,14,15); Q(13,11,12,ab(125,11,14,15,16,"gedreht"),D); N(17,15,12); M(126,16,14,94.99999999999815); L(19,16,126); L(20,19,126); L(21,19,20); Q(18,16,17,ab(126,16,19,20,21,"gedreht"),D); N(22,20,17); M(127,21,19,95.00000000000036); L(24,21,127); L(25,24,127); L(26,24,25); Q(23,21,22,ab(127,21,24,25,26,"gedreht"),D); N(73,22,101); M(8,4,2,orangerWinkel); M(128,8,4,35.00000000000003); L(37,8,128); M(129,5,2,275); L(38,129,5); Q(36,8,5,ab(128,8,37,"gedreht"),ab(129,5,38,"gedreht")); M(130,37,8,155); L(43,37,130); M(131,38,5,215.00000000000006); L(44,131,38); Q(40,37,38,ab(130,37,43,"gedreht"),ab(131,38,44,"gedreht")); M(132,44,38,275); M(71,132,44,125.00000000000001); M(69,71,132,124.99999999999997); L(134,69,71); Q(133,71,132,ab(134,71,69,"gedreht"),D); Q(72,132,44,ab(133,132,69,71,"gedreht"),D); Q(46,43,44,D,ab(132,44,69,71,72,"gedreht")); N(74,8,43); A(74,100); M(27,25,23,vierterWinkel); M(135,26,24,95.00000000000107); L(29,26,135); L(30,29,135); L(31,29,30); Q(28,26,27,ab(135,26,29,30,31,"gedreht"),D); M(136,27,25,244.99999999999994); L(103,136,27); Q(32,30,27,D,ab(136,27,103,"gedreht")); M(102,73,22,214.99999999999787); L(137,73,102); A(103,73,ab(137,73,102,"gedreht")); M(138,32,27,94.99999999999916); L(80,32,138); M(10,102,73,155.00000000000074); L(82,102,10); L(139,102,82); Q(79,32,102,ab(138,32,80,"gedreht"),ab(139,102,10,82,"gedreht")); A(10,100); M(140,31,29,94.99999999999906); L(34,31,140); M(141,32,27,244.99999999999983); L(35,141,32); Q(33,31,32,ab(140,31,34,"gedreht"),ab(141,32,35,"gedreht")); M(142,34,31,155.000000000001); L(41,34,142); M(143,35,32,214.9999999999987); L(42,143,35); Q(39,34,35,ab(142,34,41,"gedreht"),ab(143,35,42,"gedreht")); M(144,42,35,35.000000000000796); L(81,42,144); A(80,42,ab(144,42,81,"gedreht")); M(145,81,42,154.99999999999932); L(86,81,145); L(83,86,145); A(82,81,ab(145,81,83,86,"gedreht")); M(146,41,34,94.99999999999977); L(47,41,146); L(48,47,146); L(49,47,48); Q(45,41,42,ab(146,41,47,48,49,"gedreht"),D); M(147,42,35,185.00000000000034); L(88,147,42); Q(50,48,42,D,ab(147,42,88,"gedreht")); M(87,86,81,275.0000000000006); L(148,86,87); A(88,86,ab(148,86,87,"gedreht")); M(149,49,47,95.00000000000006); L(52,49,149); L(53,52,149); L(54,52,53); Q(51,49,50,ab(149,49,52,53,54,"gedreht"),D); N(84,83,74); M(150,84,74,155.0000000000001); L(85,84,150); Q(70,84,71,ab(150,84,85,"gedreht"),D); A(85,87); M(67,69,71,275); M(64,67,69,185); L(66,67,64); L(152,67,66); Q(151,69,67,D,ab(152,67,64,66,"gedreht")); Q(68,70,69,D,ab(151,69,64,66,67,"gedreht")); M(56,54,52,95); L(57,54,56); L(58,57,56); L(153,57,58); M(62,64,66,275.0000000000001); M(154,62,64,185); L(61,62,154); L(155,62,61); Q(63,64,62,D,ab(155,62,154,61,"gedreht")); Q(59,54,64,ab(153,54,56,57,58,"gedreht"),ab(154,64,61,62,63,"gedreht")); N(55,56,53); A(55,87); N(60,58,55); A(60,61); N(65,63,60); A(65,85); A(65,66); %R(74,100); %R(73,102); // oder R(73,103); %R(10,100); %R(42,80); // oder R(42,81); %R(81,82); // oder R(81,86); %R(86,87); // oder R(86,88); %R(85,87); %R(55,87); %R(60,61); %R(65,85); %R(65,66); % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LimeGreen}{rgb}{0.20,0.80,0.20} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.14/0.39, 2/3.12/0.20, 3/2.80/1.14, 4/3.78/0.95, 5/4.10/0.00, 6/2.34/1.37, 7/3.00/2.12, 8/3.98/1.93, 9/1.39/1.05, 10/4.61/3.20, 11/0.64/1.71, 12/2.25/2.78, 13/1.30/2.46, 14/0.32/2.66, 15/0.98/3.41, 16/0.00/3.61, 17/1.93/3.73, 18/0.95/3.93, 19/0.20/4.59, 20/1.14/4.91, 21/0.39/5.57, 22/2.12/4.71, 23/1.37/5.37, 24/1.05/6.32, 25/2.03/6.12, 26/1.71/7.07, 27/2.78/5.46, 28/2.46/6.41, 29/2.66/7.39, 30/3.41/6.73, 31/3.61/7.71, 32/3.73/5.78, 33/3.93/6.76, 34/4.59/7.52, 35/4.68/6.10, 36/4.30/0.98, 37/4.96/1.73, 38/5.05/0.32, 39/5.34/6.86, 40/5.71/1.07, 41/5.53/7.84, 42/5.66/5.91, 43/5.91/2.05, 44/6.03/0.12, 45/5.86/6.89, 46/6.23/1.10, 47/6.52/7.64, 48/6.84/6.69, 49/7.50/7.44, 50/6.64/5.71, 51/7.30/6.46, 52/8.25/6.78, 53/8.05/5.80, 54/9.00/6.12, 55/7.39/5.05, 56/8.34/5.37, 57/9.32/5.18, 58/8.66/4.42, 59/9.64/4.23, 60/7.71/4.10, 61/8.69/3.91, 62/9.44/3.25, 63/8.50/2.93, 64/9.25/2.27, 65/7.52/3.12, 66/8.27/2.46, 67/8.59/1.52, 68/7.61/1.71, 69/7.93/0.77, 70/6.86/2.37, 71/7.18/1.43, 72/6.98/0.44, 73/2.88/4.05, 74/4.93/2.25, 79/4.05/4.84, 80/4.71/5.59, 81/5.46/4.93, 82/4.80/4.18, 83/5.12/3.23, 84/5.87/2.57, 85/6.53/3.32, 86/5.78/3.98, 87/6.73/4.30, 88/5.98/4.96, 100/3.95/2.44, 101/3.20/3.10, 102/3.86/3.86, 103/3.54/4.80, 104/1.59/2.03} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/348.69/438.69/0.4/Blue, 7/258.69/378.69/0.4/Green, 4/228.69/438.69/0.4/Orange, 25/228.69/318.69/0.4/Violet} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 7/6, 7/3, 8/4, 9/1, 9/6, 10/102, 10/100, 11/9, 11/104, 12/104, 12/101, 13/11, 13/12, 14/11, 14/13, 15/14, 15/13, 16/14, 16/15, 17/15, 17/12, 18/16, 18/17, 19/16, 19/18, 20/19, 20/18, 21/19, 21/20, 22/20, 22/17, 23/21, 23/22, 24/21, 24/23, 25/24, 25/23, 26/24, 26/25, 27/25, 28/26, 28/27, 29/26, 29/28, 30/29, 30/28, 31/29, 31/30, 32/30, 32/27, 33/31, 33/32, 34/31, 34/33, 35/33, 35/32, 36/8, 36/5, 37/8, 37/36, 38/36, 38/5, 39/34, 39/35, 40/37, 40/38, 41/34, 41/39, 42/39, 42/35, 43/37, 43/40, 44/40, 44/38, 45/41, 45/42, 46/43, 46/44, 47/41, 47/45, 48/47, 48/45, 49/47, 49/48, 50/48, 50/42, 51/49, 51/50, 52/49, 52/51, 53/52, 53/51, 54/52, 54/53, 55/56, 55/53, 55/87, 56/54, 57/54, 57/56, 58/57, 58/56, 59/57, 59/58, 59/62, 60/58, 60/55, 60/61, 61/62, 61/59, 62/64, 63/64, 63/61, 63/62, 64/67, 65/63, 65/60, 65/85, 65/66, 66/67, 66/64, 67/69, 68/70, 68/66, 68/67, 68/69, 69/71, 70/84, 70/71, 71/46, 72/69, 72/71, 72/46, 72/44, 73/22, 73/101, 74/8, 74/43, 74/100, 79/32, 79/82, 79/102, 80/32, 80/79, 80/42, 81/42, 81/80, 82/102, 82/10, 82/81, 83/86, 83/82, 84/83, 84/74, 85/84, 85/70, 85/87, 86/81, 86/82, 87/86, 88/50, 88/42, 88/86, 88/87, 100/7, 101/7, 101/100, 102/73, 103/32, 103/27, 103/73, 103/102, 104/9, 104/6} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,74,79,...,88,100,...,104} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[LimeGreen,very thick] (p-74) -- (p-100); \draw[LimeGreen,very thick] (p-73) -- (p-102); \draw[LimeGreen,very thick] (p-10) -- (p-100); \draw[LimeGreen,very thick] (p-42) -- (p-80); \draw[LimeGreen,very thick] (p-81) -- (p-82); \draw[LimeGreen,very thick] (p-86) -- (p-87); \draw[LimeGreen,very thick] (p-85) -- (p-87); \draw[LimeGreen,very thick] (p-55) -- (p-87); \draw[LimeGreen,very thick] (p-60) -- (p-61); \draw[LimeGreen,very thick] (p-65) -- (p-85); \draw[LimeGreen,very thick] (p-65) -- (p-66); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/348.69/438.69/0.4/Blue, 7/258.69/378.69/0.4/Green, 4/228.69/438.69/0.4/Orange, 25/228.69/318.69/0.4/Violet} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/289, 2/259, 3/139, 4/19, 5/229, 6/349, 7/229, 8/139, 9/169, 10/289, 11/169, 12/336, 13/19, 14/139, 15/79, 16/139, 17/66, 18/349, 19/229, 20/49, 21/109, 22/111, 23/319, 24/199, 25/19, 26/169, 27/169, 28/229, 29/109, 30/289, 31/139, 32/139, 33/109, 34/19, 35/349, 36/109, 37/19, 38/349, 39/79, 40/79, 41/49, 42/319, 43/49, 44/319, 45/199, 46/169, 47/139, 48/319, 49/19, 50/19, 51/229, 52/49, 53/229, 54/79, 55/81, 56/199, 57/19, 58/199, 59/49, 60/126, 61/109, 62/349, 63/229, 64/19, 65/306, 66/79, 67/19, 68/139, 69/259, 70/319, 71/49, 72/349, 73/199, 74/276, 79/259, 80/19, 81/289, 82/49, 83/259, 84/199, 85/79, 86/319, 87/349, 88/259, 100/349, 101/109, 102/229, 103/79, 104/109} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ funktioniert. Dann Button "zurück(1)" und Button neue Eingabe "Rahmen zuerst" $ %Eingabe war: % %#1913-3 % % % % % % % % % % % % % % % % %P[5]=[63.52391024143834,-21.799499932205897]; P[2]=[13.517130825300598,-11.798144048978344]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(9,1,2,blauerWinkel); N(6,9,1); N(104,9,6); N(11,9,104); M(14,11,9,gruenerWinkel); N(13,14,11); N(15,14,13); N(16,14,15); M(19,16,14,orangerWinkel); N(18,19,16); N(20,19,18); N(21,19,20); M(24,21,19,vierterWinkel); N(23,24,21); N(25,24,23); N(26,24,25); M(29,26,24,fuenfterWinkel); N(28,29,26); N(30,29,28); N(31,29,30); M(34,31,29,sechsterWinkel); N(33,34,31); M(41,34,31,siebenterWinkel); N(39,41,34); M(47,41,34,achterWinkel); N(45,47,41); N(48,47,45); N(49,47,48); M(52,49,47,neunterWinkel); N(51,52,49); N(53,52,51); N(54,52,53); M(57,54,52,zehnterWinkel); N(56,57,54); N(58,57,56); N(59,57,58); M(62,59,57,elfterWinkel); N(61,62,59); N(63,62,61); N(64,62,63); M(67,64,62,zwoelfterWinkel); N(66,67,64); N(68,67,66); N(69,67,68); M(72,69,67,dreizehnterWinkel); N(71,72,69); N(46,72,71); N(44,72,46); Q(38,5,44,1*D,1*D); L(36,5,38); L(40,38,44); N(7,6,3); N(8,4,36); N(12,13,104); N(17,18,15); N(22,23,20); N(27,28,25); N(32,33,30); N(35,39,32); N(37,36,40); N(42,45,39); N(43,40,46); N(50,51,48); N(55,56,53); N(60,61,58); N(65,66,63); N(70,71,68); N(74,8,43); N(80,42,32); N(81,42,80); N(84,74,70); N(85,84,70); N(87,85,55); N(88,87,50); N(100,7,74); N(101,7,100); N(103,32,27); N(73,103,22); N(79,80,32); N(82,81,79); N(83,84,82); N(86,87,88); N(102,79,103); N(10,102,100); %A(17,12); R(17,12,"green"); %A(22,17); R(22,17,"green"); %A(32,27); R(32,27,"green"); %A(35,33); R(35,33,"green"); %A(37,8); R(37,8,"green"); %A(42,35); R(42,35,"green"); %A(43,37); R(43,37,"green"); %A(50,42); R(50,42,"green"); %A(60,55); R(60,55,"green"); %A(65,60); R(65,60,"green"); %A(85,65); R(85,65,"green"); %A(88,42); R(88,42,"green"); %A(101,12); R(101,12,"green"); %A(73,101); R(73,101,"green"); %A(86,81); R(86,81,"green"); %A(86,82); R(86,82,"green"); %A(86,83); R(86,83,"green"); %A(102,73); R(102,73,"green"); %A(102,82); R(102,82,"green"); %A(10,82); R(10,82,"green"); % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LightBlue}{rgb}{0.68,0.84,0.90} \definecolor{LightCoral}{rgb}{0.94,0.50,0.50} \definecolor{LightCyan}{rgb}{0.88,1.00,1.00} \definecolor{LightGoldenrodYellow}{rgb}{0.98,0.98,0.82} \definecolor{LightGreen}{rgb}{0.56,0.93,0.56} \definecolor{LightGray}{rgb}{0.82,0.82,0.82} \definecolor{LightPink}{rgb}{1.00,0.71,0.75} \definecolor{Lime}{rgb}{0.00,1.00,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.14/0.39, 2/3.12/0.20, 3/2.80/1.14, 4/3.78/0.95, 5/4.10/0.00, 6/2.34/1.37, 7/3.00/2.12, 8/3.98/1.93, 9/1.39/1.05, 10/4.61/3.20, 11/0.64/1.71, 12/2.25/2.78, 13/1.30/2.46, 14/0.32/2.66, 15/0.98/3.41, 16/0.00/3.61, 17/1.93/3.73, 18/0.95/3.93, 19/0.20/4.59, 20/1.14/4.91, 21/0.39/5.57, 22/2.12/4.71, 23/1.37/5.37, 24/1.05/6.32, 25/2.03/6.12, 26/1.71/7.07, 27/2.78/5.46, 28/2.46/6.41, 29/2.66/7.39, 30/3.41/6.73, 31/3.61/7.71, 32/3.73/5.78, 33/3.93/6.76, 34/4.59/7.52, 35/4.68/6.10, 36/4.30/0.98, 37/4.96/1.73, 38/5.05/0.32, 39/5.34/6.86, 40/5.71/1.07, 41/5.53/7.84, 42/5.66/5.91, 43/5.91/2.05, 44/6.03/0.12, 45/5.86/6.89, 46/6.23/1.10, 47/6.52/7.64, 48/6.84/6.69, 49/7.50/7.44, 50/6.64/5.71, 51/7.30/6.46, 52/8.25/6.78, 53/8.05/5.80, 54/9.00/6.12, 55/7.39/5.05, 56/8.34/5.37, 57/9.32/5.18, 58/8.66/4.42, 59/9.64/4.23, 60/7.71/4.10, 61/8.69/3.91, 62/9.44/3.25, 63/8.50/2.93, 64/9.25/2.27, 65/7.52/3.12, 66/8.27/2.46, 67/8.59/1.52, 68/7.61/1.71, 69/7.93/0.77, 70/6.86/2.37, 71/7.18/1.43, 72/6.98/0.44, 73/2.88/4.05, 74/4.93/2.25, 79/4.05/4.84, 80/4.71/5.59, 81/5.46/4.93, 82/4.80/4.18, 83/5.12/3.23, 84/5.87/2.57, 85/6.53/3.32, 86/5.78/3.98, 87/6.73/4.30, 88/5.98/4.96, 100/3.95/2.44, 101/3.20/3.10, 102/3.86/3.86, 103/3.54/4.80, 104/1.59/2.03} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/348.69/498.69/0.4/Blue, 11/318.69/468.69/0.4/Green, 16/288.69/438.69/0.4/Orange, 21/258.69/408.69/0.4/Violet, 26/228.69/378.69/0.4/Teal, 31/198.69/348.69/0.4/Lime, 34/168.69/378.69/0.4/LightBlue, 41/198.69/348.69/0.4/LightCoral, 49/168.69/318.69/0.4/LightCyan, 54/138.69/288.69/0.4/LightGoldenrodYellow, 59/108.69/258.69/0.4/LightGreen, 64/78.69/228.69/0.4/LightGray, 69/48.69/198.69/0.4/LightPink} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 1/3, 2/5, 3/2, 3/4, 4/2, 4/5, 6/9, 6/1, 7/6, 7/3, 8/4, 8/36, 9/1, 10/102, 10/100, 10/82, 11/9, 11/104, 12/13, 12/104, 13/14, 13/11, 14/11, 15/14, 15/13, 16/14, 16/15, 17/18, 17/15, 17/12, 18/19, 18/16, 19/16, 20/19, 20/18, 21/19, 21/20, 22/23, 22/20, 22/17, 23/24, 23/21, 24/21, 25/24, 25/23, 26/24, 26/25, 27/28, 27/25, 28/29, 28/26, 29/26, 30/29, 30/28, 31/29, 31/30, 32/33, 32/30, 32/27, 33/34, 33/31, 34/31, 35/39, 35/32, 35/33, 36/5, 36/38, 37/36, 37/40, 37/8, 38/5, 38/44, 39/41, 39/34, 40/38, 40/44, 41/34, 42/45, 42/39, 42/35, 43/40, 43/46, 43/37, 44/72, 44/46, 45/47, 45/41, 46/72, 46/71, 47/41, 48/47, 48/45, 49/47, 49/48, 50/51, 50/48, 50/42, 51/52, 51/49, 52/49, 53/52, 53/51, 54/52, 54/53, 55/56, 55/53, 56/57, 56/54, 57/54, 58/57, 58/56, 59/57, 59/58, 60/61, 60/58, 60/55, 61/62, 61/59, 62/59, 63/62, 63/61, 64/62, 64/63, 65/66, 65/63, 65/60, 66/67, 66/64, 67/64, 68/67, 68/66, 69/67, 69/68, 70/71, 70/68, 71/72, 71/69, 72/69, 73/103, 73/22, 73/101, 74/8, 74/43, 79/80, 79/32, 80/42, 80/32, 81/42, 81/80, 82/81, 82/79, 83/84, 83/82, 84/74, 84/70, 85/84, 85/70, 85/65, 86/87, 86/88, 86/81, 86/82, 86/83, 87/85, 87/55, 88/87, 88/50, 88/42, 100/7, 100/74, 101/7, 101/100, 101/12, 102/79, 102/103, 102/73, 102/82, 103/32, 103/27, 104/9, 104/6} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,74,79,...,88,100,...,104} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-17) -- (p-12); \draw[Green,very thick] (p-22) -- (p-17); \draw[Green,very thick] (p-32) -- (p-27); \draw[Green,very thick] (p-35) -- (p-33); \draw[Green,very thick] (p-37) -- (p-8); \draw[Green,very thick] (p-42) -- (p-35); \draw[Green,very thick] (p-43) -- (p-37); \draw[Green,very thick] (p-50) -- (p-42); \draw[Green,very thick] (p-60) -- (p-55); \draw[Green,very thick] (p-65) -- (p-60); \draw[Green,very thick] (p-85) -- (p-65); \draw[Green,very thick] (p-88) -- (p-42); \draw[Green,very thick] (p-101) -- (p-12); \draw[Green,very thick] (p-73) -- (p-101); \draw[Green,very thick] (p-86) -- (p-81); \draw[Green,very thick] (p-86) -- (p-82); \draw[Green,very thick] (p-86) -- (p-83); \draw[Green,very thick] (p-102) -- (p-73); \draw[Green,very thick] (p-102) -- (p-82); \draw[Green,very thick] (p-10) -- (p-82); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/348.69/498.69/0.4/Blue, 11/318.69/468.69/0.4/Green, 16/288.69/438.69/0.4/Orange, 21/258.69/408.69/0.4/Violet, 26/228.69/378.69/0.4/Teal, 31/198.69/348.69/0.4/Lime, 34/168.69/378.69/0.4/LightBlue, 41/198.69/348.69/0.4/LightCoral, 49/168.69/318.69/0.4/LightCyan, 54/138.69/288.69/0.4/LightGoldenrodYellow, 59/108.69/258.69/0.4/LightGreen, 64/78.69/228.69/0.4/LightGray, 69/48.69/198.69/0.4/LightPink} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/289, 2/319, 3/139, 4/19, 5/319, 6/49, 7/229, 8/139, 9/289, 10/289, 11/169, 12/336, 13/19, 14/199, 15/19, 16/139, 17/306, 18/289, 19/109, 20/349, 21/199, 22/111, 23/319, 24/139, 25/319, 26/169, 27/169, 28/229, 29/49, 30/349, 31/49, 32/49, 33/109, 34/19, 35/199, 36/259, 37/169, 38/199, 39/289, 40/289, 41/49, 42/319, 43/49, 44/229, 45/259, 46/169, 47/79, 48/259, 49/109, 50/19, 51/169, 52/49, 53/229, 54/349, 55/81, 56/199, 57/19, 58/199, 59/49, 60/126, 61/109, 62/349, 63/169, 64/289, 65/306, 66/139, 67/19, 68/199, 69/349, 70/319, 71/49, 72/349, 73/199, 74/96, 79/109, 80/169, 81/79, 82/199, 83/259, 84/199, 85/79, 86/19, 87/349, 88/109, 100/349, 101/109, 102/169, 103/289, 104/49} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ funktioniert auch. Randpunkt P38 unten ist nach innen gedrückt. Anschließend Button "beweglich?" gibt als Ergebnis einen beweglichen Winkel aus. Den kann man mit Buttons "-10", "+10"... variieren oder die Animation starten mit Buttons "Ausrichten horizontal entlang P16-P59" und nur "Kanten" anzeigen und dann Knopf "Start_zwoelfterWinkel" links vom Graph. Der Bereich der Animation lässt sich im großen Eingabefenster im animate-Element einstellen, anstelle von values="0;5;0;-5;0" geht values="0;30;0;-30;0". $ %Eingabe war: % %#1913-3 % % % % %blauerWinkel=149.99999999999997+(-1.00000603617127)*(zwoelfterWinkel-(149.99999999999986)); %gruenerWinkel=150.00000000000114+(1.0000071307738647)*(zwoelfterWinkel-(149.99999999999986)); %orangerWinkel=149.99999999999818+(-1.0000050952077124)*(zwoelfterWinkel-(149.99999999999986)); %vierterWinkel=150.00000000000037+(1.000003632145485)*(zwoelfterWinkel-(149.99999999999986)); %fuenfterWinkel=150.0000000000011+(-1.0000031642752918)*(zwoelfterWinkel-(149.99999999999986)); %sechsterWinkel=149.99999999999906+(0.9999986136545512)*(zwoelfterWinkel-(149.99999999999986)); %siebenterWinkel=210.00000000000082+(-0.9999972834206445)*(zwoelfterWinkel-(149.99999999999986)); %achterWinkel=149.99999999999983+(0.9999974767591252)*(zwoelfterWinkel-(149.99999999999986)); %neunterWinkel=150.00000000000003+(-0.9999977311982171)*(zwoelfterWinkel-(149.99999999999986)); %zehnterWinkel=150+(0.9999962329001859)*(zwoelfterWinkel-(149.99999999999986)); %elfterWinkel=150.00000000000006+(-0.9999973961573823)*(zwoelfterWinkel-(149.99999999999986)); %dreizehnterWinkel=149.99999999999994+(-1.0000034026393805)*(zwoelfterWinkel-(149.99999999999986)); %P[5]=[51.25119960527222,-34.889211526751666]; P[2]=[1.9917751386890765,-21.6901885213085]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(9,1,2,blauerWinkel); N(6,9,1); N(104,9,6); N(11,9,104); M(14,11,9,gruenerWinkel); N(13,14,11); N(15,14,13); N(16,14,15); M(19,16,14,orangerWinkel); N(18,19,16); N(20,19,18); N(21,19,20); M(24,21,19,vierterWinkel); N(23,24,21); N(25,24,23); N(26,24,25); M(29,26,24,fuenfterWinkel); N(28,29,26); N(30,29,28); N(31,29,30); M(34,31,29,sechsterWinkel); N(33,34,31); M(41,34,31,siebenterWinkel); N(39,41,34); M(47,41,34,achterWinkel); N(45,47,41); N(48,47,45); N(49,47,48); M(52,49,47,neunterWinkel); N(51,52,49); N(53,52,51); N(54,52,53); M(57,54,52,zehnterWinkel); N(56,57,54); N(58,57,56); N(59,57,58); M(62,59,57,elfterWinkel); N(61,62,59); N(63,62,61); N(64,62,63); M(67,64,62,zwoelfterWinkel); N(66,67,64); N(68,67,66); N(69,67,68); M(72,69,67,dreizehnterWinkel); N(71,72,69); N(46,72,71); N(44,72,46); Q(38,5,44,1*D,1*D); L(36,5,38); L(40,38,44); N(7,6,3); N(8,4,36); N(12,13,104); N(17,18,15); N(22,23,20); N(27,28,25); N(32,33,30); N(35,39,32); N(37,36,40); N(42,45,39); N(43,40,46); N(50,51,48); N(55,56,53); N(60,61,58); N(65,66,63); N(70,71,68); N(74,8,43); N(80,42,32); N(81,42,80); N(84,74,70); N(85,84,70); N(87,85,55); N(88,87,50); N(100,7,74); N(101,7,100); N(103,32,27); N(73,103,22); N(79,80,32); N(82,81,79); N(83,84,82); N(86,87,88); N(102,79,103); N(10,102,100); %A(17,12); R(17,12,"green"); %A(22,17); R(22,17,"green"); %A(32,27); R(32,27,"green"); %A(35,33); R(35,33,"green"); %A(37,8); R(37,8,"green"); %A(42,35); R(42,35,"green"); %A(43,37); R(43,37,"green"); %A(50,42); R(50,42,"green"); %A(60,55); R(60,55,"green"); %A(65,60); R(65,60,"green"); %A(85,65); R(85,65,"green"); %A(88,42); R(88,42,"green"); %A(101,12); R(101,12,"green"); %A(73,101); R(73,101,"green"); %A(86,81); R(86,81,"green"); %A(86,82); R(86,82,"green"); %A(86,83); R(86,83,"green"); %A(102,73); R(102,73,"green"); %A(102,82); R(102,82,"green"); %A(10,82); R(10,82,"green"); % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LightGray}{rgb}{0.82,0.82,0.82} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.93/0.52, 2/2.90/0.26, 3/2.64/1.22, 4/3.60/0.97, 5/3.86/0.00, 6/2.19/1.48, 7/2.90/2.19, 8/3.86/1.93, 9/1.22/1.22, 10/4.57/3.16, 11/0.52/1.93, 12/2.19/2.90, 13/1.22/2.64, 14/0.26/2.90, 15/0.97/3.60, 16/0.00/3.86, 17/1.93/3.86, 18/0.97/4.12, 19/0.26/4.83, 20/1.22/5.09, 21/0.52/5.80, 22/2.19/4.83, 23/1.48/5.54, 24/1.22/6.50, 25/2.19/6.24, 26/1.93/7.21, 27/2.90/5.54, 28/2.64/6.50, 29/2.90/7.47, 30/3.60/6.76, 31/3.86/7.73, 32/3.86/5.80, 33/4.12/6.76, 34/4.83/7.47, 35/4.83/6.05, 36/4.12/0.97, 37/4.83/1.67, 38/4.83/0.26, 39/5.54/6.76, 40/5.54/0.97, 41/5.80/7.73, 42/5.80/5.80, 43/5.80/1.93, 44/5.80/0.00, 45/6.05/6.76, 46/6.05/0.97, 47/6.76/7.47, 48/7.02/6.50, 49/7.73/7.21, 50/6.76/5.54, 51/7.47/6.24, 52/8.43/6.50, 53/8.18/5.54, 54/9.14/5.80, 55/7.47/4.83, 56/8.43/5.09, 57/9.40/4.83, 58/8.69/4.12, 59/9.66/3.86, 60/7.73/3.86, 61/8.69/3.60, 62/9.40/2.90, 63/8.43/2.64, 64/9.14/1.93, 65/7.47/2.90, 66/8.18/2.19, 67/8.43/1.22, 68/7.47/1.48, 69/7.73/0.52, 70/6.76/2.19, 71/7.02/1.22, 72/6.76/0.26, 73/2.90/4.12, 74/4.83/2.19, 79/4.12/4.83, 80/4.83/5.54, 81/5.54/4.83, 82/4.83/4.12, 83/5.09/3.16, 84/5.80/2.45, 85/6.50/3.16, 86/5.80/3.86, 87/6.76/4.12, 88/6.05/4.83, 100/3.86/2.45, 101/3.16/3.16, 102/3.86/3.86, 103/3.60/4.83, 104/1.48/2.19} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 64/75.00/225.00/0.4/LightGray} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 1/3, 2/5, 3/2, 3/4, 4/2, 4/5, 6/9, 6/1, 7/6, 7/3, 8/4, 8/36, 9/1, 10/102, 10/100, 10/82, 11/9, 11/104, 12/13, 12/104, 13/14, 13/11, 14/11, 15/14, 15/13, 16/14, 16/15, 17/18, 17/15, 17/12, 18/19, 18/16, 19/16, 20/19, 20/18, 21/19, 21/20, 22/23, 22/20, 22/17, 23/24, 23/21, 24/21, 25/24, 25/23, 26/24, 26/25, 27/28, 27/25, 28/29, 28/26, 29/26, 30/29, 30/28, 31/29, 31/30, 32/33, 32/30, 32/27, 33/34, 33/31, 34/31, 35/39, 35/32, 35/33, 36/5, 36/38, 37/36, 37/40, 37/8, 38/5, 38/44, 39/41, 39/34, 40/38, 40/44, 41/34, 42/45, 42/39, 42/35, 43/40, 43/46, 43/37, 44/72, 44/46, 45/47, 45/41, 46/72, 46/71, 47/41, 48/47, 48/45, 49/47, 49/48, 50/51, 50/48, 50/42, 51/52, 51/49, 52/49, 53/52, 53/51, 54/52, 54/53, 55/56, 55/53, 56/57, 56/54, 57/54, 58/57, 58/56, 59/57, 59/58, 60/61, 60/58, 60/55, 61/62, 61/59, 62/59, 63/62, 63/61, 64/62, 64/63, 65/66, 65/63, 65/60, 66/67, 66/64, 67/64, 68/67, 68/66, 69/67, 69/68, 70/71, 70/68, 71/72, 71/69, 72/69, 73/103, 73/22, 73/101, 74/8, 74/43, 79/80, 79/32, 80/42, 80/32, 81/42, 81/80, 82/81, 82/79, 83/84, 83/82, 84/74, 84/70, 85/84, 85/70, 85/65, 86/87, 86/88, 86/81, 86/82, 86/83, 87/85, 87/55, 88/87, 88/50, 88/42, 100/7, 100/74, 101/7, 101/100, 101/12, 102/79, 102/103, 102/73, 102/82, 103/32, 103/27, 104/9, 104/6} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,74,79,...,88,100,...,104} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-17) -- (p-12); \draw[Green,very thick] (p-22) -- (p-17); \draw[Green,very thick] (p-32) -- (p-27); \draw[Green,very thick] (p-35) -- (p-33); \draw[Green,very thick] (p-37) -- (p-8); \draw[Green,very thick] (p-42) -- (p-35); \draw[Green,very thick] (p-43) -- (p-37); \draw[Green,very thick] (p-50) -- (p-42); \draw[Green,very thick] (p-60) -- (p-55); \draw[Green,very thick] (p-65) -- (p-60); \draw[Green,very thick] (p-85) -- (p-65); \draw[Green,very thick] (p-88) -- (p-42); \draw[Green,very thick] (p-101) -- (p-12); \draw[Green,very thick] (p-73) -- (p-101); \draw[Green,very thick] (p-86) -- (p-81); \draw[Green,very thick] (p-86) -- (p-82); \draw[Green,very thick] (p-86) -- (p-83); \draw[Green,very thick] (p-102) -- (p-73); \draw[Green,very thick] (p-102) -- (p-82); \draw[Green,very thick] (p-10) -- (p-82); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 64/75.00/225.00/0.4/LightGray} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/285, 2/315, 3/135, 4/15, 5/315, 6/45, 7/225, 8/135, 9/225, 10/285, 11/255, 12/243, 13/315, 14/135, 15/75, 16/135, 17/62, 18/285, 19/225, 20/45, 21/195, 22/108, 23/255, 24/195, 25/15, 26/75, 27/165, 28/285, 29/105, 30/285, 31/135, 32/45, 33/105, 34/15, 35/345, 36/255, 37/15, 38/345, 39/285, 40/285, 41/45, 42/315, 43/45, 44/315, 45/195, 46/165, 47/75, 48/255, 49/15, 50/15, 51/225, 52/45, 53/285, 54/345, 55/77, 56/135, 57/315, 58/255, 59/315, 60/243, 61/165, 62/345, 63/165, 64/15, 65/302, 66/135, 67/15, 68/195, 69/345, 70/315, 71/45, 72/225, 73/195, 74/92, 79/105, 80/15, 81/75, 82/195, 83/255, 84/195, 85/75, 86/225, 87/345, 88/105, 100/345, 101/105, 102/165, 103/285, 104/45} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Dann Buttons "neu zeichnen", "Ausrichten, "Kanten", "Start_zwoelfter_Winkel". Diesen letzten Graph nehme ich als Ausgangspunkt, um Graph #1907-2 einzugeben. nur zwei Punkte und zwei Kanten löschen, dann fünf neue Kanten ergänzen 87 Knoten, 85×Grad 4, 2×Grad 7, 0 Überschneidungen 177 Kanten, minimal 0.99999999999958744112, maximal 1.00000000000010214052 $ %Eingabe war: % %#1913-3 % % % %blauerWinkel=149.99999999999997+(-1.00000603617127)*(zwoelfterWinkel-(149.99999999999986)); %gruenerWinkel=150.00000000000114+(1.0000071307738647)*(zwoelfterWinkel-(149.99999999999986)); %orangerWinkel=149.99999999999818+(-1.0000050952077124)*(zwoelfterWinkel-(149.99999999999986)); %vierterWinkel=150.00000000000037+(1.000003632145485)*(zwoelfterWinkel-(149.99999999999986)); %fuenfterWinkel=150.0000000000011+(-1.0000031642752918)*(zwoelfterWinkel-(149.99999999999986)); %sechsterWinkel=149.99999999999906+(0.9999986136545512)*(zwoelfterWinkel-(149.99999999999986)); %siebenterWinkel=210.00000000000082+(-0.9999972834206445)*(zwoelfterWinkel-(149.99999999999986)); %achterWinkel=149.99999999999983+(0.9999974767591252)*(zwoelfterWinkel-(149.99999999999986)); %neunterWinkel=150.00000000000003+(-0.9999977311982171)*(zwoelfterWinkel-(149.99999999999986)); %zehnterWinkel=150+(0.9999962329001859)*(zwoelfterWinkel-(149.99999999999986)); %elfterWinkel=150.00000000000006+(-0.9999973961573823)*(zwoelfterWinkel-(149.99999999999986)); %dreizehnterWinkel=149.99999999999994+(-1.0000034026393805)*(zwoelfterWinkel-(149.99999999999986)); %P[5]=[51.25119960527222,-34.889211526751666]; P[2]=[1.9917751386890765,-21.6901885213085]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(9,1,2,blauerWinkel); N(6,9,1); N(104,9,6); N(11,9,104); M(14,11,9,gruenerWinkel); N(13,14,11); N(15,14,13); N(16,14,15); M(19,16,14,orangerWinkel); N(18,19,16); N(20,19,18); N(21,19,20); M(24,21,19,vierterWinkel); N(23,24,21); N(25,24,23); N(26,24,25); M(29,26,24,fuenfterWinkel); N(28,29,26); N(30,29,28); N(31,29,30); M(34,31,29,sechsterWinkel); N(33,34,31); M(41,34,31,siebenterWinkel); N(39,41,34); M(47,41,34,achterWinkel); N(45,47,41); N(48,47,45); N(49,47,48); M(52,49,47,neunterWinkel); N(51,52,49); N(53,52,51); N(54,52,53); M(57,54,52,zehnterWinkel); N(56,57,54); N(58,57,56); N(59,57,58); M(62,59,57,elfterWinkel); N(61,62,59); N(63,62,61); N(64,62,63); M(67,64,62,zwoelfterWinkel); N(66,67,64); N(68,67,66); N(69,67,68); M(72,69,67,dreizehnterWinkel); N(71,72,69); N(46,72,71); N(44,72,46); Q(38,5,44,1*D,1*D); L(36,5,38); L(40,38,44); N(7,6,3); N(8,4,36); N(12,13,104); N(17,18,15); N(22,23,20); N(27,28,25); N(32,33,30); N(35,39,32); N(37,36,40); N(42,45,39); N(43,40,46); N(50,51,48); N(55,56,53); N(60,61,58); N(65,66,63); N(70,71,68); N(74,8,43); N(80,42,32); N(81,42,80); N(84,74,70); N(85,84,70); N(87,85,55); N(88,87,50); N(100,7,74); N(101,7,100); N(103,32,27); N(73,103,22); N(79,80,32); N(82,81,79); N(83,84,82); N(86,87,88); N(102,79,103); N(10,102,100); %A(17,12); R(17,12,"green"); %A(22,17); R(22,17,"green"); %A(32,27); R(32,27,"green"); %A(35,33); R(35,33,"green"); %A(37,8); R(37,8,"green"); %A(42,35); R(42,35,"green"); %A(43,37); R(43,37,"green"); %A(50,42); R(50,42,"green"); %A(60,55); R(60,55,"green"); %A(65,60); R(65,60,"green"); %A(85,65); R(85,65,"green"); %A(88,42); R(88,42,"green"); %A(101,12); R(101,12,"green"); %A(73,101); R(73,101,"green"); %A(86,81); R(86,81,"green"); %A(86,82); R(86,82,"green"); %A(86,83); R(86,83,"green"); %A(102,73); R(102,73,"green"); %A(102,82); R(102,82,"green"); %A(10,82); R(10,82,"green"); Z(100); Z(10); Z(17,12); Z(102,73); A(17,73); A(101,102); A(74,83); A(82,86); A(12,7); % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LightGray}{rgb}{0.82,0.82,0.82} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.93/0.52, 2/2.90/0.26, 3/2.64/1.22, 4/3.60/0.97, 5/3.86/0.00, 6/2.19/1.48, 7/2.90/2.19, 8/3.86/1.93, 9/1.22/1.22, 11/0.52/1.93, 12/2.19/2.90, 13/1.22/2.64, 14/0.26/2.90, 15/0.97/3.60, 16/0.00/3.86, 17/1.93/3.86, 18/0.97/4.12, 19/0.26/4.83, 20/1.22/5.09, 21/0.52/5.80, 22/2.19/4.83, 23/1.48/5.54, 24/1.22/6.50, 25/2.19/6.24, 26/1.93/7.21, 27/2.90/5.54, 28/2.64/6.50, 29/2.90/7.47, 30/3.60/6.76, 31/3.86/7.73, 32/3.86/5.80, 33/4.12/6.76, 34/4.83/7.47, 35/4.83/6.05, 36/4.12/0.97, 37/4.83/1.67, 38/4.83/0.26, 39/5.54/6.76, 40/5.54/0.97, 41/5.80/7.73, 42/5.80/5.80, 43/5.80/1.93, 44/5.80/0.00, 45/6.05/6.76, 46/6.05/0.97, 47/6.76/7.47, 48/7.02/6.50, 49/7.73/7.21, 50/6.76/5.54, 51/7.47/6.24, 52/8.43/6.50, 53/8.18/5.54, 54/9.14/5.80, 55/7.47/4.83, 56/8.43/5.09, 57/9.40/4.83, 58/8.69/4.12, 59/9.66/3.86, 60/7.73/3.86, 61/8.69/3.60, 62/9.40/2.90, 63/8.43/2.64, 64/9.14/1.93, 65/7.47/2.90, 66/8.18/2.19, 67/8.43/1.22, 68/7.47/1.48, 69/7.73/0.52, 70/6.76/2.19, 71/7.02/1.22, 72/6.76/0.26, 73/2.90/4.12, 74/4.83/2.19, 79/4.12/4.83, 80/4.83/5.54, 81/5.54/4.83, 82/4.83/4.12, 83/5.09/3.16, 84/5.80/2.45, 85/6.50/3.16, 86/5.80/3.86, 87/6.76/4.12, 88/6.05/4.83, 101/3.16/3.16, 102/3.86/3.86, 103/3.60/4.83, 104/1.48/2.19} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 64/75.00/225.00/0.4/LightGray} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 1/3, 2/5, 3/2, 3/4, 4/2, 4/5, 6/9, 6/1, 7/6, 7/3, 8/4, 8/36, 9/1, 11/9, 11/104, 12/13, 12/104, 12/7, 13/14, 13/11, 14/11, 15/14, 15/13, 16/14, 16/15, 17/18, 17/15, 17/73, 18/19, 18/16, 19/16, 20/19, 20/18, 21/19, 21/20, 22/23, 22/20, 22/17, 23/24, 23/21, 24/21, 25/24, 25/23, 26/24, 26/25, 27/28, 27/25, 28/29, 28/26, 29/26, 30/29, 30/28, 31/29, 31/30, 32/33, 32/30, 32/27, 33/34, 33/31, 34/31, 35/39, 35/32, 35/33, 36/5, 36/38, 37/36, 37/40, 37/8, 38/5, 38/44, 39/41, 39/34, 40/38, 40/44, 41/34, 42/45, 42/39, 42/35, 43/40, 43/46, 43/37, 44/72, 44/46, 45/47, 45/41, 46/72, 46/71, 47/41, 48/47, 48/45, 49/47, 49/48, 50/51, 50/48, 50/42, 51/52, 51/49, 52/49, 53/52, 53/51, 54/52, 54/53, 55/56, 55/53, 56/57, 56/54, 57/54, 58/57, 58/56, 59/57, 59/58, 60/61, 60/58, 60/55, 61/62, 61/59, 62/59, 63/62, 63/61, 64/62, 64/63, 65/66, 65/63, 65/60, 66/67, 66/64, 67/64, 68/67, 68/66, 69/67, 69/68, 70/71, 70/68, 71/72, 71/69, 72/69, 73/103, 73/22, 73/101, 74/8, 74/43, 74/83, 79/80, 79/32, 80/42, 80/32, 81/42, 81/80, 82/81, 82/79, 83/84, 83/82, 84/74, 84/70, 85/84, 85/70, 85/65, 86/87, 86/88, 86/81, 86/83, 87/85, 87/55, 88/87, 88/50, 88/42, 101/7, 101/12, 101/102, 102/79, 102/103, 102/82, 103/32, 103/27, 104/9, 104/6} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,9,11,...,74,79,...,88,101,...,104} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %\draw[Green,very thick] (p-17) -- (p-12); \draw[Green,very thick] (p-22) -- (p-17); \draw[Green,very thick] (p-32) -- (p-27); \draw[Green,very thick] (p-35) -- (p-33); \draw[Green,very thick] (p-37) -- (p-8); \draw[Green,very thick] (p-42) -- (p-35); \draw[Green,very thick] (p-43) -- (p-37); \draw[Green,very thick] (p-50) -- (p-42); \draw[Green,very thick] (p-60) -- (p-55); \draw[Green,very thick] (p-65) -- (p-60); \draw[Green,very thick] (p-85) -- (p-65); \draw[Green,very thick] (p-88) -- (p-42); \draw[Green,very thick] (p-101) -- (p-12); \draw[Green,very thick] (p-73) -- (p-101); \draw[Green,very thick] (p-86) -- (p-81); %\draw[Green,very thick] (p-86) -- (p-82); \draw[Green,very thick] (p-86) -- (p-83); %\draw[Green,very thick] (p-102) -- (p-73); \draw[Green,very thick] (p-102) -- (p-82); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 64/75.00/225.00/0.4/LightGray} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/285, 2/315, 3/135, 4/15, 5/315, 6/45, 7/285, 8/135, 9/225, 11/255, 12/165, 13/315, 14/135, 15/75, 16/135, 17/225, 18/285, 19/225, 20/45, 21/195, 22/105, 23/255, 24/195, 25/15, 26/75, 27/165, 28/285, 29/105, 30/285, 31/135, 32/45, 33/105, 34/15, 35/345, 36/255, 37/15, 38/345, 39/285, 40/285, 41/45, 42/315, 43/45, 44/315, 45/195, 46/165, 47/75, 48/255, 49/15, 50/15, 51/225, 52/45, 53/285, 54/345, 55/77, 56/135, 57/315, 58/255, 59/315, 60/243, 61/165, 62/345, 63/165, 64/15, 65/302, 66/135, 67/15, 68/195, 69/345, 70/315, 71/45, 72/225, 73/345, 74/225, 79/105, 80/15, 81/285, 82/345, 83/105, 84/345, 85/75, 86/225, 87/345, 88/105, 101/45, 102/225, 103/285, 104/45} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Dann wieder Button neue Eingabe "Rahmen zuerst" und "beweglich?", "Ausrichten", "Kanten", "Start_dreizehnterWinkel". Jetzt funktioniert auch folgende Eingabe, die linke Hälfte im letzten Graph komplett löschen (bei gedrückter Alt-Taste mit Mauszeiger ohne Klick auf die Punktbezeichnungen bewegen) $ %Eingabe war: % %#1913-3 % % % %blauerWinkel=149.9999999999835+(1.0000023482695477)*(dreizehnterWinkel-(150.00000000000006)); %gruenerWinkel=90.00000000000811+(-1.0000021637670722)*(dreizehnterWinkel-(150.00000000000006)); %orangerWinkel=150+(1.00000979126476)*(dreizehnterWinkel-(150.00000000000006)); %vierterWinkel=150.00000000000114+(-1.0000097912627721)*(dreizehnterWinkel-(150.00000000000006)); %fuenfterWinkel=149.99999999999815+(0.9999951589733953)*(dreizehnterWinkel-(150.00000000000006)); %sechsterWinkel=150.00000000000034+(-0.9999943365337726)*(dreizehnterWinkel-(150.00000000000006)); %siebenterWinkel=150.0000000000011+(1.000007711914726)*(dreizehnterWinkel-(150.00000000000006)); %achterWinkel=149.99999999999903+(-1.0000070946544908)*(dreizehnterWinkel-(150.00000000000006)); %neunterWinkel=210.0000000000009+(1.0000104530354992)*(dreizehnterWinkel-(150.00000000000006)); %zehnterWinkel=149.99999999999983+(-1.0000079451126966)*(dreizehnterWinkel-(150.00000000000006)); %elfterWinkel=150.00000000000006+(1.0000034831303415)*(dreizehnterWinkel-(150.00000000000006)); %zwoelfterWinkel=150+(-1.0000054004222794)*(dreizehnterWinkel-(150.00000000000006)); %P[44]=[149.77004853844232,-34.88921152675218]; P[38]=[100.51062407185725,-21.69018852131626]; D=ab(44,38); A(38,44); N(40,38,44); M(36,38,44,blauerWinkel); N(5,38,36); M(4,5,38,gruenerWinkel); N(2,5,4); N(3,2,4); N(1,2,3); M(9,1,2,orangerWinkel); N(6,9,1); N(104,9,6); N(11,9,104); M(14,11,9,vierterWinkel); N(13,14,11); N(15,14,13); N(16,14,15); M(19,16,14,fuenfterWinkel); N(18,19,16); N(20,19,18); N(21,19,20); M(24,21,19,sechsterWinkel); N(23,24,21); N(25,24,23); N(26,24,25); M(29,26,24,siebenterWinkel); N(28,29,26); N(30,29,28); N(31,29,30); M(34,31,29,achterWinkel); N(33,34,31); M(41,34,31,neunterWinkel); N(39,41,34); M(47,41,34,zehnterWinkel); N(45,47,41); N(48,47,45); N(49,47,48); M(52,49,47,elfterWinkel); N(51,52,49); N(53,52,51); N(54,52,53); M(57,54,52,zwoelfterWinkel); N(56,57,54); N(58,57,56); N(59,57,58); M(62,59,57,dreizehnterWinkel); N(61,62,59); N(63,62,61); N(64,62,63); Q(69,64,44,2*D,2*D); A(69,44); H(72,44,69,2); A(72,44); L(46,44,72); A(69,64); H(67,64,69,2); A(67,64); L(66,67,64); A(67,69); L(68,69,67); A(68,66); A(72,69); L(71,72,69); A(46,71); N(7,6,3); N(8,4,36); N(12,104,7); N(17,18,15); N(22,20,17); N(27,28,25); N(32,30,27); N(35,33,32); N(37,8,40); N(42,39,35); N(43,37,46); N(50,48,42); N(55,56,53); N(60,58,55); N(65,63,60); N(70,71,68); N(73,22,17); N(74,8,43); N(80,42,32); N(81,42,80); N(84,74,70); N(85,70,65); N(87,85,55); N(88,50,42); N(101,12,7); N(103,32,27); N(79,80,32); N(82,81,79); N(83,84,82); N(86,81,83); N(102,82,103); %A(12,13); R(12,13,"green"); %A(22,23); R(22,23,"green"); %A(32,33); R(32,33,"green"); %A(35,39); R(35,39,"green"); %A(37,36); R(37,36,"green"); %A(42,45); R(42,45,"green"); %A(43,40); R(43,40,"green"); %A(50,51); R(50,51,"green"); %A(60,61); R(60,61,"green"); %A(65,66); R(65,66,"green"); %A(85,84); R(85,84,"green"); %A(88,87); R(88,87,"green"); %A(101,73); R(101,73,"green"); %A(103,73); R(103,73,"green"); %A(83,74); R(83,74,"green"); %A(86,87); R(86,87,"green"); %A(86,88); R(86,88,"green"); %A(102,101); R(102,101,"green"); %A(102,79); R(102,79,"green"); Z(31); Z(29); Z(30); Z(33); Z(32); Z(79); Z(103); Z(102); Z(8); Z(36); Z(5); Z(4); Z(3); Z(2); Z(7); Z(101); Z(73); Z(27); Z(28); Z(26); Z(24); Z(25); Z(23,22); Z(23); Z(21); Z(20); Z(22); Z(17); Z(18); Z(19); Z(16); Z(15); Z(13); Z(12); Z(104); Z(6); Z(9); Z(1); Z(11); Z(14); % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LightPink}{rgb}{1.00,0.71,0.75} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 34/0.00/7.47, 35/0.00/6.05, 37/0.00/1.67, 38/0.00/0.26, 39/0.71/6.76, 40/0.71/0.97, 41/0.97/7.73, 42/0.97/5.80, 43/0.97/1.93, 44/0.97/0.00, 45/1.22/6.76, 46/1.22/0.97, 47/1.93/7.47, 48/2.19/6.50, 49/2.90/7.21, 50/1.93/5.54, 51/2.64/6.24, 52/3.60/6.50, 53/3.35/5.54, 54/4.31/5.80, 55/2.64/4.83, 56/3.60/5.09, 57/4.57/4.83, 58/3.86/4.12, 59/4.83/3.86, 60/2.90/3.86, 61/3.86/3.60, 62/4.57/2.90, 63/3.60/2.64, 64/4.31/1.93, 65/2.64/2.90, 66/3.35/2.19, 67/3.60/1.22, 68/2.64/1.48, 69/2.90/0.52, 70/1.93/2.19, 71/2.19/1.22, 72/1.93/0.26, 74/0.00/2.19, 80/0.00/5.54, 81/0.71/4.83, 82/0.00/4.12, 83/0.26/3.16, 84/0.97/2.45, 85/1.67/3.16, 86/0.97/3.86, 87/1.93/4.12, 88/1.22/4.83} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 59/105.00/255.00/0.4/LightPink} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 35/39, 37/40, 38/44, 39/41, 39/34, 40/38, 40/44, 41/34, 42/39, 42/35, 42/45, 43/37, 43/46, 43/40, 45/47, 45/41, 46/44, 46/72, 46/71, 47/41, 48/47, 48/45, 49/47, 49/48, 50/48, 50/42, 50/51, 51/52, 51/49, 52/49, 53/52, 53/51, 54/52, 54/53, 55/56, 55/53, 56/57, 56/54, 57/54, 58/57, 58/56, 59/57, 59/58, 60/58, 60/55, 60/61, 61/62, 61/59, 62/59, 63/62, 63/61, 64/62, 64/63, 65/63, 65/60, 65/66, 66/67, 66/64, 67/64, 67/69, 68/69, 68/67, 68/66, 70/71, 70/68, 71/72, 71/69, 72/44, 72/69, 74/43, 80/42, 81/42, 81/80, 82/81, 83/84, 83/82, 83/74, 84/74, 84/70, 85/70, 85/65, 85/84, 86/81, 86/83, 86/87, 86/88, 87/85, 87/55, 88/50, 88/42, 88/87} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {34,...,35,37,...,72,74,...,74,80,...,104} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-35) -- (p-39); \draw[Green,very thick] (p-42) -- (p-45); \draw[Green,very thick] (p-43) -- (p-40); \draw[Green,very thick] (p-50) -- (p-51); \draw[Green,very thick] (p-60) -- (p-61); \draw[Green,very thick] (p-65) -- (p-66); \draw[Green,very thick] (p-85) -- (p-84); \draw[Green,very thick] (p-88) -- (p-87); \draw[Green,very thick] (p-83) -- (p-74); \draw[Green,very thick] (p-86) -- (p-87); \draw[Green,very thick] (p-86) -- (p-88); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 59/105.00/255.00/0.4/LightPink} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 34/165, 35/195, 37/165, 38/195, 39/75, 40/285, 41/45, 42/315, 43/45, 44/225, 45/195, 46/165, 47/15, 48/315, 49/15, 50/15, 51/225, 52/45, 53/225, 54/345, 55/78, 56/135, 57/315, 58/255, 59/315, 60/243, 61/165, 62/345, 63/165, 64/15, 65/303, 66/135, 67/315, 68/195, 69/255, 70/315, 71/45, 72/285, 74/225, 80/165, 81/285, 82/167, 83/105, 84/195, 85/75, 86/225, 87/345, 88/255} \node[anchor=\a] (P\i) at (p-\i) {\i}; \draw (-5,0) -- (-5.01,0);%verschiebt den halben Graph nach rechts \end{tikzpicture} $ Dann die rechte Hälfte kopieren mit Eingabe A(34,38,ab(34,38,[1,105],"gespiegelt")); und Button "neu zeichnen". Es entstehen dabei doppelte Punkte entlang der Symmetrieachse P34-P38. Eigentlich müsste man diese Punkte beim Kopieren auslassen und nachträglich fehlende Kanten ergänzen. Doch Button "Knoten im Abstand kleiner D*0.0001 zusammenfassen" (wird nach Button "weitere..." angezeigt) geht hier auch 89 Knoten, 86×Grad 4, 1×Grad 6, 2×Grad 7, 0 Überschneidungen 182 Kanten, minimal 0.99999999999987543298, maximal 1.00000000000035904613 $ %Eingabe war: % %#1913-3 % % % %blauerWinkel=149.9999999999835+(1.0000023482695477)*(dreizehnterWinkel-(150.00000000000006)); %gruenerWinkel=90.00000000000811+(-1.0000021637670722)*(dreizehnterWinkel-(150.00000000000006)); %orangerWinkel=150+(1.00000979126476)*(dreizehnterWinkel-(150.00000000000006)); %vierterWinkel=150.00000000000114+(-1.0000097912627721)*(dreizehnterWinkel-(150.00000000000006)); %fuenfterWinkel=149.99999999999815+(0.9999951589733953)*(dreizehnterWinkel-(150.00000000000006)); %sechsterWinkel=150.00000000000034+(-0.9999943365337726)*(dreizehnterWinkel-(150.00000000000006)); %siebenterWinkel=150.0000000000011+(1.000007711914726)*(dreizehnterWinkel-(150.00000000000006)); %achterWinkel=149.99999999999903+(-1.0000070946544908)*(dreizehnterWinkel-(150.00000000000006)); %neunterWinkel=210.0000000000009+(1.0000104530354992)*(dreizehnterWinkel-(150.00000000000006)); %zehnterWinkel=149.99999999999983+(-1.0000079451126966)*(dreizehnterWinkel-(150.00000000000006)); %elfterWinkel=150.00000000000006+(1.0000034831303415)*(dreizehnterWinkel-(150.00000000000006)); %zwoelfterWinkel=150+(-1.0000054004222794)*(dreizehnterWinkel-(150.00000000000006)); %P[44]=[149.77004853844232,-34.88921152675218]; P[38]=[100.51062407185725,-21.69018852131626]; D=ab(44,38); A(38,44); N(40,38,44); M(36,38,44,blauerWinkel); N(5,38,36); M(4,5,38,gruenerWinkel); N(2,5,4); N(3,2,4); N(1,2,3); M(9,1,2,orangerWinkel); N(6,9,1); N(104,9,6); N(11,9,104); M(14,11,9,vierterWinkel); N(13,14,11); N(15,14,13); N(16,14,15); M(19,16,14,fuenfterWinkel); N(18,19,16); N(20,19,18); N(21,19,20); M(24,21,19,sechsterWinkel); N(23,24,21); N(25,24,23); N(26,24,25); M(29,26,24,siebenterWinkel); N(28,29,26); N(30,29,28); N(31,29,30); M(34,31,29,achterWinkel); N(33,34,31); M(41,34,31,neunterWinkel); N(39,41,34); M(47,41,34,zehnterWinkel); N(45,47,41); N(48,47,45); N(49,47,48); M(52,49,47,elfterWinkel); N(51,52,49); N(53,52,51); N(54,52,53); M(57,54,52,zwoelfterWinkel); N(56,57,54); N(58,57,56); N(59,57,58); M(62,59,57,dreizehnterWinkel); N(61,62,59); N(63,62,61); N(64,62,63); Q(69,64,44,2*D,2*D); A(69,44); H(72,44,69,2); A(72,44); L(46,44,72); A(69,64); H(67,64,69,2); A(67,64); L(66,67,64); A(67,69); L(68,69,67); A(68,66); A(72,69); L(71,72,69); A(46,71); N(7,6,3); N(8,4,36); N(12,104,7); N(17,18,15); N(22,20,17); N(27,28,25); N(32,30,27); N(35,33,32); N(37,8,40); N(42,39,35); N(43,37,46); N(50,48,42); N(55,56,53); N(60,58,55); N(65,63,60); N(70,71,68); N(73,22,17); N(74,8,43); N(80,42,32); N(81,42,80); N(84,74,70); N(85,70,65); N(87,85,55); N(88,50,42); N(101,12,7); N(103,32,27); N(79,80,32); N(82,81,79); N(83,84,82); N(86,81,83); N(102,82,103); %A(12,13); R(12,13,"green"); %A(22,23); R(22,23,"green"); %A(32,33); R(32,33,"green"); %A(35,39); R(35,39,"green"); %A(37,36); R(37,36,"green"); %A(42,45); R(42,45,"green"); %A(43,40); R(43,40,"green"); %A(50,51); R(50,51,"green"); %A(60,61); R(60,61,"green"); %A(65,66); R(65,66,"green"); %A(85,84); R(85,84,"green"); %A(88,87); R(88,87,"green"); %A(101,73); R(101,73,"green"); %A(103,73); R(103,73,"green"); %A(83,74); R(83,74,"green"); %A(86,87); R(86,87,"green"); %A(86,88); R(86,88,"green"); %A(102,101); R(102,101,"green"); %A(102,79); R(102,79,"green"); Z(31); Z(29); Z(30); Z(33); Z(32); Z(79); Z(103); Z(102); Z(8); Z(36); Z(5); Z(4); Z(3); Z(2); Z(7); Z(101); Z(73); Z(27); Z(28); Z(26); Z(24); Z(25); Z(23,22); Z(23); Z(21); Z(20); Z(22); Z(17); Z(18); Z(19); Z(16); Z(15); Z(13); Z(12); Z(104); Z(6); Z(9); Z(1); Z(11); Z(14); %A(34,38,ab(34,38,[1,105],"gespiegelt")); % %//ergänzt von Button "Knoten zusammenfassen": %C(35,89); C(37,90); C(74,125); C(80,126); C(82,128); % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{LightPink}{rgb}{1.00,0.71,0.75} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 34/4.83/7.47, 35/4.83/6.05, 37/4.83/1.67, 38/4.83/0.26, 39/5.54/6.76, 40/5.54/0.97, 41/5.80/7.73, 42/5.80/5.80, 43/5.80/1.93, 44/5.80/0.00, 45/6.05/6.76, 46/6.05/0.97, 47/6.76/7.47, 48/7.02/6.50, 49/7.73/7.21, 50/6.76/5.54, 51/7.47/6.24, 52/8.43/6.50, 53/8.18/5.54, 54/9.14/5.80, 55/7.47/4.83, 56/8.43/5.09, 57/9.40/4.83, 58/8.69/4.12, 59/9.66/3.86, 60/7.73/3.86, 61/8.69/3.60, 62/9.40/2.90, 63/8.43/2.64, 64/9.14/1.93, 65/7.47/2.90, 66/8.18/2.19, 67/8.43/1.22, 68/7.47/1.48, 69/7.73/0.52, 70/6.76/2.19, 71/7.02/1.22, 72/6.76/0.26, 74/4.83/2.19, 80/4.83/5.54, 81/5.54/4.83, 82/4.83/4.12, 83/5.09/3.16, 84/5.80/2.45, 85/6.50/3.16, 86/5.80/3.86, 87/6.76/4.12, 88/6.05/4.83, 91/4.12/6.76, 92/4.12/0.97, 93/3.86/7.73, 94/3.86/5.80, 95/3.86/1.93, 96/3.86/0.00, 97/3.60/6.76, 98/3.60/0.97, 99/2.90/7.47, 100/2.64/6.50, 101/1.93/7.21, 102/2.90/5.54, 103/2.19/6.24, 104/1.22/6.50, 105/1.48/5.54, 106/0.52/5.80, 107/2.19/4.83, 108/1.22/5.09, 109/0.26/4.83, 110/0.97/4.12, 111/0.00/3.86, 112/1.93/3.86, 113/0.97/3.60, 114/0.26/2.90, 115/1.22/2.64, 116/0.52/1.93, 117/2.19/2.90, 118/1.48/2.19, 119/1.22/1.22, 120/2.19/1.48, 121/1.93/0.52, 122/2.90/2.19, 123/2.64/1.22, 124/2.90/0.26, 127/4.12/4.83, 129/4.57/3.16, 130/3.86/2.45, 131/3.16/3.16, 132/3.86/3.86, 133/2.90/4.12, 134/3.60/4.83} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 59/105.00/255.00/0.4/LightPink} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 34/39, 34/41, 34/91, 34/93, 35/39, 35/91, 35/94, 35/42, 37/40, 37/43, 37/92, 37/95, 38/44, 38/96, 38/40, 38/92, 39/41, 39/42, 40/44, 40/43, 41/45, 41/47, 42/45, 42/50, 42/80, 42/81, 42/88, 43/46, 43/74, 44/46, 44/72, 45/47, 45/48, 46/72, 46/71, 47/48, 47/49, 48/49, 48/50, 49/51, 49/52, 50/51, 50/88, 51/52, 51/53, 52/53, 52/54, 53/54, 53/55, 54/56, 54/57, 55/56, 55/60, 55/87, 56/57, 56/58, 57/58, 57/59, 58/59, 58/60, 59/61, 59/62, 60/61, 60/65, 61/62, 61/63, 62/63, 62/64, 63/64, 63/65, 64/66, 64/67, 65/66, 65/85, 66/67, 66/68, 67/69, 67/68, 68/69, 68/70, 69/71, 69/72, 70/71, 70/84, 70/85, 71/72, 74/83, 74/84, 74/95, 74/129, 74/130, 80/81, 80/94, 80/127, 81/82, 81/86, 82/83, 82/127, 82/129, 83/84, 83/86, 84/85, 85/87, 86/87, 86/88, 87/88, 91/93, 91/94, 92/96, 92/95, 93/97, 93/99, 94/97, 94/102, 94/127, 94/134, 95/98, 96/98, 96/124, 97/99, 97/100, 98/123, 98/124, 99/100, 99/101, 100/101, 100/102, 101/103, 101/104, 102/103, 102/134, 103/104, 103/105, 104/105, 104/106, 105/106, 105/107, 106/108, 106/109, 107/108, 107/112, 107/133, 108/109, 108/110, 109/110, 109/111, 110/111, 110/112, 111/113, 111/114, 112/113, 112/117, 113/114, 113/115, 114/115, 114/116, 115/116, 115/117, 116/118, 116/119, 117/118, 117/131, 118/119, 118/120, 119/121, 119/120, 120/121, 120/122, 121/123, 121/124, 122/123, 122/130, 122/131, 123/124, 127/132, 129/130, 129/132, 130/131, 131/133, 132/133, 132/134, 133/134} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {34,...,35,37,...,72,74,...,74,80,...,88,91,...,124,127,...,127,129,...,134} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-35) -- (p-39); \draw[Green,very thick] (p-42) -- (p-45); \draw[Green,very thick] (p-43) -- (p-40); \draw[Green,very thick] (p-50) -- (p-51); \draw[Green,very thick] (p-60) -- (p-61); \draw[Green,very thick] (p-65) -- (p-66); \draw[Green,very thick] (p-85) -- (p-84); \draw[Green,very thick] (p-88) -- (p-87); \draw[Green,very thick] (p-83) -- (p-74); \draw[Green,very thick] (p-86) -- (p-87); \draw[Green,very thick] (p-86) -- (p-88); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 59/105.00/255.00/0.4/LightPink} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 34/15, 35/195, 37/15, 38/345, 39/75, 40/285, 41/45, 42/315, 43/45, 44/225, 45/195, 46/165, 47/15, 48/315, 49/15, 50/15, 51/225, 52/45, 53/225, 54/345, 55/78, 56/135, 57/315, 58/255, 59/315, 60/243, 61/165, 62/345, 63/165, 64/15, 65/303, 66/135, 67/315, 68/195, 69/255, 70/315, 71/45, 72/285, 74/315, 80/165, 81/285, 82/272, 83/105, 84/195, 85/75, 86/225, 87/345, 88/255, 91/105, 92/105, 93/45, 94/225, 95/135, 96/315, 97/285, 98/75, 99/45, 100/225, 101/165, 102/165, 103/15, 104/195, 105/255, 106/195, 107/108, 108/45, 109/225, 110/285, 111/225, 112/302, 113/15, 114/135, 115/315, 116/255, 117/242, 118/45, 119/225, 120/45, 121/285, 122/225, 123/135, 124/315, 127/255, 129/75, 130/345, 131/105, 132/315, 133/195, 134/285} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ und man kann mit irgendeinem Button für neue Eingabe die Entstehungsgeschichte verschwinden lassen. \quoteon(2020-02-23 19:08 - haribo in Beitrag No. 1914) oh haua haa! da werd ich noch einige zeit dran knabbern müssen um etwas davon zu verstehen, wie ein eichhörnchen schönes wochenende noch haribo \quoteoff Das wünsche ich auch. Ich hoffe, daß ich das Eichhörnchen nicht verscheucht habe mit den Fehlern und Mängeln. Jetzt sollte es bekömmlicher sein (obwohl ich auch schon wieder etliche neue kleinere Fehler gefunden habe). Zu Knabbern gibt es jedenfalls genug und auch für mich ist wieder etwas dabei: Wenn ich den Graph vom Anfang des Beitrages nach oben verschiebe mit Button "Pfeil hoch", dann entstehen auf einmal nicht passende Kanten 89 Knoten, 2×Grad 3, 82×Grad 4, 2×Grad 5, 1×Grad 6, 2×Grad 7, 0 Überschneidungen 182 Kanten, minimal 0.99951406899459527278, maximal 1.00146102569387052128 nicht passende Kanten: |P12-P101|=0.99971865144157223693 |P13-P15|=1.00146102569387052128 |P15-P16|=0.99951406899459527278 |P104-P12|=1.00024360833936909465 $ %Eingabe war: % %#1913-3 % % % % % % % % % %P[1]=[-36.489648590837135,48.2032118342492]; P[2]=[13.517130825300598,38.201855951021656]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(38,5,4,blauerWinkel); N(36,5,38); N(8,4,36); N(37,8,36); N(40,37,38); N(43,37,40); N(44,40,38); N(46,43,44); N(72,46,44); N(74,8,43); N(71,46,72); N(69,71,72); M(100,74,8,gruenerWinkel); N(7,3,100); N(101,7,100); N(6,1,7); N(9,1,6); M(104,9,1,orangerWinkel); N(11,9,104); M(84,74,8,vierterWinkel); N(70,84,71); N(85,84,70); N(68,70,69); N(67,68,69); N(66,68,67); N(64,66,67); N(65,85,66); N(63,65,64); N(62,63,64); N(61,63,62); N(59,61,62); N(60,65,61); N(58,60,59); N(57,58,59); N(56,58,57); N(54,56,57); N(55,60,56); N(87,85,55); N(53,55,54); N(52,53,54); N(51,53,52); N(49,51,52); M(88,87,85,fuenfterWinkel); N(50,88,51); N(86,87,88); N(42,88,50); N(48,50,49); N(81,86,42); N(82,86,81); N(83,84,82); N(45,42,48); N(47,45,48); N(80,81,42); N(41,45,47); N(79,82,80); N(102,82,79); N(32,79,80); N(35,32,42); N(39,41,35); N(103,102,32); N(27,103,32); N(33,32,35); N(34,33,41); N(31,33,34); N(30,32,31); N(28,27,30); N(29,28,30); N(26,28,29); N(25,27,26); N(24,25,26); N(23,25,24); N(21,23,24); M(22,23,25,sechsterWinkel); N(20,22,21); N(19,20,21); N(18,20,19); N(16,18,19); N(17,22,18); N(14,16,11); N(15,14,17); N(13,14,11); N(12,17,13); %A(83,86); R(83,86,"green"); %A(47,49); R(47,49,"green"); %A(39,42); R(39,42,"green"); %A(34,39); R(34,39,"green"); %A(29,31); R(29,31,"green"); %A(15,16); R(15,16,"green"); %A(13,15); R(13,15,"green"); A(6,104); A(104,12); A(12,101); L(10,82,102); A(100,10); N(73,101,102); A(73,22); A(73,103); % % % % % % % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{Lime}{rgb}{0.00,1.00,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.14319686050388868992/0.39223227027636820008, 2/3.12377753619480857949/0.19611613513818415555, 3/2.80332875347103760433/1.14338197831572307983, 4/3.78390942916195793799/0.94726584317753892428, 5/4.10435821188572891316/0.00000000000000000000, 6/2.33931299564207284547/1.37281294596728820068, 7/2.99944488860922220397/2.12396265400664274736, 8/3.98002556430014253763/1.92784651886845925794, 9/1.39204715246453414323/1.05236416324351811369, 10/4.60684260746500662265/3.19556105832525227939, 11/0.64089744442517959655/1.71249605621066769423, 12/2.24856172870202408731/2.78418459761163195054, 13/1.30145228749203911711/2.46327385243330265752, 14/0.32098222183251085005/2.65994222901072907561, 15/0.98026921876273298562/3.41183361457032541253, 16/0.00000000000000000000/3.60702744865438074129, 17/1.92784650790772627005/3.73136026619210436905, 18/0.94726581492790373762/3.92747631488575787984, 19/0.19611604869365814596/4.58760814163420249656, 20/1.14338186362156202236/4.90805700786557874693, 21/0.39223209738731601437/5.56818883461402336366, 22/2.12396255660138422172/4.71194095917192523615, 23/1.37281279036713810271/5.37207278592036985287, 24/1.05236392413575630123/6.31933860084827170311, 25/2.03294461711557872263/6.12322255215461908051, 26/1.71249575088419625502/7.07048836708252181893, 27/2.78409432515493060478/5.46309065918746661339, 28/2.46364545892354636081/6.41035647411536757545, 29/2.65976159406173717770/7.39093714980628657685, 30/3.41091130210108772758/6.73080525683913144519, 31/3.60702743723928032082/7.71138593253004867023, 32/3.73136016833247152746/5.78353944191122959495, 33/3.92747630347066367662/6.76412011760214770817, 34/4.58760813021910252019/7.51526988383639693581, 35/4.67862601151001289423/6.10398822463499257651, 36/4.30047434702391306871/0.98058067569092033366, 37/4.96060623999106198312/1.73173038373027510239, 38/5.05162405506326805948/0.32044878272377019801, 39/5.33875783825845395825/6.85513799086924091597, 40/5.71175594803041697389/1.07159849076312529981, 41/5.53487397339664521922/7.83571866656015902919, 42/5.65920670448983553769/5.90787217594133462484, 43/5.90787208316860201762/2.05217916645404541143, 44/6.03220473075418883724/0.12433264758558643104, 45/5.85532283962801791688/6.88845285163225451441, 46/6.22832086589237121643/1.10491332327650693124, 47/6.51545466637646519814/7.63960261786649752480, 48/6.83590353260783878397/6.69233680293859301003, 49/7.49603549179368311428/7.44348645278305642847, 50/6.63978739746965551660/5.71175612724767312045, 51/7.29991935665549984691/6.46290577709213565072, 52/8.24718519983303899323/6.78335455981590751406, 53/8.05106906469485572586/5.80277388412498673631, 54/8.99833490787239398401/6.12322266684875859966, 55/7.39093717172770503510/5.05162417608563263371, 56/8.33820301490524329324/5.37207295880940627342, 57/9.31878369059616318282/5.17595682367121945333, 58/8.65865179762901249205/4.42480711563186623891, 59/9.63923247331993238163/4.22869098049368030701, 60/7.71138595445147334573/4.10435833290809348739, 61/8.69196663014239234712/3.90824219776990799957, 62/9.44311633818174911426/3.24811030480275997334, 63/8.49585049500420907975/2.92766152207898722182, 64/9.24700020304356584688/2.26752962911183919559, 65/7.51526981931329007836/3.12377765721717315373, 66/8.26641952735264595731/2.46364576425002379523, 67/8.58686831007641693247/1.51637992107248487095, 68/7.60628763438549615472/1.71249605621066947059, 69/7.92673641710926624171/0.76523021303313043529, 70/6.85513792634613938759/2.37262794917781683068, 71/7.17558670906991036276/1.42536210600027835049, 72/6.97947057393172798356/0.44478143030935829438, 73/2.87511224102364204569/4.05180917287510400371, 74/4.92729140747768123987/2.24829530159223045516, 79/4.05180903456384733374/4.83627362698332596835, 80/4.71194086131229283865/5.58742339321757075510, 81/5.46309056935164338853/4.92729150025041562344, 82/4.80295874260319699545/4.17614173401617083670, 83/5.12340744181938489987/3.22887586258901304603, 84/5.87455725065521949801/2.56874408431600231850, 85/6.53468914362236930060/3.31989379235535642110, 86/5.78353943558301875072/3.98002568532251155276, 87/6.73080527876055878522/4.30047446804627586658, 88/5.97965557072120823534/4.96060636101343011006, 100/3.94671073178676090620/2.44441143673041416662, 101/3.19556102374740591543/3.10454332969756352512, 102/3.85569289942565562868/3.85569295129240696696, 103/3.53524403319427937831/4.80295876622031059355, 104/1.58816328760271874287/2.03294483893443800326} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 5/108.69/378.69/0.4/Blue, 74/198.69/528.69/0.4/Green, 9/318.69/438.69/0.4/Orange, 74/198.69/378.69/0.3/Violet, 87/258.69/498.69/0.4/Teal, 23/48.69/318.69/0.4/Lime} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 6/7, 6/104, 7/3, 7/100, 8/4, 8/36, 9/1, 9/6, 10/82, 10/102, 11/9, 11/104, 12/17, 12/13, 12/101, 13/14, 13/11, 13/15, 14/16, 14/11, 15/14, 15/17, 15/16, 16/18, 16/19, 17/22, 17/18, 18/20, 18/19, 19/20, 19/21, 20/22, 20/21, 21/23, 21/24, 22/23, 23/25, 23/24, 24/25, 24/26, 25/27, 25/26, 26/28, 26/29, 27/103, 27/32, 28/27, 28/30, 29/28, 29/30, 29/31, 30/32, 30/31, 31/33, 31/34, 32/79, 32/80, 33/32, 33/35, 34/33, 34/41, 34/39, 35/32, 35/42, 36/5, 36/38, 37/8, 37/36, 38/5, 39/41, 39/35, 39/42, 40/37, 40/38, 41/45, 41/47, 42/88, 42/50, 43/37, 43/40, 44/40, 44/38, 45/42, 45/48, 46/43, 46/44, 47/45, 47/48, 47/49, 48/50, 48/49, 49/51, 49/52, 50/88, 50/51, 51/53, 51/52, 52/53, 52/54, 53/55, 53/54, 54/56, 54/57, 55/60, 55/56, 56/58, 56/57, 57/58, 57/59, 58/60, 58/59, 59/61, 59/62, 60/65, 60/61, 61/63, 61/62, 62/63, 62/64, 63/65, 63/64, 64/66, 64/67, 65/85, 65/66, 66/68, 66/67, 67/68, 67/69, 68/70, 68/69, 69/71, 69/72, 70/84, 70/71, 71/46, 71/72, 72/46, 72/44, 73/101, 73/102, 73/22, 73/103, 74/8, 74/43, 79/82, 79/80, 80/81, 80/42, 81/86, 81/42, 82/86, 82/81, 83/84, 83/82, 83/86, 84/74, 85/84, 85/70, 86/87, 86/88, 87/85, 87/55, 88/87, 100/74, 100/10, 101/7, 101/100, 102/82, 102/79, 103/102, 103/32, 104/9, 104/12} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,74,79,...,88,100,...,104} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-83) -- (p-86); \draw[Green,very thick] (p-47) -- (p-49); \draw[Green,very thick] (p-39) -- (p-42); \draw[Green,very thick] (p-34) -- (p-39); \draw[Green,very thick] (p-29) -- (p-31); \draw[Green,very thick] (p-15) -- (p-16); \draw[Green,very thick] (p-13) -- (p-15); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); \draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-12) -- (p-101); \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-13) -- (p-15); \draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-15) -- (p-16); \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-104) -- (p-12); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 5/108.69/378.69/0.4/Blue, 74/198.69/528.69/0.4/Green, 9/318.69/438.69/0.4/Orange, 74/198.69/378.69/0.3/Violet, 87/258.69/498.69/0.4/Teal, 23/48.69/318.69/0.4/Lime} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/289, 2/259, 3/139, 4/19, 5/319, 6/49, 7/229, 8/139, 9/229, 10/289, 11/259, 12/336, 13/319, 14/259, 15/79, 16/229, 17/306, 18/349, 19/169, 20/349, 21/109, 22/111, 23/319, 24/139, 25/319, 26/79, 27/169, 28/229, 29/169, 30/349, 31/139, 32/49, 33/109, 34/169, 35/349, 36/109, 37/19, 38/199, 39/79, 40/289, 41/139, 42/319, 43/49, 44/319, 45/199, 46/169, 47/139, 48/319, 49/19, 50/19, 51/229, 52/109, 53/289, 54/349, 55/81, 56/139, 57/319, 58/199, 59/49, 60/246, 61/109, 62/349, 63/229, 64/289, 65/306, 66/139, 67/319, 68/139, 69/349, 70/319, 71/49, 72/349, 73/199, 74/96, 79/259, 80/19, 81/79, 82/49, 83/259, 84/199, 85/79, 86/19, 87/349, 88/109, 100/349, 101/109, 102/319, 103/289, 104/49} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Dass bei fortgesetztem Löschen und neu Eingeben von Punkten und Kanten sich Rundungsfehler bemerkbar machen ist ja zu erwarten. Aber so auffällig allein beim Verschieben des Graphen, da muss ich schon herausfinden warum. So kann man ja einen Rekordgraph glatt übersehen, weil offensichtlich nicht passende Kanten.


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StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
Mitteilungen: 4165
Wohnort: Raun
  Beitrag No.1917, eingetragen 2020-03-07

Diese Ungenauigkeit nach dem Verschieben tritt bereits bei Graph #1913-2 auf. Die Koordinaten des Punktes P14 (Button "javascript") \sourceon P[14]=[-129.4173267960915, 163.84986335153042]; P[14]=[-129.44453682015543,113.84066706214874]; \sourceoff unterscheiden sich neben der y-Verschiebung um 50 zusätzlich in den Nachkommastellen um immerhin knapp 0.03 bei der x-Koordinate. Dieser Punkt P14 wird gezeichnet beim Anfügen zweier Kanten an die Punkte P11 und P16 (Button "Beschreibung" und anschließend bis Button "N(14,16,11)" scrollen), um den Rahmen auf der linken Seite des Graph zu schließen 83 Knoten, 7×Grad 2, 10×Grad 3, 63×Grad 4, 1×Grad 5, 1×Grad 6, 1×Grad 7, 0 Überschneidungen, 157 Kanten, minimal 0.99999999999999900080, maximal 1.00000000000000111022, Einsetzkanten=Beweglichkeit-6, einzustellende Kanten, Abstände und Winkel: |P16-P11|=1.99999968280633511064 $ %Eingabe war: % %#1913-2 % % % % % % % % % %P[1]=[-36.489648590837135,48.2032118342492]; P[2]=[13.517130825300598,38.201855951021656]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(38,5,4,blauerWinkel); N(36,5,38); N(8,4,36); N(37,8,36); N(40,37,38); N(43,37,40); N(44,40,38); N(46,43,44); N(72,46,44); N(74,8,43); N(71,46,72); N(69,71,72); M(100,74,8,gruenerWinkel); N(7,3,100); N(101,7,100); N(6,1,7); N(9,1,6); M(104,9,1,orangerWinkel); N(11,9,104); M(84,74,8,vierterWinkel); N(70,84,71); N(85,84,70); N(68,70,69); N(67,68,69); N(66,68,67); N(64,66,67); N(65,85,66); N(63,65,64); N(62,63,64); N(61,63,62); N(59,61,62); N(60,65,61); N(58,60,59); N(57,58,59); N(56,58,57); N(54,56,57); N(55,60,56); N(87,85,55); N(53,55,54); N(52,53,54); N(51,53,52); N(49,51,52); M(88,87,85,fuenfterWinkel); N(50,88,51); N(86,87,88); N(42,88,50); N(48,50,49); N(81,86,42); N(82,86,81); N(83,84,82); N(45,42,48); N(47,45,48); N(80,81,42); N(41,45,47); N(79,82,80); N(102,82,79); N(32,79,80); N(35,32,42); N(39,41,35); N(103,102,32); N(27,103,32); N(33,32,35); N(34,33,41); N(31,33,34); N(30,32,31); N(28,27,30); N(29,28,30); N(26,28,29); N(25,27,26); N(24,25,26); N(23,25,24); N(21,23,24); M(22,23,25,sechsterWinkel); N(20,22,21); N(19,20,21); N(18,20,19); N(16,18,19); N(17,22,18); R(16,11); % % % % % % % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{Lime}{rgb}{0.00,1.00,0.00} \definecolor{LimeGreen}{rgb}{0.20,0.80,0.20} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.14/0.39, 2/3.12/0.20, 3/2.80/1.14, 4/3.78/0.95, 5/4.10/0.00, 6/2.34/1.37, 7/3.00/2.12, 8/3.98/1.93, 9/1.39/1.05, 11/0.64/1.71, 16/0.00/3.61, 17/1.93/3.73, 18/0.95/3.93, 19/0.20/4.59, 20/1.14/4.91, 21/0.39/5.57, 22/2.12/4.71, 23/1.37/5.37, 24/1.05/6.32, 25/2.03/6.12, 26/1.71/7.07, 27/2.78/5.46, 28/2.46/6.41, 29/2.66/7.39, 30/3.41/6.73, 31/3.61/7.71, 32/3.73/5.78, 33/3.93/6.76, 34/4.59/7.52, 35/4.68/6.10, 36/4.30/0.98, 37/4.96/1.73, 38/5.05/0.32, 39/5.34/6.86, 40/5.71/1.07, 41/5.53/7.84, 42/5.66/5.91, 43/5.91/2.05, 44/6.03/0.12, 45/5.86/6.89, 46/6.23/1.10, 47/6.52/7.64, 48/6.84/6.69, 49/7.50/7.44, 50/6.64/5.71, 51/7.30/6.46, 52/8.25/6.78, 53/8.05/5.80, 54/9.00/6.12, 55/7.39/5.05, 56/8.34/5.37, 57/9.32/5.18, 58/8.66/4.42, 59/9.64/4.23, 60/7.71/4.10, 61/8.69/3.91, 62/9.44/3.25, 63/8.50/2.93, 64/9.25/2.27, 65/7.52/3.12, 66/8.27/2.46, 67/8.59/1.52, 68/7.61/1.71, 69/7.93/0.77, 70/6.86/2.37, 71/7.18/1.43, 72/6.98/0.44, 74/4.93/2.25, 79/4.05/4.84, 80/4.71/5.59, 81/5.46/4.93, 82/4.80/4.18, 83/5.12/3.23, 84/5.87/2.57, 85/6.53/3.32, 86/5.78/3.98, 87/6.73/4.30, 88/5.98/4.96, 100/3.95/2.44, 101/3.20/3.10, 102/3.86/3.86, 103/3.54/4.80, 104/1.59/2.03} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 5/108.69/378.69/0.4/Blue, 74/198.69/528.69/0.4/Green, 9/318.69/438.69/0.4/Orange, 74/198.69/378.69/0.3/Violet, 87/258.69/498.69/0.4/Teal, 23/48.69/318.69/0.4/Lime} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 6/7, 7/3, 7/100, 8/4, 8/36, 9/1, 9/6, 11/9, 11/104, 16/18, 16/19, 17/22, 17/18, 18/20, 18/19, 19/20, 19/21, 20/22, 20/21, 21/23, 21/24, 22/23, 23/25, 23/24, 24/25, 24/26, 25/27, 25/26, 26/28, 26/29, 27/103, 27/32, 28/27, 28/30, 29/28, 29/30, 30/32, 30/31, 31/33, 31/34, 32/79, 32/80, 33/32, 33/35, 34/33, 34/41, 35/32, 35/42, 36/5, 36/38, 37/8, 37/36, 38/5, 39/41, 39/35, 40/37, 40/38, 41/45, 41/47, 42/88, 42/50, 43/37, 43/40, 44/40, 44/38, 45/42, 45/48, 46/43, 46/44, 47/45, 47/48, 48/50, 48/49, 49/51, 49/52, 50/88, 50/51, 51/53, 51/52, 52/53, 52/54, 53/55, 53/54, 54/56, 54/57, 55/60, 55/56, 56/58, 56/57, 57/58, 57/59, 58/60, 58/59, 59/61, 59/62, 60/65, 60/61, 61/63, 61/62, 62/63, 62/64, 63/65, 63/64, 64/66, 64/67, 65/85, 65/66, 66/68, 66/67, 67/68, 67/69, 68/70, 68/69, 69/71, 69/72, 70/84, 70/71, 71/46, 71/72, 72/46, 72/44, 74/8, 74/43, 79/82, 79/80, 80/81, 80/42, 81/86, 81/42, 82/86, 82/81, 83/84, 83/82, 84/74, 85/84, 85/70, 86/87, 86/88, 87/85, 87/55, 88/87, 100/74, 101/7, 101/100, 102/82, 102/79, 103/102, 103/32, 104/9} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,9,11,...,11,16,...,72,74,...,74,79,...,88,100,...,104} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[LimeGreen,very thick,dashed] (p-16) -- (p-11); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 5/108.69/378.69/0.4/Blue, 74/198.69/528.69/0.4/Green, 9/318.69/438.69/0.4/Orange, 74/198.69/378.69/0.3/Violet, 87/258.69/498.69/0.4/Teal, 23/48.69/318.69/0.4/Lime} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/289, 2/259, 3/139, 4/19, 5/319, 6/49, 7/229, 8/139, 9/169, 11/169, 16/229, 17/306, 18/349, 19/169, 20/349, 21/109, 22/36, 23/319, 24/139, 25/319, 26/79, 27/169, 28/229, 29/49, 30/349, 31/139, 32/49, 33/109, 34/19, 35/349, 36/109, 37/19, 38/199, 39/336, 40/289, 41/139, 42/49, 43/49, 44/319, 45/199, 46/169, 47/19, 48/319, 49/109, 50/19, 51/229, 52/109, 53/289, 54/349, 55/81, 56/139, 57/319, 58/199, 59/49, 60/246, 61/109, 62/349, 63/229, 64/289, 65/306, 66/139, 67/319, 68/139, 69/349, 70/319, 71/49, 72/349, 74/96, 79/259, 80/19, 81/79, 82/199, 83/216, 84/199, 85/79, 86/319, 87/349, 88/109, 100/349, 101/109, 102/229, 103/289, 104/49} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Der Abstand P11-P16 ist theoretisch 2, kann aber beim Verschieben auch 1.9999996828 werden, das liegt noch im Bereich der üblichen Schwankung. Dann aber zwei Kanten der Länge 1 anfügen führt zu dieser großen Abweichung quer zur Verbindungsrichtung, das muss ich vermeiden. Ursache ist schon Rundungsfehler, aber das wird ja geradewegs provoziert. So egal soll Button "egal wie" nicht sein. Im geänderten Streichholzgraph-1898.htm wird dieses Anfügen nur noch bei Abstand kleiner 1.99 ausgeführt. Button neue Eingabe "egal wie" sucht sich jetzt einen anderen Weg über P15 und P13, um den Rahmen zu schließen. 85 Knoten, 5×Grad 2, 16×Grad 3, 60×Grad 4, 2×Grad 5, 2×Grad 7, 0 Überschneidungen, 161 Kanten, minimal 0.99999999999999900080, maximal 1.00000000000000088818, Einsetzkanten=Beweglichkeit-6, $ %Eingabe war: % %Automatisch generierte Eingabe zu: #1913-2 % % % % % % % % % %P[1]=[-36.489648590837135,-1.7967881657507974]; P[2]=[13.517130825300598,-11.798144048978344]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(38,5,4,blauerWinkel); N(36,5,38); N(8,4,36); N(37,8,36); N(40,37,38); N(43,37,40); N(44,40,38); N(46,43,44); N(72,46,44); N(74,8,43); N(71,46,72); N(69,71,72); M(100,74,8,gruenerWinkel); N(7,3,100); N(101,7,100); N(6,1,7); N(9,1,6); M(104,9,1,orangerWinkel); N(11,9,104); M(84,74,8,vierterWinkel); N(70,84,71); N(85,84,70); N(68,70,69); N(67,68,69); N(66,68,67); N(64,66,67); N(65,85,66); N(63,65,64); N(62,63,64); N(61,63,62); N(59,61,62); N(60,65,61); N(58,60,59); N(57,58,59); N(56,58,57); N(54,56,57); N(55,60,56); N(87,85,55); N(53,55,54); N(52,53,54); N(51,53,52); N(49,51,52); M(88,87,85,fuenfterWinkel); N(86,87,88); N(83,84,86); N(82,83,86); N(81,82,86); N(42,81,88); N(50,42,88); N(80,81,42); N(48,50,49); N(79,82,80); N(102,82,79); N(32,79,80); N(35,32,42); N(39,35,42); N(45,42,48); N(47,45,48); N(103,102,32); N(27,103,32); N(33,32,35); N(34,33,39); N(41,34,39); N(31,33,34); N(30,32,31); N(28,27,30); N(29,28,30); N(26,28,29); N(25,27,26); N(24,25,26); N(23,25,24); N(21,23,24); M(22,23,25,sechsterWinkel); N(20,22,21); N(19,20,21); N(18,20,19); N(16,18,19); N(17,22,18); N(15,17,16); N(13,15,11); % % % % % % % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{Lime}{rgb}{0.00,1.00,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/2.14/0.39, 2/3.12/0.20, 3/2.80/1.14, 4/3.78/0.95, 5/4.10/0.00, 6/2.34/1.37, 7/3.00/2.12, 8/3.98/1.93, 9/1.39/1.05, 11/0.64/1.71, 13/1.30/2.46, 15/0.98/3.41, 16/0.00/3.61, 17/1.93/3.73, 18/0.95/3.93, 19/0.20/4.59, 20/1.14/4.91, 21/0.39/5.57, 22/2.12/4.71, 23/1.37/5.37, 24/1.05/6.32, 25/2.03/6.12, 26/1.71/7.07, 27/2.78/5.46, 28/2.46/6.41, 29/2.66/7.39, 30/3.41/6.73, 31/3.61/7.71, 32/3.73/5.78, 33/3.93/6.76, 34/4.59/7.52, 35/4.68/6.10, 36/4.30/0.98, 37/4.96/1.73, 38/5.05/0.32, 39/5.34/6.86, 40/5.71/1.07, 41/5.53/7.84, 42/5.66/5.91, 43/5.91/2.05, 44/6.03/0.12, 45/5.86/6.89, 46/6.23/1.10, 47/6.52/7.64, 48/6.84/6.69, 49/7.50/7.44, 50/6.64/5.71, 51/7.30/6.46, 52/8.25/6.78, 53/8.05/5.80, 54/9.00/6.12, 55/7.39/5.05, 56/8.34/5.37, 57/9.32/5.18, 58/8.66/4.42, 59/9.64/4.23, 60/7.71/4.10, 61/8.69/3.91, 62/9.44/3.25, 63/8.50/2.93, 64/9.25/2.27, 65/7.52/3.12, 66/8.27/2.46, 67/8.59/1.52, 68/7.61/1.71, 69/7.93/0.77, 70/6.86/2.37, 71/7.18/1.43, 72/6.98/0.44, 74/4.93/2.25, 79/4.05/4.84, 80/4.71/5.59, 81/5.46/4.93, 82/4.80/4.18, 83/5.12/3.23, 84/5.87/2.57, 85/6.53/3.32, 86/5.78/3.98, 87/6.73/4.30, 88/5.98/4.96, 100/3.95/2.44, 101/3.20/3.10, 102/3.86/3.86, 103/3.54/4.80, 104/1.59/2.03} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 5/108.69/378.69/0.4/Blue, 74/198.69/528.69/0.4/Green, 9/318.69/438.69/0.4/Orange, 74/198.69/378.69/0.3/Violet, 87/258.69/498.69/0.4/Teal, 23/48.69/318.69/0.4/Lime} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 2/1, 3/1, 3/2, 4/3, 4/2, 5/4, 5/2, 6/1, 6/7, 7/3, 7/100, 8/4, 8/36, 9/1, 9/6, 11/9, 11/104, 13/15, 13/11, 15/17, 15/16, 16/18, 16/19, 17/22, 17/18, 18/20, 18/19, 19/20, 19/21, 20/22, 20/21, 21/23, 21/24, 22/23, 23/25, 23/24, 24/25, 24/26, 25/27, 25/26, 26/28, 26/29, 27/103, 27/32, 28/27, 28/30, 29/28, 29/30, 30/32, 30/31, 31/33, 31/34, 32/79, 32/80, 33/32, 33/35, 34/33, 34/39, 35/32, 35/42, 36/5, 36/38, 37/8, 37/36, 38/5, 39/35, 39/42, 40/37, 40/38, 41/34, 41/39, 42/81, 42/88, 43/37, 43/40, 44/40, 44/38, 45/42, 45/48, 46/43, 46/44, 47/45, 47/48, 48/50, 48/49, 49/51, 49/52, 50/42, 50/88, 51/53, 51/52, 52/53, 52/54, 53/55, 53/54, 54/56, 54/57, 55/60, 55/56, 56/58, 56/57, 57/58, 57/59, 58/60, 58/59, 59/61, 59/62, 60/65, 60/61, 61/63, 61/62, 62/63, 62/64, 63/65, 63/64, 64/66, 64/67, 65/85, 65/66, 66/68, 66/67, 67/68, 67/69, 68/70, 68/69, 69/71, 69/72, 70/84, 70/71, 71/46, 71/72, 72/46, 72/44, 74/8, 74/43, 79/82, 79/80, 80/81, 80/42, 81/82, 81/86, 82/83, 82/86, 83/84, 83/86, 84/74, 85/84, 85/70, 86/87, 86/88, 87/85, 87/55, 88/87, 100/74, 101/7, 101/100, 102/82, 102/79, 103/102, 103/32, 104/9} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,9,11,...,11,13,...,13,15,...,72,74,...,74,79,...,88,100,...,104} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 5/108.69/378.69/0.4/Blue, 74/198.69/528.69/0.4/Green, 9/318.69/438.69/0.4/Orange, 74/198.69/378.69/0.3/Violet, 87/258.69/498.69/0.4/Teal, 23/48.69/318.69/0.4/Lime} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/199, 2/259, 3/139, 4/19, 5/319, 6/49, 7/229, 8/139, 9/169, 11/169, 13/351, 15/156, 16/229, 17/306, 18/349, 19/169, 20/349, 21/199, 22/36, 23/319, 24/139, 25/19, 26/79, 27/169, 28/289, 29/49, 30/349, 31/139, 32/139, 33/259, 34/169, 35/349, 36/109, 37/169, 38/199, 39/79, 40/289, 41/49, 42/49, 43/49, 44/229, 45/199, 46/109, 47/79, 48/319, 49/109, 50/19, 51/229, 52/109, 53/289, 54/349, 55/81, 56/139, 57/319, 58/199, 59/49, 60/246, 61/169, 62/49, 63/229, 64/19, 65/306, 66/139, 67/19, 68/199, 69/349, 70/319, 71/49, 72/229, 74/276, 79/259, 80/19, 81/79, 82/199, 83/259, 84/199, 85/79, 86/229, 87/349, 88/259, 100/349, 101/109, 102/229, 103/289, 104/49} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Auch bei sehr nahe beieinandeliegenden Punkten im Abstand kleinergleich 0.01 werden jetzt keine zwei Kanten mehr angefügt und das alles auch bei den Buttons "wenig Winkel" und "Rahmen zuerst". Dadurch nimmt die neue Eingabe einen etwas anderen Verlauf, eventuell mit weiteren Winkeln, was aber für diesen Zweck sicherlich akzeptabel ist. Interessanter Nebeneffekt ist, Button "beweglich?" liefert jetzt die richtige Antwort 2-fach beweglich anstatt vorher 1-fach bewglich. Das scheint auch dafür eine wesentliche Verbesserung der Genauigkeit zu sein. Über dem Graph habe ich die Knotengradabweichungsgleichung Einsetzkanten=Beweglichkeit+(Knotengradabweichung/2+3) ergänzt mit der Bedeutung, wenn bei Button neuer Eingabe beispielsweise i bewegliche Winkel verwendet werden, dann bleiben am Ende der Eingabe i+(Knotengradabweichung/2+3) Einsetzkanten übrig, welche dann auch passen müssen. Speziell die Ausgabe Einsetzkanten=Beweglichkeit-1 bedeutet, weil Einsetzkanten nicht weniger als 0 Stück sein können, muss der Graph mindestens 1-fach beweglich sein. Das ist eine einfache Vergleichsmöglichkeit, ob Button "beweglich?" diese Bewegungsmöglichkeit findet.


   Profil
StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
Mitteilungen: 4165
Wohnort: Raun
  Beitrag No.1918, eingetragen 2020-03-08

Weiter mit Button "Newtonpolynom(10)". Es kann ja nicht sein, dass dieser fehlerlos ist. Zum Testen habe ich den Graph #1768-2 ausgesucht, dort die nicht passenden Kanten entfernt und extra noch Kante P14-P16. Dann Graph entlang P1-P2 horizontal ausgerichtet und noch Button neue Eingabe "Rahmen zuerst" 53 Knoten, 1×Grad 2, 6×Grad 3, 46×Grad 4, 0 Überschneidungen, 102 Kanten, minimal 0.99999999999998334665, maximal 1.00000000000001665335, Einsetzkanten=Beweglichkeit-1, $ %Eingabe war: % %#1768A = #1768 modifiziert % % % % % % % % % %P[7]=[121.77225001445532,-27.49959090912219]; P[5]=[53.55568587581774,-27.49959090912219]; D=ab(7,5); A(5,7); N(6,5,7); N(4,5,6); N(2,5,4); N(3,2,4); N(1,2,3); M(9,1,2,blauerWinkel); N(8,9,1); N(10,9,8); N(11,9,10); M(13,11,9,gruenerWinkel); N(12,13,11); N(14,13,12); N(15,13,14); M(17,15,13,orangerWinkel); N(16,17,15); M(19,17,15,vierterWinkel); N(18,19,17); N(20,19,18); N(21,19,20); M(23,21,19,fuenfterWinkel); N(22,23,21); N(24,23,22); N(25,23,24); N(26,25,24); N(27,25,26); M(29,27,25,sechsterWinkel); N(28,29,27); N(30,29,28); N(31,29,30); N(32,31,30); N(33,31,32); Q(37,33,7,2*D,2*D); A(37,33); A(37,7); H(39,7,37,2); A(39,7); L(40,7,39); H(35,33,37,2); A(35,33); L(34,35,33); A(35,37); L(36,37,35); A(36,34); A(39,37); L(38,39,37); A(40,38); N(41,12,10); N(42,8,3); N(43,28,26); N(44,36,34); N(46,42,6); N(47,20,18); N(48,40,38); N(50,22,43); N(51,44,32); N(45,42,46); N(52,44,51); N(53,41,47); N(49,53,52); %A(48,46); R(48,46,"green"); %A(50,47); R(50,47,"green"); %A(51,43); R(51,43,"green"); %A(45,41); R(45,41,"green"); %A(49,45); R(49,45,"green"); % % % % % % % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{Lime}{rgb}{0.00,1.00,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.29/0.00, 2/2.29/0.00, 3/1.79/0.87, 4/2.79/0.87, 5/3.29/0.00, 6/3.79/0.87, 7/4.29/0.00, 8/1.63/0.94, 9/0.64/0.77, 10/0.98/1.71, 11/0.00/1.53, 12/0.92/1.92, 13/0.12/2.52, 14/1.04/2.92, 15/0.24/3.52, 16/1.16/3.91, 17/0.36/4.51, 18/1.33/4.26, 19/1.06/5.22, 20/2.03/4.97, 21/1.76/5.94, 22/2.15/5.02, 23/2.75/5.82, 24/3.15/4.90, 25/3.75/5.70, 26/4.14/4.78, 27/4.74/5.58, 28/4.32/4.67, 29/5.32/4.76, 30/4.90/3.85, 31/5.89/3.94, 32/5.47/3.03, 33/6.47/3.12, 34/5.49/2.90, 35/6.17/2.17, 36/5.20/1.95, 37/5.88/1.21, 38/4.95/1.60, 39/5.08/0.61, 40/4.16/0.99, 41/1.90/2.10, 42/2.13/1.81, 43/3.72/3.87, 44/4.52/2.68, 45/2.80/2.55, 46/3.11/1.60, 47/2.30/4.01, 48/4.03/1.98, 49/2.78/3.55, 50/3.08/4.64, 51/4.70/3.67, 52/3.76/3.33, 53/1.89/3.10} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/360.00/490.04/0.4/Blue, 11/310.04/443.09/0.4/Green, 15/263.09/443.09/0.4/Orange, 17/263.09/405.55/0.4/Violet, 21/225.55/353.09/0.4/Teal, 27/173.09/305.20/0.4/Lime} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 1/3, 2/5, 2/4, 3/2, 3/4, 4/5, 4/6, 5/7, 6/5, 6/7, 8/9, 8/1, 9/1, 10/9, 10/8, 11/9, 11/10, 12/13, 12/11, 13/11, 14/13, 14/12, 15/13, 15/14, 16/17, 16/15, 17/15, 18/19, 18/17, 19/17, 20/19, 20/18, 21/19, 21/20, 22/23, 22/21, 23/21, 24/23, 24/22, 25/23, 25/24, 26/25, 26/24, 27/25, 27/26, 28/29, 28/27, 29/27, 30/29, 30/28, 31/29, 31/30, 32/31, 32/30, 33/31, 33/32, 34/35, 34/33, 35/33, 35/37, 36/37, 36/35, 36/34, 38/39, 38/37, 39/7, 39/37, 40/7, 40/39, 40/38, 41/12, 41/10, 42/8, 42/3, 43/28, 43/26, 44/36, 44/34, 45/42, 45/46, 45/41, 46/42, 46/6, 47/20, 47/18, 48/40, 48/38, 48/46, 49/53, 49/52, 49/45, 50/22, 50/43, 50/47, 51/44, 51/32, 51/43, 52/44, 52/51, 53/41, 53/47} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,53} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-48) -- (p-46); \draw[Green,very thick] (p-50) -- (p-47); \draw[Green,very thick] (p-51) -- (p-43); \draw[Green,very thick] (p-45) -- (p-41); \draw[Green,very thick] (p-49) -- (p-45); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/360.00/490.04/0.4/Blue, 11/310.04/443.09/0.4/Green, 15/263.09/443.09/0.4/Orange, 17/263.09/405.55/0.4/Violet, 21/225.55/353.09/0.4/Teal, 27/173.09/305.20/0.4/Lime} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/210, 2/270, 3/90, 4/90, 5/210, 6/30, 7/247, 8/340, 9/220, 10/100, 11/160, 12/353, 13/173, 14/353, 15/113, 16/353, 17/196, 18/256, 19/76, 20/316, 21/143, 22/263, 23/83, 24/263, 25/83, 26/263, 27/23, 28/215, 29/335, 30/275, 31/95, 32/275, 33/335, 34/43, 35/43, 36/223, 37/7, 38/127, 39/307, 40/127, 41/241, 42/198, 43/280, 44/290, 45/78, 46/318, 47/316, 48/127, 49/61, 50/11, 51/50, 52/170, 53/151} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Über dem Graph wird Einsetzkanten=Beweglichkeit-1 ausgegeben, also der Graph ist garantiert beweglich. Vor Testbutton "Newtonpolynom(10)" will ich nochmal dessen Funktion etwas erläutern: Wenn man den Winkel orangerWinkel=180 in P15 um 1 Grad vergrößert (Winkel oder Winkelbezeichnung anklicken, dann Button "+1") 53 Knoten, 1×Grad 2, 6×Grad 3, 46×Grad 4, 0 Überschneidungen, 102 Kanten, minimal 0.79835145115160566220, maximal 1.11539982150941563432, Einsetzkanten=Beweglichkeit-1, nicht passende Kanten: |P48-P46|=0.79835145115160566220 |P49-P45|=1.03880603820090344769 |P51-P43|=1.11539982150941563432 $ %Eingabe war: % %#1768A = #1768 modifiziert % % % % % % % % % %P[7]=[121.77225001445532,-27.49959090912219]; P[5]=[53.55568587581774,-27.49959090912219]; D=ab(7,5); A(5,7); N(6,5,7); N(4,5,6); N(2,5,4); N(3,2,4); N(1,2,3); M(9,1,2,blauerWinkel); N(8,9,1); N(10,9,8); N(11,9,10); M(13,11,9,gruenerWinkel); N(12,13,11); N(14,13,12); N(15,13,14); M(17,15,13,orangerWinkel); N(16,17,15); M(19,17,15,vierterWinkel); N(18,19,17); N(20,19,18); N(21,19,20); M(23,21,19,fuenfterWinkel); N(22,23,21); N(24,23,22); N(25,23,24); N(26,25,24); N(27,25,26); M(29,27,25,sechsterWinkel); N(28,29,27); N(30,29,28); N(31,29,30); N(32,31,30); N(33,31,32); Q(37,33,7,2*D,2*D); A(37,33); A(37,7); H(39,7,37,2); A(39,7); L(40,7,39); H(35,33,37,2); A(35,33); L(34,35,33); A(35,37); L(36,37,35); A(36,34); A(39,37); L(38,39,37); A(40,38); N(41,12,10); N(42,8,3); N(43,28,26); N(44,36,34); N(46,42,6); N(47,20,18); N(48,40,38); N(50,22,43); N(51,44,32); N(45,42,46); N(52,44,51); N(53,41,47); N(49,53,52); %A(48,46); R(48,46,"green"); %A(50,47); R(50,47,"green"); %A(51,43); R(51,43,"green"); %A(45,41); R(45,41,"green"); %A(49,45); R(49,45,"green"); % % % % % % % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{Lime}{rgb}{0.00,1.00,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.29/0.00, 2/2.29/0.00, 3/1.79/0.87, 4/2.79/0.87, 5/3.29/0.00, 6/3.79/0.87, 7/4.29/0.00, 8/1.63/0.94, 9/0.64/0.77, 10/0.98/1.71, 11/0.00/1.53, 12/0.92/1.92, 13/0.12/2.52, 14/1.04/2.92, 15/0.24/3.52, 16/1.15/3.92, 17/0.34/4.51, 18/1.32/4.28, 19/1.03/5.24, 20/2.00/5.00, 21/1.72/5.96, 22/2.13/5.05, 23/2.71/5.86, 24/3.12/4.95, 25/3.71/5.76, 26/4.12/4.84, 27/4.70/5.65, 28/4.30/4.74, 29/5.29/4.85, 30/4.890/3.932, 31/5.88/4.04, 32/5.481/3.125, 33/6.48/3.23, 34/5.486/3.086, 35/6.11/2.30, 36/5.12/2.16, 37/5.74/1.37, 38/4.78/1.66, 39/5.01/0.69, 40/4.06/0.97, 41/1.90/2.10, 42/2.13/1.81, 43/3.71/3.93, 44/4.50/2.94, 45/2.80/2.55, 46/3.11/1.60, 47/2.29/4.05, 48/3.83/1.95, 49/2.85/3.59, 50/3.06/4.68, 51/4.828/3.882, 52/3.85/3.70, 53/1.98/3.09} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/360.00/490.04/0.4/Blue, 11/310.04/443.09/0.4/Green, 15/263.09/444.09/0.4/Orange, 17/264.09/406.55/0.4/Violet, 21/226.55/354.09/0.4/Teal, 27/174.09/306.20/0.4/Lime} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 1/3, 2/5, 2/4, 3/2, 3/4, 4/5, 4/6, 5/7, 6/5, 6/7, 8/9, 8/1, 9/1, 10/9, 10/8, 11/9, 11/10, 12/13, 12/11, 13/11, 14/13, 14/12, 15/13, 15/14, 16/17, 16/15, 17/15, 18/19, 18/17, 19/17, 20/19, 20/18, 21/19, 21/20, 22/23, 22/21, 23/21, 24/23, 24/22, 25/23, 25/24, 26/25, 26/24, 27/25, 27/26, 28/29, 28/27, 29/27, 30/29, 30/28, 31/29, 31/30, 32/31, 32/30, 33/31, 33/32, 34/35, 34/33, 35/33, 35/37, 36/37, 36/35, 36/34, 38/39, 38/37, 39/7, 39/37, 40/7, 40/39, 40/38, 41/12, 41/10, 42/8, 42/3, 43/28, 43/26, 44/36, 44/34, 45/42, 45/46, 45/41, 46/42, 46/6, 47/20, 47/18, 48/40, 48/38, 48/46, 49/53, 49/52, 49/45, 50/22, 50/43, 50/47, 51/44, 51/32, 51/43, 52/44, 52/51, 53/41, 53/47} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,53} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-48) -- (p-46); \draw[Green,very thick] (p-50) -- (p-47); \draw[Green,very thick] (p-51) -- (p-43); \draw[Green,very thick] (p-45) -- (p-41); \draw[Green,very thick] (p-49) -- (p-45); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); \draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-48) -- (p-46); \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-49) -- (p-45); \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-51) -- (p-43); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/360.00/490.04/0.4/Blue, 11/310.04/443.09/0.4/Green, 15/263.09/444.09/0.4/Orange, 17/264.09/406.55/0.4/Violet, 21/226.55/354.09/0.4/Teal, 27/174.09/306.20/0.4/Lime} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/210, 2/270, 3/90, 4/90, 5/210, 6/30, 7/253, 8/340, 9/220, 10/100, 11/160, 12/353, 13/173, 14/353, 15/234, 16/354, 17/114, 18/257, 19/77, 20/77, 21/144, 22/204, 23/84, 24/204, 25/24, 26/264, 27/24, 28/156, 29/36, 30/156, 31/336, 32/216, 33/38, 34/158, 35/338, 36/158, 37/13, 38/13, 39/313, 40/253, 41/239, 42/198, 43/208, 44/158, 45/78, 46/318, 47/317, 48/133, 49/61, 50/12, 51/41, 52/161, 53/150} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ so entstehen wie zu erwarten nicht passende Kanten. Diese anschließend mit Button "Feinjustieren(5,5)" (vorher im großen Eingabefenster Anzahl="5,6" auf "5,5" umstellen und Button "neu zeichnen") zurechtziehen. Man erhält nahezu wieder den Ausgangsgraph, jetzt mit orangerWinkel=181. Bei Testbutton "Newtonpolynom(10)" wiederholt sich das ganze 10 mal, so dass man schließlich bei orangerWinkel=190 herauskommt. Soweit funktioniert das. Jetzt beginne ich das ganze nochmal bei orangerWinkel=170 53 Knoten, 1×Grad 2, 6×Grad 3, 46×Grad 4, 0 Überschneidungen, 102 Kanten, minimal 0.99999999999998745448, maximal 1.00000000000001332268, Einsetzkanten=Beweglichkeit-1, $ %Eingabe war: % %#1768B = #1768A mit orangerWinkel=170 % % % % % % % % % %P[7]=[121.77225001445532,-27.49959090912219]; P[5]=[53.55568587581774,-27.49959090912219]; D=ab(7,5); A(5,7); N(6,5,7); N(4,5,6); N(2,5,4); N(3,2,4); N(1,2,3); M(9,1,2,blauerWinkel); N(8,9,1); N(10,9,8); N(11,9,10); M(13,11,9,gruenerWinkel); N(12,13,11); N(14,13,12); N(15,13,14); M(17,15,13,orangerWinkel); N(16,17,15); M(19,17,15,vierterWinkel); N(18,19,17); N(20,19,18); N(21,19,20); M(23,21,19,fuenfterWinkel); N(22,23,21); N(24,23,22); N(25,23,24); N(26,25,24); N(27,25,26); M(29,27,25,sechsterWinkel); N(28,29,27); N(30,29,28); N(31,29,30); N(32,31,30); N(33,31,32); Q(37,33,7,2*D,2*D); A(37,33); A(37,7); H(39,7,37,2); A(39,7); L(40,7,39); H(35,33,37,2); A(35,33); L(34,35,33); A(35,37); L(36,37,35); A(36,34); A(39,37); L(38,39,37); A(40,38); N(41,12,10); N(42,8,3); N(43,28,26); N(44,36,34); N(46,42,6); N(47,20,18); N(48,40,38); N(50,22,43); N(51,44,32); N(45,42,46); N(52,44,51); N(53,41,47); N(49,53,52); %A(48,46); R(48,46,"green"); %A(50,47); R(50,47,"green"); %A(51,43); R(51,43,"green"); %A(45,41); R(45,41,"green"); %A(49,45); R(49,45,"green"); % % % % % % % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{Lime}{rgb}{0.00,1.00,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.29/0.00, 2/2.29/0.00, 3/1.79/0.87, 4/2.79/0.87, 5/3.29/0.00, 6/3.79/0.87, 7/4.29/0.00, 8/1.63/0.94, 9/0.64/0.77, 10/0.98/1.71, 11/0.00/1.53, 12/0.91/1.95, 13/0.09/2.53, 14/0.99/2.95, 15/0.17/3.52, 16/1.14/3.78, 17/0.43/4.49, 18/1.40/4.25, 19/1.12/5.21, 20/2.09/4.97, 21/1.81/5.93, 22/2.21/5.01, 23/2.81/5.82, 24/3.20/4.90, 25/3.80/5.70, 26/4.20/4.78, 27/4.79/5.58, 28/4.37/4.68, 29/5.36/4.76, 30/4.94/3.85, 31/5.93/3.94, 32/5.51/3.03, 33/6.50/3.11, 34/5.52/2.91, 35/6.19/2.16, 36/5.21/1.96, 37/5.88/1.22, 38/4.95/1.60, 39/5.08/0.61, 40/4.16/0.99, 41/1.89/2.13, 42/2.13/1.81, 43/3.77/3.87, 44/4.54/2.71, 45/2.80/2.55, 46/3.11/1.60, 47/2.37/4.01, 48/4.03/1.98, 49/2.82/3.55, 50/3.14/4.65, 51/4.75/3.69, 52/3.80/3.38, 53/1.91/3.13} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/360.00/490.08/0.4/Blue, 11/310.08/445.03/0.4/Green, 15/265.03/435.03/0.4/Orange, 17/255.03/406.24/0.4/Violet, 21/226.24/353.24/0.4/Teal, 27/173.24/304.74/0.4/Lime} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 1/3, 2/5, 2/4, 3/2, 3/4, 4/5, 4/6, 5/7, 6/5, 6/7, 8/9, 8/1, 9/1, 10/9, 10/8, 11/9, 11/10, 12/13, 12/11, 13/11, 14/13, 14/12, 15/13, 15/14, 16/17, 16/15, 17/15, 18/19, 18/17, 19/17, 20/19, 20/18, 21/19, 21/20, 22/23, 22/21, 23/21, 24/23, 24/22, 25/23, 25/24, 26/25, 26/24, 27/25, 27/26, 28/29, 28/27, 29/27, 30/29, 30/28, 31/29, 31/30, 32/31, 32/30, 33/31, 33/32, 34/35, 34/33, 35/33, 35/37, 36/37, 36/35, 36/34, 38/39, 38/37, 39/7, 39/37, 40/7, 40/39, 40/38, 41/12, 41/10, 42/8, 42/3, 43/28, 43/26, 44/36, 44/34, 45/42, 45/46, 45/41, 46/42, 46/6, 47/20, 47/18, 48/40, 48/38, 48/46, 49/53, 49/52, 49/45, 50/22, 50/43, 50/47, 51/44, 51/32, 51/43, 52/44, 52/51, 53/41, 53/47} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,53} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-48) -- (p-46); \draw[Green,very thick] (p-50) -- (p-47); \draw[Green,very thick] (p-51) -- (p-43); \draw[Green,very thick] (p-45) -- (p-41); \draw[Green,very thick] (p-49) -- (p-45); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/360.00/490.08/0.4/Blue, 11/310.08/445.03/0.4/Green, 15/265.03/435.03/0.4/Orange, 17/255.03/406.24/0.4/Violet, 21/226.24/353.24/0.4/Teal, 27/173.24/304.74/0.4/Lime} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/210, 2/270, 3/90, 4/90, 5/210, 6/30, 7/330, 8/340, 9/280, 10/40, 11/160, 12/295, 13/175, 14/355, 15/115, 16/345, 17/196, 18/316, 19/136, 20/316, 21/143, 22/263, 23/83, 24/263, 25/83, 26/263, 27/23, 28/215, 29/35, 30/155, 31/335, 32/275, 33/335, 34/102, 35/42, 36/222, 37/282, 38/7, 39/247, 40/187, 41/239, 42/198, 43/279, 44/162, 45/78, 46/318, 47/316, 48/127, 49/59, 50/12, 51/48, 52/168, 53/149} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ und ich verstelle orangerWinkel=170 um 1 Grad (wieder Winkel oder Winkelbezeichnung anklicken und Button "+1"). 53 Knoten, 1×Grad 2, 6×Grad 3, 46×Grad 4, 0 Überschneidungen, 102 Kanten, minimal 0.78755010480619003221, maximal 1.12827361691598992977, Einsetzkanten=Beweglichkeit-1, nicht passende Kanten: |P48-P46|=0.78755010480619003221 |P49-P53|=1.00480676111201061573 |P49-P52|=1.00480676111201061573 |P49-P45|=0.90287419364266785493 |P51-P43|=1.12827361691598992977 $ %Eingabe war: % %#1768B = #1768A mit orangerWinkel=170 % % % % % % % % % %P[7]=[121.77225001445532,-27.49959090912219]; P[5]=[53.55568587581774,-27.49959090912219]; D=ab(7,5); A(5,7); N(6,5,7); N(4,5,6); N(2,5,4); N(3,2,4); N(1,2,3); M(9,1,2,blauerWinkel); N(8,9,1); N(10,9,8); N(11,9,10); M(13,11,9,gruenerWinkel); N(12,13,11); N(14,13,12); N(15,13,14); M(17,15,13,orangerWinkel); N(16,17,15); M(19,17,15,vierterWinkel); N(18,19,17); N(20,19,18); N(21,19,20); M(23,21,19,fuenfterWinkel); N(22,23,21); N(24,23,22); N(25,23,24); N(26,25,24); N(27,25,26); M(29,27,25,sechsterWinkel); N(28,29,27); N(30,29,28); N(31,29,30); N(32,31,30); N(33,31,32); Q(37,33,7,2*D,2*D); A(37,33); A(37,7); H(39,7,37,2); A(39,7); L(40,7,39); H(35,33,37,2); A(35,33); L(34,35,33); A(35,37); L(36,37,35); A(36,34); A(39,37); L(38,39,37); A(40,38); N(41,12,10); N(42,8,3); N(43,28,26); N(44,36,34); N(46,42,6); N(47,20,18); N(48,40,38); N(50,22,43); N(51,44,32); N(45,42,46); N(52,44,51); N(53,41,47); N(49,53,52); %A(48,46); R(48,46,"green"); %A(50,47); R(50,47,"green"); %A(51,43); R(51,43,"green"); %A(45,41); R(45,41,"green"); %A(49,45); R(49,45,"green"); % % % % % % % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{Lime}{rgb}{0.00,1.00,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.29/0.00, 2/2.29/0.00, 3/1.79/0.87, 4/2.79/0.87, 5/3.29/0.00, 6/3.79/0.87, 7/4.29/0.00, 8/1.63/0.94, 9/0.64/0.77, 10/0.98/1.71, 11/0.00/1.53, 12/0.91/1.95, 13/0.09/2.53, 14/0.99/2.95, 15/0.17/3.52, 16/1.13/3.80, 17/0.41/4.49, 18/1.39/4.27, 19/1.09/5.23, 20/2.07/5.01, 21/1.77/5.96, 22/2.18/5.05, 23/2.77/5.86, 24/3.18/4.95, 25/3.76/5.76, 26/4.17/4.85, 27/4.76/5.66, 28/4.35/4.75, 29/5.34/4.85, 30/4.930/3.937, 31/5.93/4.04, 32/5.514/3.125, 33/6.51/3.23, 34/5.517/3.100, 35/6.12/2.30, 36/5.13/2.18, 37/5.73/1.38, 38/4.77/1.66, 39/5.01/0.69, 40/4.05/0.97, 41/1.89/2.13, 42/2.13/1.81, 43/3.76/3.94, 44/4.53/2.97, 45/2.80/2.55, 46/3.11/1.60, 47/2.37/4.05, 48/3.81/1.94, 49/2.95/3.44, 50/3.12/4.71, 51/4.890/3.906, 52/3.90/3.76, 53/1.99/3.12} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/360.00/490.08/0.4/Blue, 11/310.08/445.03/0.4/Green, 15/265.03/436.03/0.4/Orange, 17/256.03/407.24/0.4/Violet, 21/227.24/354.24/0.4/Teal, 27/174.24/305.74/0.4/Lime} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 1/3, 2/5, 2/4, 3/2, 3/4, 4/5, 4/6, 5/7, 6/5, 6/7, 8/9, 8/1, 9/1, 10/9, 10/8, 11/9, 11/10, 12/13, 12/11, 13/11, 14/13, 14/12, 15/13, 15/14, 16/17, 16/15, 17/15, 18/19, 18/17, 19/17, 20/19, 20/18, 21/19, 21/20, 22/23, 22/21, 23/21, 24/23, 24/22, 25/23, 25/24, 26/25, 26/24, 27/25, 27/26, 28/29, 28/27, 29/27, 30/29, 30/28, 31/29, 31/30, 32/31, 32/30, 33/31, 33/32, 34/35, 34/33, 35/33, 35/37, 36/37, 36/35, 36/34, 38/39, 38/37, 39/7, 39/37, 40/7, 40/39, 40/38, 41/12, 41/10, 42/8, 42/3, 43/28, 43/26, 44/36, 44/34, 45/42, 45/46, 45/41, 46/42, 46/6, 47/20, 47/18, 48/40, 48/38, 48/46, 49/53, 49/52, 49/45, 50/22, 50/43, 50/47, 51/44, 51/32, 51/43, 52/44, 52/51, 53/41, 53/47} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,53} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-48) -- (p-46); \draw[Green,very thick] (p-50) -- (p-47); \draw[Green,very thick] (p-51) -- (p-43); \draw[Green,very thick] (p-45) -- (p-41); \draw[Green,very thick] (p-49) -- (p-45); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); \draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-48) -- (p-46); \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-49) -- (p-53); \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-49) -- (p-52); \draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-49) -- (p-45); \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-51) -- (p-43); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/360.00/490.08/0.4/Blue, 11/310.08/445.03/0.4/Green, 15/265.03/436.03/0.4/Orange, 17/256.03/407.24/0.4/Violet, 21/227.24/354.24/0.4/Teal, 27/174.24/305.74/0.4/Lime} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/210, 2/270, 3/90, 4/90, 5/210, 6/30, 7/330, 8/340, 9/280, 10/40, 11/160, 12/295, 13/175, 14/355, 15/115, 16/346, 17/106, 18/197, 19/197, 20/17, 21/77, 22/264, 23/84, 24/264, 25/144, 26/324, 27/96, 28/216, 29/36, 30/156, 31/36, 32/216, 33/37, 34/37, 35/277, 36/217, 37/14, 38/14, 39/14, 40/134, 41/237, 42/198, 43/209, 44/279, 45/78, 46/318, 47/317, 48/134, 49/52, 50/13, 51/39, 52/159, 53/144} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Diesmal entsteht im Inneren des Graphen ein Abstand P52-P53 größer 2, so dass die beiden Kanten P49-P52 und P49-P53 nicht passend eingesetzt werden können. In dem Fall nimmt das Streichholzprogramm die Mitte zwischen P52 und P53 als P49. Wenn jetzt bei Button "Feinjustieren(5,5)" alle Winkel geringfügig variiert werden, so bleibt P49 immer auf der Geraden P52-P3 und es geht dadurch irgendwie die Information verloren, dass P49 oberhalb von P52-P53 hin muss. Button "Feinjustieren(5,5)" funktioniert nicht und folglich auch nicht Testbutton "Newtonpolynom(10)". Naheliegender Ausweg wäre, annstelle um 1 Grad nur 0.9 Grad weitergehen, das würde hier schon reichen. Bei orangerWinkel=121 allerdings wäre nur 0.1 Grad möglich, in solchen Schritten den Graph weiterbewegen ist nicht so richtig überzeugend, mit "Newtonpolynom(10)" würde man nur 1 Grad weiterkommen. Deshalb mit Button "-1" zurück auf orangerWinkel=170 Grad und folgender Versuch: Button "beweglich?" 53 Knoten, 1×Grad 2, 6×Grad 3, 46×Grad 4, 0 Überschneidungen, 102 Kanten, minimal 0.99999999999998745448, maximal 1.00000000000001332268, Einsetzkanten=Beweglichkeit-1, $ %Eingabe war: % %#1768B = #1768A mit orangerWinkel=170 % % % % %blauerWinkel=130.08435157152414+(0.00029649747375683043)*(orangerWinkel-(170)); %vierterWinkel=151.2114945161103+(-0.9048421600846203)*(orangerWinkel-(170)); %fuenfterWinkel=126.99167593829996+(0.06075165547794758)*(orangerWinkel-(170)); %sechsterWinkel=131.50142550440444+(0.07093482927755061)*(orangerWinkel-(170)); %gruenerWinkel=134.94748139411323+(-0.18086180886322561)*(orangerWinkel-(170)); %P[7]=[121.77225001445532,-27.49959090912219]; P[5]=[53.55568587581774,-27.49959090912219]; D=ab(7,5); A(5,7); N(6,5,7); N(4,5,6); N(2,5,4); N(3,2,4); N(1,2,3); M(9,1,2,blauerWinkel); N(8,9,1); N(10,9,8); N(11,9,10); M(13,11,9,gruenerWinkel); N(12,13,11); N(14,13,12); N(15,13,14); M(17,15,13,orangerWinkel); N(16,17,15); M(19,17,15,vierterWinkel); N(18,19,17); N(20,19,18); N(21,19,20); M(23,21,19,fuenfterWinkel); N(22,23,21); N(24,23,22); N(25,23,24); N(26,25,24); N(27,25,26); M(29,27,25,sechsterWinkel); N(28,29,27); N(30,29,28); N(31,29,30); N(32,31,30); N(33,31,32); Q(37,33,7,2*D,2*D); A(37,33); A(37,7); H(39,7,37,2); A(39,7); L(40,7,39); H(35,33,37,2); A(35,33); L(34,35,33); A(35,37); L(36,37,35); A(36,34); A(39,37); L(38,39,37); A(40,38); N(41,12,10); N(42,8,3); N(43,28,26); N(44,36,34); N(46,42,6); N(47,20,18); N(48,40,38); N(50,22,43); N(51,44,32); N(45,42,46); N(52,44,51); N(53,41,47); N(49,53,52); %A(48,46); R(48,46,"green"); %A(50,47); R(50,47,"green"); %A(51,43); R(51,43,"green"); %A(45,41); R(45,41,"green"); %A(49,45); R(49,45,"green"); % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.29/0.00, 2/2.29/0.00, 3/1.79/0.87, 4/2.79/0.87, 5/3.29/0.00, 6/3.79/0.87, 7/4.29/0.00, 8/1.63/0.94, 9/0.64/0.77, 10/0.98/1.71, 11/0.00/1.53, 12/0.91/1.95, 13/0.09/2.53, 14/0.99/2.95, 15/0.17/3.52, 16/1.14/3.78, 17/0.43/4.49, 18/1.40/4.25, 19/1.12/5.21, 20/2.09/4.97, 21/1.81/5.93, 22/2.21/5.01, 23/2.81/5.82, 24/3.20/4.90, 25/3.80/5.70, 26/4.20/4.78, 27/4.79/5.58, 28/4.37/4.68, 29/5.36/4.76, 30/4.94/3.85, 31/5.93/3.94, 32/5.51/3.03, 33/6.50/3.11, 34/5.52/2.91, 35/6.19/2.16, 36/5.21/1.96, 37/5.88/1.22, 38/4.95/1.60, 39/5.08/0.61, 40/4.16/0.99, 41/1.89/2.13, 42/2.13/1.81, 43/3.77/3.87, 44/4.54/2.71, 45/2.80/2.55, 46/3.11/1.60, 47/2.37/4.01, 48/4.03/1.98, 49/2.82/3.55, 50/3.14/4.65, 51/4.75/3.69, 52/3.80/3.38, 53/1.91/3.13} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 15/265.03/435.03/0.4/Orange} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 1/3, 2/5, 2/4, 3/2, 3/4, 4/5, 4/6, 5/7, 6/5, 6/7, 8/9, 8/1, 9/1, 10/9, 10/8, 11/9, 11/10, 12/13, 12/11, 13/11, 14/13, 14/12, 15/13, 15/14, 16/17, 16/15, 17/15, 18/19, 18/17, 19/17, 20/19, 20/18, 21/19, 21/20, 22/23, 22/21, 23/21, 24/23, 24/22, 25/23, 25/24, 26/25, 26/24, 27/25, 27/26, 28/29, 28/27, 29/27, 30/29, 30/28, 31/29, 31/30, 32/31, 32/30, 33/31, 33/32, 34/35, 34/33, 35/33, 35/37, 36/37, 36/35, 36/34, 38/39, 38/37, 39/7, 39/37, 40/7, 40/39, 40/38, 41/12, 41/10, 42/8, 42/3, 43/28, 43/26, 44/36, 44/34, 45/42, 45/46, 45/41, 46/42, 46/6, 47/20, 47/18, 48/40, 48/38, 48/46, 49/53, 49/52, 49/45, 50/22, 50/43, 50/47, 51/44, 51/32, 51/43, 52/44, 52/51, 53/41, 53/47} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,53} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-48) -- (p-46); \draw[Green,very thick] (p-50) -- (p-47); \draw[Green,very thick] (p-51) -- (p-43); \draw[Green,very thick] (p-45) -- (p-41); \draw[Green,very thick] (p-49) -- (p-45); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 15/265.03/435.03/0.4/Orange} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/210, 2/270, 3/90, 4/90, 5/210, 6/30, 7/330, 8/340, 9/280, 10/40, 11/160, 12/295, 13/175, 14/355, 15/115, 16/345, 17/196, 18/316, 19/136, 20/316, 21/143, 22/263, 23/83, 24/263, 25/83, 26/263, 27/23, 28/215, 29/35, 30/155, 31/335, 32/275, 33/335, 34/102, 35/42, 36/222, 37/282, 38/7, 39/247, 40/187, 41/239, 42/198, 43/279, 44/162, 45/78, 46/318, 47/316, 48/127, 49/59, 50/12, 51/48, 52/168, 53/149} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ liefert ja nicht nur das Ergebnis, dass ein Winkel frei beweglich ist, sondern auch die Abhängigkeit der übrigen Winkel, in dem Fall \sourceon nameDerSprache blauerWinkel=130.08435157152414+(0.00029649747375683043)*(orangerWinkel-(170)); vierterWinkel=151.2114945161103+(-0.9048421600846203)*(orangerWinkel-(170)); fuenfterWinkel=126.99167593829996+(0.06075165547794758)*(orangerWinkel-(170)); sechsterWinkel=131.50142550440444+(0.07093482927755061)*(orangerWinkel-(170)); gruenerWinkel=134.94748139411323+(-0.18086180886322561)*(orangerWinkel-(170)); \sourceoff Jetzt Button "+1" führt nicht mehr zu zu dem großen Abstand P52-P53 und ich kann sogar Button "+10" verwenden, ohne dass P52-P53 zu groß wird 53 Knoten, 1×Grad 2, 6×Grad 3, 46×Grad 4, 0 Überschneidungen, 102 Kanten, minimal 0.96396671005231859830, maximal 1.02170730181491964395, Einsetzkanten=Beweglichkeit-1, nicht passende Kanten: |P45-P41|=1.00119866627664322323 |P48-P46|=1.02170730181491964395 |P49-P45|=0.96396671005231859830 |P50-P47|=0.99888329956612575966 |P51-P43|=0.99264270784106312107 $ %Eingabe war: % %#1768B = #1768A mit orangerWinkel=170 % % % % %blauerWinkel=130.08435157152414+(0.00029649747375683043)*(orangerWinkel-(170)); %vierterWinkel=151.2114945161103+(-0.9048421600846203)*(orangerWinkel-(170)); %fuenfterWinkel=126.99167593829996+(0.06075165547794758)*(orangerWinkel-(170)); %sechsterWinkel=131.50142550440444+(0.07093482927755061)*(orangerWinkel-(170)); %gruenerWinkel=134.94748139411323+(-0.18086180886322561)*(orangerWinkel-(170)); %P[7]=[121.77225001445532,-27.49959090912219]; P[5]=[53.55568587581774,-27.49959090912219]; D=ab(7,5); A(5,7); N(6,5,7); N(4,5,6); N(2,5,4); N(3,2,4); N(1,2,3); M(9,1,2,blauerWinkel); N(8,9,1); N(10,9,8); N(11,9,10); M(13,11,9,gruenerWinkel); N(12,13,11); N(14,13,12); N(15,13,14); M(17,15,13,orangerWinkel); N(16,17,15); M(19,17,15,vierterWinkel); N(18,19,17); N(20,19,18); N(21,19,20); M(23,21,19,fuenfterWinkel); N(22,23,21); N(24,23,22); N(25,23,24); N(26,25,24); N(27,25,26); M(29,27,25,sechsterWinkel); N(28,29,27); N(30,29,28); N(31,29,30); N(32,31,30); N(33,31,32); Q(37,33,7,2*D,2*D); A(37,33); A(37,7); H(39,7,37,2); A(39,7); L(40,7,39); H(35,33,37,2); A(35,33); L(34,35,33); A(35,37); L(36,37,35); A(36,34); A(39,37); L(38,39,37); A(40,38); N(41,12,10); N(42,8,3); N(43,28,26); N(44,36,34); N(46,42,6); N(47,20,18); N(48,40,38); N(50,22,43); N(51,44,32); N(45,42,46); N(52,44,51); N(53,41,47); N(49,53,52); %A(48,46); R(48,46,"green"); %A(50,47); R(50,47,"green"); %A(51,43); R(51,43,"green"); %A(45,41); R(45,41,"green"); %A(49,45); R(49,45,"green"); % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.29/0.00, 2/2.29/0.00, 3/1.79/0.87, 4/2.79/0.87, 5/3.29/0.00, 6/3.79/0.87, 7/4.29/0.00, 8/1.63/0.94, 9/0.64/0.77, 10/0.98/1.71, 11/0.00/1.53, 12/0.92/1.92, 13/0.12/2.52, 14/1.04/2.91, 15/0.24/3.52, 16/1.16/3.92, 17/0.35/4.51, 18/1.31/4.26, 19/1.05/5.22, 20/2.02/4.97, 21/1.75/5.93, 22/2.14/5.01, 23/2.75/5.81, 24/3.14/4.89, 25/3.74/5.69, 26/4.13/4.77, 27/4.73/5.56, 28/4.31/4.66, 29/5.31/4.75, 30/4.89/3.84, 31/5.88/3.93, 32/5.47/3.02, 33/6.46/3.11, 34/5.49/2.88, 35/6.18/2.16, 36/5.20/1.92, 37/5.89/1.20, 38/4.97/1.59, 39/5.09/0.60, 40/4.17/0.99, 41/1.90/2.10, 42/2.13/1.81, 43/3.71/3.86, 44/4.52/2.65, 45/2.80/2.55, 46/3.11/1.60, 47/2.28/4.00, 48/4.05/1.99, 49/2.77/3.51, 50/3.06/4.62, 51/4.68/3.64, 52/3.74/3.28, 53/1.86/3.10} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 15/263.05/444.05/0.4/Orange} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 1/3, 2/5, 2/4, 3/2, 3/4, 4/5, 4/6, 5/7, 6/5, 6/7, 8/9, 8/1, 9/1, 10/9, 10/8, 11/9, 11/10, 12/13, 12/11, 13/11, 14/13, 14/12, 15/13, 15/14, 16/17, 16/15, 17/15, 18/19, 18/17, 19/17, 20/19, 20/18, 21/19, 21/20, 22/23, 22/21, 23/21, 24/23, 24/22, 25/23, 25/24, 26/25, 26/24, 27/25, 27/26, 28/29, 28/27, 29/27, 30/29, 30/28, 31/29, 31/30, 32/31, 32/30, 33/31, 33/32, 34/35, 34/33, 35/33, 35/37, 36/37, 36/35, 36/34, 38/39, 38/37, 39/7, 39/37, 40/7, 40/39, 40/38, 41/12, 41/10, 42/8, 42/3, 43/28, 43/26, 44/36, 44/34, 45/42, 45/46, 45/41, 46/42, 46/6, 47/20, 47/18, 48/40, 48/38, 48/46, 49/53, 49/52, 49/45, 50/22, 50/43, 50/47, 51/44, 51/32, 51/43, 52/44, 52/51, 53/41, 53/47} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,53} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-48) -- (p-46); \draw[Green,very thick] (p-50) -- (p-47); \draw[Green,very thick] (p-51) -- (p-43); \draw[Green,very thick] (p-45) -- (p-41); \draw[Green,very thick] (p-49) -- (p-45); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-45) -- (p-41); \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-48) -- (p-46); \draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-49) -- (p-45); \draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-50) -- (p-47); \draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-51) -- (p-43); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 15/263.05/444.05/0.4/Orange} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/210, 2/270, 3/90, 4/90, 5/210, 6/30, 7/330, 8/340, 9/280, 10/40, 11/233, 12/353, 13/173, 14/353, 15/234, 16/354, 17/195, 18/195, 19/195, 20/15, 21/143, 22/263, 23/143, 24/323, 25/143, 26/323, 27/23, 28/155, 29/335, 30/155, 31/335, 32/215, 33/335, 34/103, 35/283, 36/283, 37/7, 38/67, 39/7, 40/127, 41/242, 42/198, 43/280, 44/291, 45/78, 46/318, 47/315, 48/127, 49/61, 50/10, 51/51, 52/171, 53/151} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ Nur kann ich jetzt nicht Button "Feinjustieren(5,5)" anwenden, weil die Winkel nicht mehr einzeln verstellbar sind. Was jetzt fehlt, ist ein Button, mit dem die aktuellen Winkel zurückgespeichert werden in die Situation wie vor Button "beweglich?". Einen solchen Button habe ich nun in Streichholzgraph-1898.htm ergänzt, rechts neben Button "beweglich?", nachdem dieser angeklickt wurde, ein Button "zurück mit aktuellen Winkeln". Damit erhalte ich folgenden Graph 53 Knoten, 1×Grad 2, 6×Grad 3, 46×Grad 4, 0 Überschneidungen, 102 Kanten, minimal 0.96396671005231859830, maximal 1.02170730181491964395, Einsetzkanten=Beweglichkeit-1, nicht passende Kanten: |P45-P41|=1.00119866627664322323 |P48-P46|=1.02170730181491964395 |P49-P45|=0.96396671005231859830 |P50-P47|=0.99888329956612575966 |P51-P43|=0.99264270784106312107 $ %Eingabe war: % %#1768B = #1768A mit orangerWinkel=170 % % % % % % % % % %P[7]=[121.77225001445532,-27.49959090912219]; P[5]=[53.55568587581774,-27.49959090912219]; D=ab(7,5); A(5,7); N(6,5,7); N(4,5,6); N(2,5,4); N(3,2,4); N(1,2,3); M(9,1,2,blauerWinkel); N(8,9,1); N(10,9,8); N(11,9,10); M(13,11,9,gruenerWinkel); N(12,13,11); N(14,13,12); N(15,13,14); M(17,15,13,orangerWinkel); N(16,17,15); M(19,17,15,vierterWinkel); N(18,19,17); N(20,19,18); N(21,19,20); M(23,21,19,fuenfterWinkel); N(22,23,21); N(24,23,22); N(25,23,24); N(26,25,24); N(27,25,26); M(29,27,25,sechsterWinkel); N(28,29,27); N(30,29,28); N(31,29,30); N(32,31,30); N(33,31,32); Q(37,33,7,2*D,2*D); A(37,33); A(37,7); H(39,7,37,2); A(39,7); L(40,7,39); H(35,33,37,2); A(35,33); L(34,35,33); A(35,37); L(36,37,35); A(36,34); A(39,37); L(38,39,37); A(40,38); N(41,12,10); N(42,8,3); N(43,28,26); N(44,36,34); N(46,42,6); N(47,20,18); N(48,40,38); N(50,22,43); N(51,44,32); N(45,42,46); N(52,44,51); N(53,41,47); N(49,53,52); %A(48,46); R(48,46,"green"); %A(50,47); R(50,47,"green"); %A(51,43); R(51,43,"green"); %A(45,41); R(45,41,"green"); %A(49,45); R(49,45,"green"); % % % % % % % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{Lime}{rgb}{0.00,1.00,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.29/0.00, 2/2.29/0.00, 3/1.79/0.87, 4/2.79/0.87, 5/3.29/0.00, 6/3.79/0.87, 7/4.29/0.00, 8/1.63/0.94, 9/0.64/0.77, 10/0.98/1.71, 11/0.00/1.53, 12/0.92/1.92, 13/0.12/2.52, 14/1.04/2.91, 15/0.24/3.52, 16/1.16/3.92, 17/0.35/4.51, 18/1.31/4.26, 19/1.05/5.22, 20/2.02/4.97, 21/1.75/5.93, 22/2.14/5.01, 23/2.75/5.81, 24/3.14/4.89, 25/3.74/5.69, 26/4.13/4.77, 27/4.73/5.56, 28/4.31/4.66, 29/5.31/4.75, 30/4.89/3.84, 31/5.88/3.93, 32/5.47/3.02, 33/6.46/3.11, 34/5.49/2.88, 35/6.18/2.16, 36/5.20/1.92, 37/5.89/1.20, 38/4.97/1.59, 39/5.09/0.60, 40/4.17/0.99, 41/1.90/2.10, 42/2.13/1.81, 43/3.71/3.86, 44/4.52/2.65, 45/2.80/2.55, 46/3.11/1.60, 47/2.28/4.00, 48/4.05/1.99, 49/2.77/3.51, 50/3.06/4.62, 51/4.68/3.64, 52/3.74/3.28, 53/1.86/3.10} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/360.00/490.09/0.4/Blue, 11/310.09/443.05/0.4/Green, 15/263.05/444.05/0.4/Orange, 17/264.05/405.30/0.4/Violet, 21/225.30/352.96/0.4/Teal, 27/172.96/305.25/0.4/Lime} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 1/3, 2/5, 2/4, 3/2, 3/4, 4/5, 4/6, 5/7, 6/5, 6/7, 8/9, 8/1, 9/1, 10/9, 10/8, 11/9, 11/10, 12/13, 12/11, 13/11, 14/13, 14/12, 15/13, 15/14, 16/17, 16/15, 17/15, 18/19, 18/17, 19/17, 20/19, 20/18, 21/19, 21/20, 22/23, 22/21, 23/21, 24/23, 24/22, 25/23, 25/24, 26/25, 26/24, 27/25, 27/26, 28/29, 28/27, 29/27, 30/29, 30/28, 31/29, 31/30, 32/31, 32/30, 33/31, 33/32, 34/35, 34/33, 35/33, 35/37, 36/37, 36/35, 36/34, 38/39, 38/37, 39/7, 39/37, 40/7, 40/39, 40/38, 41/12, 41/10, 42/8, 42/3, 43/28, 43/26, 44/36, 44/34, 45/42, 45/46, 45/41, 46/42, 46/6, 47/20, 47/18, 48/40, 48/38, 48/46, 49/53, 49/52, 49/45, 50/22, 50/43, 50/47, 51/44, 51/32, 51/43, 52/44, 52/51, 53/41, 53/47} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,53} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-48) -- (p-46); \draw[Green,very thick] (p-50) -- (p-47); \draw[Green,very thick] (p-51) -- (p-43); \draw[Green,very thick] (p-45) -- (p-41); \draw[Green,very thick] (p-49) -- (p-45); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-45) -- (p-41); \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-48) -- (p-46); \draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-49) -- (p-45); \draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-50) -- (p-47); \draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-51) -- (p-43); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/360.00/490.09/0.4/Blue, 11/310.09/443.05/0.4/Green, 15/263.05/444.05/0.4/Orange, 17/264.05/405.30/0.4/Violet, 21/225.30/352.96/0.4/Teal, 27/172.96/305.25/0.4/Lime} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/210, 2/270, 3/90, 4/90, 5/210, 6/30, 7/330, 8/340, 9/280, 10/40, 11/233, 12/353, 13/173, 14/353, 15/234, 16/354, 17/195, 18/195, 19/195, 20/15, 21/143, 22/263, 23/143, 24/323, 25/143, 26/323, 27/23, 28/155, 29/335, 30/155, 31/335, 32/215, 33/335, 34/103, 35/283, 36/283, 37/7, 38/67, 39/7, 40/127, 41/242, 42/198, 43/280, 44/291, 45/78, 46/318, 47/315, 48/127, 49/61, 50/10, 51/51, 52/171, 53/151} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ den ich mit Button "Feinjustieren(5,6)" noch zurechtziehen kann. Ich muss also die Newtonpolynome mit den von Button "beweglich?" gelieferten Polynomen beginnen lassen und das ist dann eine Hermiteinterpolation, beginnend mit dem Funktionswert und der Ableitung im ersten Punkt. Einen solchen Button habe ich gleich mit in der aktuellen Version ergänzt, Testbutton "+10° Hermiteinterpolation" rechts neben Testbutton "Newtonpolynom(10)". Zum Ausprobieren der Graph mit Startwert orangerWinkel=121 Grad 53 Knoten, 1×Grad 2, 6×Grad 3, 46×Grad 4, 0 Überschneidungen, 102 Kanten, minimal 0.99999999999996869171, maximal 1.00000000000001887379, Einsetzkanten=Beweglichkeit-1, $ %Eingabe war: % %#1768C = #1768A mit orangerWinkel=121 und Feinjustieren(5,5) % % % % % % % % % %P[7]=[117.84606497385661,-27.499572346086406]; P[5]=[46.53408464089239,-27.49957234608639]; D=ab(7,5); A(5,7); N(6,5,7); N(4,5,6); N(2,5,4); N(3,2,4); N(1,2,3); M(9,1,2,blauerWinkel); N(8,9,1); N(10,9,8); N(11,9,10); M(13,11,9,gruenerWinkel); N(12,13,11); N(14,13,12); N(15,13,14); M(17,15,13,orangerWinkel); N(16,17,15); M(19,17,15,vierterWinkel); N(18,19,17); N(20,19,18); N(21,19,20); M(23,21,19,fuenfterWinkel); N(22,23,21); N(24,23,22); N(25,23,24); N(26,25,24); N(27,25,26); M(29,27,25,sechsterWinkel); N(28,29,27); N(30,29,28); N(31,29,30); N(32,31,30); N(33,31,32); Q(37,33,7,2*D,2*D); A(37,33); A(37,7); H(39,7,37,2); A(39,7); L(40,7,39); H(35,33,37,2); A(35,33); L(34,35,33); A(35,37); L(36,37,35); A(36,34); A(39,37); L(38,39,37); A(40,38); N(41,12,10); N(42,8,3); N(43,28,26); N(44,36,34); N(46,42,6); N(47,20,18); N(48,40,38); N(50,22,43); N(51,44,32); N(45,42,46); N(52,44,51); N(53,41,47); N(49,53,52); %A(48,46); R(48,46,"green"); %A(50,47); R(50,47,"green"); %A(51,43); R(51,43,"green"); %A(45,41); R(45,41,"green"); %A(49,45); R(49,45,"green"); % % % % % % % % % % % % % % % % % % % % % % %Ende der Eingabe. \begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize] \definecolor{Blue}{rgb}{0.00,0.00,1.00} \definecolor{Green}{rgb}{0.00,0.50,0.00} \definecolor{Lime}{rgb}{0.00,1.00,0.00} \definecolor{Orange}{rgb}{1.00,0.64,0.00} \definecolor{Teal}{rgb}{0.00,0.50,0.50} \definecolor{Violet}{rgb}{0.93,0.51,0.93} %Koordinaten als \coordinate (p-1) at (0,0); \foreach \i/\x/\y in { 1/1.29/0.00, 2/2.29/0.00, 3/1.79/0.87, 4/2.79/0.87, 5/3.29/0.00, 6/3.79/0.87, 7/4.29/0.00, 8/1.63/0.94, 9/0.65/0.77, 10/0.99/1.71, 11/0.01/1.54, 12/0.87/2.04, 13/0.00/2.54, 14/0.868/3.040, 15/0.00/3.54, 16/0.877/3.056, 17/0.86/4.06, 18/1.85/3.96, 19/1.44/4.87, 20/2.434/4.768, 21/2.02/5.68, 22/2.484/4.792, 23/3.02/5.64, 24/3.48/4.75, 25/4.02/5.59, 26/4.48/4.70, 27/5.02/5.55, 28/4.57/4.65, 29/5.57/4.71, 30/5.12/3.82, 31/6.12/3.88, 32/5.676/2.985, 33/6.67/3.05, 34/5.681/2.929, 35/6.28/2.13, 36/5.28/2.01, 37/5.88/1.21, 38/4.96/1.60, 39/5.09/0.60, 40/4.16/0.99, 41/1.86/2.21, 42/2.13/1.80, 43/4.04/3.81, 44/4.69/2.81, 45/2.80/2.55, 46/3.11/1.60, 47/2.85/3.86, 48/4.04/1.98, 49/3.05/3.52, 50/3.47/4.64, 51/5.03/3.75, 52/4.05/3.58, 53/2.11/3.18} \coordinate (p-\i) at (\x,\y); %Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle; %gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle; \foreach \i/\a/\b/\r/\c in { 1/0.00/129.79/0.4/Blue, 11/309.79/450.24/0.4/Green, 15/270.24/391.24/0.4/Orange, 17/211.24/414.29/0.4/Violet, 21/234.29/357.49/0.4/Teal, 27/177.49/303.47/0.4/Lime} \fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle; %Kanten als \draw[gray,thick] (p-1) -- (p-2); \foreach \i/\j in { 1/2, 1/3, 2/5, 2/4, 3/2, 3/4, 4/5, 4/6, 5/7, 6/5, 6/7, 8/9, 8/1, 9/1, 10/9, 10/8, 11/9, 11/10, 12/13, 12/11, 13/11, 14/13, 14/12, 15/13, 15/14, 16/17, 16/15, 17/15, 18/19, 18/17, 19/17, 20/19, 20/18, 21/19, 21/20, 22/23, 22/21, 23/21, 24/23, 24/22, 25/23, 25/24, 26/25, 26/24, 27/25, 27/26, 28/29, 28/27, 29/27, 30/29, 30/28, 31/29, 31/30, 32/31, 32/30, 33/31, 33/32, 34/35, 34/33, 35/33, 35/37, 36/37, 36/35, 36/34, 38/39, 38/37, 39/7, 39/37, 40/7, 40/39, 40/38, 41/12, 41/10, 42/8, 42/3, 43/28, 43/26, 44/36, 44/34, 45/42, 45/46, 45/41, 46/42, 46/6, 47/20, 47/18, 48/40, 48/38, 48/46, 49/53, 49/52, 49/45, 50/22, 50/43, 50/47, 51/44, 51/32, 51/43, 52/44, 52/51, 53/41, 53/47} \draw[gray,thick] (p-\i) -- (p-\j); %Punkte als \fill[red] (p-1) circle (1.125pt) \foreach \i in {1,...,53} \fill[red] (p-\i) circle (1.125pt); %einzustellende Kanten als \draw[green] (p-1) -- (p-2); \draw[Green,very thick] (p-48) -- (p-46); \draw[Green,very thick] (p-50) -- (p-47); \draw[Green,very thick] (p-51) -- (p-43); \draw[Green,very thick] (p-45) -- (p-41); \draw[Green,very thick] (p-49) -- (p-45); %nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2); %Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm); \foreach \i/\a/\b/\r/\c in { 1/0.00/129.79/0.4/Blue, 11/309.79/450.24/0.4/Green, 15/270.24/391.24/0.4/Orange, 17/211.24/414.29/0.4/Violet, 21/234.29/357.49/0.4/Teal, 27/177.49/303.47/0.4/Lime} { \draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm); \fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i); } %Punktnummern als \node[anchor=30] (P1) at (p-1) {1}; \foreach \i/\a in { 1/280, 2/330, 3/150, 4/150, 5/330, 6/90, 7/330, 8/40, 9/280, 10/100, 11/160, 12/360, 13/180, 14/360, 15/120, 16/301, 17/61, 18/324, 19/144, 20/24, 21/84, 22/207, 23/27, 24/207, 25/27, 26/327, 27/27, 28/213, 29/33, 30/273, 31/33, 32/213, 33/37, 34/37, 35/337, 36/217, 37/7, 38/127, 39/307, 40/127, 41/230, 42/198, 43/210, 44/280, 45/78, 46/318, 47/324, 48/127, 49/50, 50/24, 51/40, 52/160, 53/140} \node[anchor=\a] (P\i) at (p-\i) {\i}; \end{tikzpicture} $ den ins große Eingabefenster vom Streichholzprogramm kopieren und Button "neu zeichen". Anschließend reihum Buttons "beweglich?", "+10° Hermiteinterpolation", "+10", "zurück mit aktuellen Winkeln" so kann man sich bis über orangerWinkel=190 Grad hindurchhangeln. Huuuuiuuauauuuu, diese Buttons waren eine harte Nuss, unter uns Eichhörnchen gesagt. Ab jetzt geht es nur noch abwärts!


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Dabei seit: 23.03.2005
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Wohnort: Westerburg
  Beitrag No.1919, vom Themenstarter, eingetragen 2020-03-08

Besten Dank für die harte Arbeit am Programm, Stefan!


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