| |
| Autor |
 Streichholzgraphen 4-regulär und 4/n-regulär (n>4) und 2/5 |
|
StefanVogel
Senior 
Dabei seit: 26.11.2005
Mitteilungen: 4328
Wohnort: Raun
 |  Beitrag No.1680, eingetragen 2019-02-02
|
Mit den zuletzt 17 zusätzlichen Abstandshaltern ist der Graph starr. Von diesen werden die 9 grünen gebraucht, um die Eckpunkte auf dem regelmäßigen 16-Eck zu halten. Die übrigen 8 (braun und violett) können bis zur Überschneidung verändert oder ganz entfernt werden und man erhält dadurch im Inneren achtfache Beweglichkeit.
\quoteon(2019-01-26 15:09 - Slash in Beitrag No. 1656)
@ Stefan: "limegreen" der nicht passenden Kanten wird schwarz angezeigt, daher auf "red" gesetzt. :-?
\quoteoff
Jetzt werden alle Webfarben vom aktualisierten Streichholzgraph-1554.htm ins fedgeo und TikZ übersetzt.
$
%Eingabe war:
%
%#1649 P81, P82, P6 fertig, achtzehnterWinkel, P70, P71 fertig, Start P72, Feinjustieren(14), 0.8, F(15), F(16), 0.85, 0.86, F(17), 0.87, 0.9, fertig 1.0, 3x verbessert
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%P[1]=[142.95082422289,58.095211353618694]; P[2]=[98.85951332256333,118.37613335988418]; D=ab(1,2); A(2,1,Bew(1));
% M(3,1,2,blauerWinkel);
% M(4,3,1,gruenerWinkel);
% M(5,3,4,orangerWinkel);
% M(6,5,3,achtzehnterWinkel); N(7,2,4);
% N(8,4,6);
% M(9,8,4,vierterWinkel);
% N(10,9,7);
% M(11,5,6,fuenfterWinkel);
% M(12,11,5,sechsterWinkel);
% N(13,6,12);
% N(14,13,9);
% M(15,10,9,siebenterWinkel);
% N(16,15,14);
% N(17,12,16);
% M(18,11,12,achterWinkel);
% N(19,17,18);
% M(20,1,2,neunterWinkel);
% M(21,20,1,zehnterWinkel);
% M(22,20,21,elfterWinkel);
% N(23,2,21);
% M(24,22,20,zwölfterWinkel);
% N(25,24,21);
% M(26,22,24,dreizehnterWinkel);
% M(27,26,22,vierzehnterWinkel);
% N(28,27,24);
% M(29,28,24,fuenfzehnterWinkel);
% N(30,25,29);
% N(31,23,30);
% M(32,26,27,sechzehnterWinkel);
% A(18,32,ab(32,18,[1,32]));
% N(63,50,27);
% N(64,29,63);
% N(65,19,58);
% N(66,60,65);
% N(67,62,15);
% N(68,31,47);
% RA(66,67);
% RA(68,64);
%
%M(69,3,1,180*14/16);
%M(70,69,3,180*14/16);
%M(71,70,69,180*14/16);
%M(72,71,70,180*14/16);
%M(73,72,71,180*14/16);
%M(74,73,72,180*14/16);
%M(75,74,73,180*14/16);
%M(76,75,74,180*14/16);
%M(77,76,75,180*14/16);
%M(78,77,76,180*14/16);
%M(79,78,77,180*14/16);
%M(80,79,78,180*14/16);
%M(81,80,79,180*14/16);
%M(82,81,80,180*14/16);
%
%R(82,21); R(81,24);
%//R(11,65,"brown",1.28*D);
%R(2,9,"brown",1.052*D); R(80,27); R(69,6); R(19,12,"brown",0.13*D); RW(22,26,28,26,1.74); R(70,12);
%//RW(30,23,21,23,1.57);
%R(31,21,"brown",1.033*D);
%R(71,19);
%//RW(15,10,23,10,2);
%R(67,23,"brown",1.044*D);
%//R(62,15,"brown",1.996*D);
%RW(5,3,8,3,3.4);
%R(14,4,"brown",1.08*D);
%//R(64,24,"brown",1.18*D);
%R(68,29,"brown",1.035*D);
%R(72,58); RW(20,22,25,22); RW(11,5,13,5);
%
%
%
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Brown}{rgb}{0.64,0.16,0.16}
\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{LightSeaGreen}{rgb}{0.13,0.70,0.66}
\definecolor{LightSkyBlue}{rgb}{0.53,0.80,0.98}
\definecolor{LightSteelBlue}{rgb}{0.69,0.77,0.87}
\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 {
1/9.21/2.06,
2/8.033/3.670,
3/7.75/0.70,
4/6.580/2.320,
5/5.87173847304487495080/0.00000000000000000000,
6/5.32/1.92,
7/8.49/1.72,
8/6.52/0.32,
9/6.420/2.318,
10/7.921/3.640,
11/3.87315115809701638/0.07515813016238558,
12/3.79/2.07,
13/4.37/0.16,
14/4.43/2.16,
15/6.189/4.641,
16/6.37/2.65,
17/4.75/3.83,
18/2.0554590151006824/0.9094214418868060,
19/3.57/2.21,
20/10.0475769368991710/3.8731511580969791,
21/8.054/3.710,
22/10.1227350670615479/5.8717384730448385,
23/6.277/4.629,
24/8.25/5.16,
25/10.00/4.18,
26/9.427345871654783/7.746954158482524,
27/7.94/6.41,
28/9.93/6.25,
29/7.989/5.775,
30/8.039/3.776,
31/7.919/5.772,
32/8.067276051960864/9.213313625174697,
33/0.909421441886798/8.067276051960853,
34/2.090/6.453,
35/2.375780908578968/9.427345871654776,
36/3.542/7.803,
37/4.250996594016670/10.122735067061503,
38/4.80/8.20,
39/1.63/8.40,
40/3.61/9.80,
41/3.703/7.804,
42/2.202/6.483,
43/6.249583908964533/10.047576936899116,
44/6.33/8.05,
45/5.75/9.96,
46/5.70/7.96,
47/3.934/5.482,
48/3.76/7.47,
49/5.37/6.29,
50/6.55/7.91,
51/0.075158130162376/6.249583908964524,
52/2.069/6.412,
53/0.000000000000000/4.250996594016666,
54/3.845/5.494,
55/1.87/4.96,
56/0.13/5.94,
57/0.6953891954067645/2.3757809085789789,
58/2.18/3.71,
59/0.19/3.87,
60/2.134/4.348,
61/2.083/6.347,
62/2.204/4.351,
63/8.51/8.33,
64/6.76/7.35,
65/1.62/1.79,
66/3.36/2.77,
67/4.19/4.59,
68/5.93/5.53,
69/5.87173847304487495080/0.00000000000000000000,
70/3.87315115809701638/0.07515813016238740,
71/2.0554590151006846/0.9094214418868116,
72/0.6953891954067645/2.3757809085789821,
73/0.000000000000038/4.250996594016684,
74/0.075158130162426/6.249583908964543,
75/0.909421441886851/8.067276051960874,
76/2.375780908579022/9.427345871654795,
77/4.250996594016723/10.122735067061519,
78/6.249583908964582/10.047576936899132,
79/8.067276051960912/9.213313625174704,
80/9.427345871654833/7.746954158482533,
81/10.1227350670615586/5.8717384730448314,
82/10.0475769368991692/3.8731511580969729}
\coordinate (p-\i) at (\x,\y);
%Dreiecke als \fill[black!3] (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 {
1/126.18/222.85/0.4/Blue,
3/42.85/125.69/0.4/Green,
3/125.69/200.35/0.3/Orange,
5/20.35/106.03/0.4/LightSteelBlue,
8/88.21/92.80/0.4/Violet,
5/106.03/177.85/0.3/Teal,
11/357.85/452.32/0.4/Lime,
10/221.37/509.98/0.4/LightBlue,
11/92.32/155.35/0.3/LightCoral,
1/126.18/425.35/0.3/LightCyan,
20/245.35/544.67/0.4/LightGoldenrodYellow,
20/184.67/447.85/0.3/LightGreen,
22/267.85/560.80/0.4/LightGray,
22/200.80/470.35/0.3/LightPink,
26/290.35/581.88/0.4/LightSalmon,
28/212.93/553.71/0.4/LightSeaGreen,
26/221.88/492.85/0.3/LightSkyBlue}
\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-66) -- (p-67);
\draw[LimeGreen,very thick] (p-68) -- (p-64);
\draw[LimeGreen,very thick] (p-82) -- (p-21);
\draw[LimeGreen,very thick] (p-81) -- (p-24);
\draw[Brown,very thick] (p-2) -- (p-9);
\draw[LimeGreen,very thick] (p-80) -- (p-27);
\draw[LimeGreen,very thick] (p-69) -- (p-6);
\draw[Brown,very thick] (p-19) -- (p-12);
\draw[Violet,very thick] (p-22) -- (p-26);
\draw[LimeGreen,very thick] (p-70) -- (p-12);
\draw[Brown,very thick] (p-31) -- (p-21);
\draw[LimeGreen,very thick] (p-71) -- (p-19);
\draw[Brown,very thick] (p-67) -- (p-23);
\draw[Violet,very thick] (p-5) -- (p-3);
\draw[Brown,very thick] (p-14) -- (p-4);
\draw[Brown,very thick] (p-68) -- (p-29);
\draw[LimeGreen,very thick] (p-72) -- (p-58);
\draw[Violet,very thick] (p-20) -- (p-22);
\draw[Violet,very thick] (p-11) -- (p-5);
%Kanten als \draw[line width=0] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1,
4/3,
5/3,
6/5,
7/2, 7/4,
8/4, 8/6,
9/8,
10/9, 10/7,
11/5,
12/11,
13/6, 13/12,
14/13, 14/9,
15/10,
16/15, 16/14,
17/12, 17/16,
18/11, 18/57,
19/17, 19/18,
20/1,
21/20,
22/20,
23/2, 23/21,
24/22,
25/24, 25/21,
26/22,
27/26,
28/27, 28/24,
29/28,
30/25, 30/29,
31/23, 31/30,
32/26, 32/43,
34/33,
35/33,
36/35,
37/35,
38/37,
39/34, 39/36,
40/36, 40/38,
41/40,
42/39, 42/41,
43/37,
44/43,
45/38, 45/44,
46/41, 46/45,
47/42,
48/46, 48/47,
49/44, 49/48,
50/49, 50/32,
51/33,
52/51,
53/51,
54/34, 54/52,
55/53,
56/52, 56/55,
57/53,
58/57,
59/55, 59/58,
60/59,
61/56, 61/60,
62/54, 62/61,
63/50, 63/27,
64/29, 64/63,
65/19, 65/58,
66/60, 66/65, 66/67,
67/62, 67/15,
68/31, 68/47, 68/64,
69/3,
70/69,
71/70,
72/71,
73/72,
74/73,
75/74,
76/75,
77/76,
78/77,
79/78,
80/79,
81/80,
82/81}
\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 {
1/126.18/222.85/0.4/Blue,
3/42.85/125.69/0.4/Green,
3/125.69/200.35/0.3/Orange,
5/20.35/106.03/0.4/LightSteelBlue,
8/88.21/92.80/0.4/Violet,
5/106.03/177.85/0.3/Teal,
11/357.85/452.32/0.4/Lime,
10/221.37/509.98/0.4/LightBlue,
11/92.32/155.35/0.3/LightCoral,
1/126.18/425.35/0.3/LightCyan,
20/245.35/544.67/0.4/LightGoldenrodYellow,
20/184.67/447.85/0.3/LightGreen,
22/267.85/560.80/0.4/LightGray,
22/200.80/470.35/0.3/LightPink,
26/290.35/581.88/0.4/LightSalmon,
28/212.93/553.71/0.4/LightSeaGreen,
26/221.88/492.85/0.3/LightSkyBlue}
{
\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 {
1/278,
2/40,
3/346,
4/308,
5/324,
6/277,
7/317,
8/110,
9/51,
10/76,
11/306,
12/177,
13/87,
14/139,
15/125,
16/147,
17/105,
18/191,
19/306,
20/38,
21/266,
22/57,
23/186,
24/4,
25/175,
26/79,
27/37,
28/197,
29/145,
30/234,
31/67,
32/11,
33/98,
34/220,
35/166,
36/128,
37/144,
38/97,
39/137,
40/290,
41/231,
42/256,
43/126,
44/357,
45/267,
46/319,
47/305,
48/327,
49/285,
50/126,
51/218,
52/86,
53/237,
54/6,
55/184,
56/355,
57/259,
58/217,
59/17,
60/325,
61/54,
62/247,
63/225,
64/99,
65/45,
66/279,
67/39,
68/219,
69/282,
70/259,
71/237,
72/214,
73/192,
74/169,
75/147,
76/124,
77/102,
78/79,
79/57,
80/34,
81/12,
82/270}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
$
Die Winkel sind mit Pfeil gezeichnet, damit man den kleinen Winkel in P8 nicht übersieht.
|
 Profil
|
Slash
Aktiv 
Dabei seit: 23.03.2005
Mitteilungen: 9212
Wohnort: Pferdehof
 | Beitrag No.1681, vom Themenstarter, eingetragen 2019-02-02
|
@ Stefan: Kann man diesen Abstandhalter-Algorithmus generell für jeden Graphen benutzen um ihn zurechtzuziehen oder muss der äußere Kreis fest vorgegeben sein? Könnte man für #1674 eine Lösung finden?
|
Profil
|
StefanVogel
Senior
Dabei seit: 26.11.2005
Mitteilungen: 4328
Wohnort: Raun
| Beitrag No.1682, eingetragen 2019-02-03
|
#1674-2 ist dann wohl der neue Rekord. Kantenlängen ändern führt nur zu einem isomorphen Graph, das zählt nicht als neuer Graph. Na wenigstens habe ich die Ehre und darf als erster gratulieren: Gratulation!!!
60 Knoten, 60×Grad 3, 0 Dreiecke,
90 Kanten, minimal 0.99999999999999622524, maximal 1.00000000000000133227
einzustellende Kanten, Abstände und Winkel:
|P16-P19|=0.99999999999999944489
|P18-P51|=0.99999999999999622524
|P21-P57|=1.00000000000000044409
|P58-P15|=0.99999999999999877875
|P58-P37|=1.03100000000001257305
|P58-P12|=1.04299999999999037925
|P9-P2|=1.08000000000000029310
∠(P7-P1,P3-P1)=3.14499999999998269828°
|P6-P11|=1.05000000000000026645
∠(P8-P3,P5-P3)=2.09999999999999653610°
|P7-P21|=1.03499999999999903189
$
%Eingabe war:
%
%3-reg. girth 5 mit 60 Knoten, Feinjustieren(11), P18-P51=1, P16-P19=1, P58-P15=1, ohne \spy
%
%
%
%
%
%
%
%
%
%
%
%
%
%P[1]=[24.96744706730899,18.904171093103333];
%P[2]=[-8.749307725799035,93.85736688700575]; D=ab(1,2);
%A(2,1,Bew(1)); M(3,1,2,blauerWinkel); M(4,3,1,gruenerWinkel);
%M(5,3,4,orangerWinkel);
%M(6,5,3,360-36-blauerWinkel-gruenerWinkel-orangerWinkel);N(7,2,4); N(8,4,6);
%M(9,8,4,vierterWinkel); N(10,9,7);
%M(11,5,6,fuenfterWinkel);M(12,11,5,sechsterWinkel); N(13,6,12); N(14,13,9);
%M(15,10,9,siebenterWinkel);
%N(16,15,14);
%M(17,11,12,achterWinkel); M(18,1,2,neunterWinkel);
%M(19,12,11,zehnterWinkel); N(20,17,19);
%M(21,18,1,elfterWinkel); A(16,19); R(16,19,"green",1*D);
%A(17,20,ab(18,21,[1,21])); A(38,40,ab(18,21,[1,16],18));
%N(57,52,56);
%A(18,51); R(18,51,"green",1*D); A(21,57); R(21,57,"green",1*D);
%N(58,23,20); N(59,42,40); N(60,2,21);
%A(58,15); R(58,15,"green",1*D); A(36,59); A(55,60);
%R(58,37,"brown",1.031*D); //RW(3,31,58,31,3.2); //R(58,12,"brown",1.012*D);
%R(58,12,"brown",1.043*D); //RW(58,20,19,20,3.4); //R(58,37,"brown",1.006*D);
%R(9,2,"brown",1.08*D);
%RW(3,1,7,1,3.145); //RW(4,10,16,10,9);
%//R(2,3,"brown",1.2*D);
%//R(8,16,"brown",1.08*D);
%//R(16,12,"brown",1.06*D);
%//RW(11,5,13,5,0.67);
%R(6,11,"brown",1.05*D);
%RW(5,3,8,3,2.1);
%R(7,21,"brown",1.035*D);
%//R(4,5,"brown",1.034*D); //RW(11,5,13,5,2.6);
%
%
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Brown}{rgb}{0.64,0.16,0.16}
\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{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 {
1/7.34/0.28,
2/6.523/2.106,
3/5.36/0.00,
4/5.21/1.99,
5/3.47/0.64,
6/3.88/2.60,
7/6.03/0.17,
8/3.78/0.60,
9/4.400/2.502,
10/6.367/2.139,
11/1.902/1.883,
12/2.00/3.88,
13/2.010/1.881,
14/2.81/3.71,
15/5.837/4.068,
16/4.473/2.605,
17/0.70/3.48,
18/8.62/1.82,
19/3.897/4.520,
20/1.964/5.030,
21/6.643/2.144,
22/0.00/5.35,
23/1.990/5.153,
24/0.75/7.21,
25/2.55/6.34,
26/2.25/8.53,
27/3.74/7.20,
28/0.56/6.55,
29/2.06/8.28,
30/3.394/6.794,
31/2.097/5.272,
32/4.108/9.266,
33/5.79/8.18,
34/4.052/9.174,
35/5.24/7.57,
36/4.032/4.766,
37/3.447/6.679,
38/6.09/9.51,
39/5.394/6.220,
40/6.802/7.640,
41/8.07/9.18,
42/6.896/7.555,
43/9.30/7.60,
44/7.65/6.48,
45/9.69/5.64,
46/7.79/5.02,
47/8.82/8.10,
48/9.57/5.93,
49/7.615/5.518,
50/6.945/7.403,
51/9.399/3.665,
52/7.62/2.75,
53/9.347/3.759,
54/7.36/3.53,
55/5.539/5.980,
56/7.488/5.531,
57/6.117/4.074,
58/3.932/4.674,
59/5.510/6.113,
60/5.967/4.027}
\coordinate (p-\i) at (\x,\y);
%Dreiecke als \fill[black!3] (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 {
1/114.22/188.10/0.4/Blue,
3/8.10/94.29/0.4/Green,
3/94.29/161.35/0.3/Orange,
8/44.21/71.96/0.4/Violet,
5/78.22/141.56/0.4/Teal,
11/321.56/447.12/0.4/Lime,
10/169.55/465.34/0.4/LightBlue,
11/87.12/126.99/0.3/LightCoral,
1/114.22/410.45/0.3/LightCyan,
12/267.12/378.65/0.4/LightGoldenrodYellow,
18/230.45/530.77/0.4/LightGreen}
\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[Green,very thick] (p-16) -- (p-19);
\draw[Green,very thick] (p-18) -- (p-51);
\draw[Green,very thick] (p-21) -- (p-57);
\draw[Green,very thick] (p-58) -- (p-15);
\draw[Brown,very thick] (p-58) -- (p-37);
\draw[Brown,very thick] (p-58) -- (p-12);
\draw[Brown,very thick] (p-9) -- (p-2);
\draw[Violet,very thick] (p-3) -- (p-1);
\draw[Brown,very thick] (p-6) -- (p-11);
\draw[Violet,very thick] (p-5) -- (p-3);
\draw[Brown,very thick] (p-7) -- (p-21);
%Kanten als \draw[line width=0] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1,
4/3,
5/3,
6/5,
7/2, 7/4,
8/4, 8/6,
9/8,
10/9, 10/7,
11/5,
12/11,
13/6, 13/12,
14/13, 14/9,
15/10,
16/15, 16/14, 16/19,
17/11, 17/22,
18/1, 18/51,
19/12,
20/17, 20/19,
21/18, 21/57,
23/22,
24/22,
25/24,
26/24,
27/26,
28/23, 28/25,
29/25, 29/27,
30/29,
31/28, 31/30,
32/26,
33/32,
34/27, 34/33,
35/30, 35/34,
36/31, 36/59,
37/35, 37/36, 37/39,
38/32, 38/41,
39/33,
40/38, 40/39,
42/41,
43/41,
44/43,
45/43,
46/45,
47/42, 47/44,
48/44, 48/46,
49/48,
50/47, 50/49,
51/45,
52/51,
53/46, 53/52,
54/49, 54/53,
55/50, 55/60,
56/54, 56/55,
57/52, 57/56,
58/23, 58/20, 58/15,
59/42, 59/40,
60/2, 60/21}
\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 {
1/114.22/188.10/0.4/Blue,
3/8.10/94.29/0.4/Green,
3/94.29/161.35/0.3/Orange,
8/44.21/71.96/0.4/Violet,
5/78.22/141.56/0.4/Teal,
11/321.56/447.12/0.4/Lime,
10/169.55/465.34/0.4/LightBlue,
11/87.12/126.99/0.3/LightCoral,
1/114.22/410.45/0.3/LightCyan,
12/267.12/378.65/0.4/LightGoldenrodYellow,
18/230.45/530.77/0.4/LightGreen}
{
\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 {
1/265,
2/3,
3/310,
4/262,
5/292,
6/52,
7/97,
8/68,
9/123,
10/320,
11/207,
12/147,
13/58,
14/107,
15/79,
16/259,
17/263,
18/23,
19/65,
20/111,
21/231,
22/145,
23/243,
24/190,
25/142,
26/172,
27/292,
28/337,
29/308,
30/3,
31/200,
32/87,
33/27,
34/298,
35/347,
36/319,
37/139,
38/143,
39/305,
40/351,
41/25,
42/123,
43/70,
44/22,
45/52,
46/172,
47/217,
48/188,
49/243,
50/80,
51/327,
52/267,
53/178,
54/227,
55/199,
56/19,
57/185,
58/79,
59/319,
60/199}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
$
Von den 11 einzustellenden Abständen werden nur die ersten 4 (grün) gebraucht, damit der Graph stimmt. Die übrigen 5 braun und 2 Winkel violett kannst du nach belieben verändern (geringfügig, anschließend immer Button "Feinjustierern(11)") damit der Graph in die gewünschte Schachtel passt, oder durch andere ersetzen oder weglassen. Ich habe nur soweit gemacht, dass kein \spy-Fenster mehr nötig ist.
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haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 4639
| Beitrag No.1683, eingetragen 2019-02-03
|
gratulation auch meinerseits zum "90 hölzer 3-reg.girth5"
ich hab mich noch etwas mit dem 1649 beschäftigt und ihn versucht abzuwickeln
https://www.matheplanet.com/matheplanet/nuke/html/uploads/b/35059_dreier-girth5-1649.png
https://www.matheplanet.com/matheplanet/nuke/html/uploads/b/35059_dreier-girth5-1649-abgewickelt.png
gummibandtechnisch-programmatisch-a-la-vogel könnte man also doch wohl damit starten, innen die drei (bzw sechs) vermassten 1-langen gummis spannen und aussen drei 0-lange extra starke gummis obenherum zwischen A-A B-B C-C setzen und dann die innere dunklerblaue fläche nachdem sie sich aneinandergelegt hat miteinander verschmelzen, (ok diese dunkelblaue aussenkannte muss wohl dabei auch elastisch nachgeben?... also wohl auch aus gummielementen bestehen... wie lang die jetzt dann sein sollen ist entweder egal oder auch nicht...)
das ganze hab ich gemacht in der hoffnung dabei strukturen zu erkennen die man weglassen könnte...
https://www.matheplanet.com/matheplanet/nuke/html/uploads/b/35059_dreier-girth5-1649-abgewickelt-modifiziert.png
hier also eine erster modifizierungsversuch... etwas herausschneiden und dann einen 7er (schwarz anstelle eines 5ers einsetzen)
gäb also dann, fals das so klappt, auch einen eingewickeltes 14eck
und ein paar fragen sind offen: bleibt die kante schwarz 7er nach rechts zum alten 7er zwei lang? oder wird sie 1 lang also beides dann 6er flächen? oder geht das so gar nicht, weil linksdavon mit der logic dann ein 4er entsteht?
haribo
p.s. als nächstes muss ich wohl versuchen deinen neuen 90er abzuwickeln
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Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9212
Wohnort: Pferdehof
| Beitrag No.1684, vom Themenstarter, eingetragen 2019-02-03
|
Danke fürs Zurechtziehen, Stefan! Dass das rechte der beiden äußeren H's so stark geknickt werden muss hätte ich nicht gedacht. Und da diesmal wieder jeder seinen Anteil an dem Ding hatte ist es ein echter Team-Graph. So soll es sein. :-)
https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/8038_slash_haribo_Stefan_3reg_girth5_60.png
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haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 4639
| Beitrag No.1685, eingetragen 2019-02-03
|
für mich völlig unerwartet hat dieser graph sowohl innen als auch aussenherum jeweils die gleiche länge, 15
unerwartet ist die gleichheit
und die daraus resultierende fragen:
-könnte er innen auch ne längere kante haben als aussen?
-könnte es einen umstülpbaren graphen geben bei welchem innen und aussen wechseln?
haribo
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Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9212
Wohnort: Pferdehof
| Beitrag No.1686, vom Themenstarter, eingetragen 2019-02-03
|
Es wäre wirklich cool, wenn man den Graphen im Raum von Hand verformen könnte. Vielleicht ein Magnet-Modell aus Stäben und Kugel-Knoten. Es gibt ja so Spielzeug, aber leider sind die Stäbe und Kugeln zu klobig. Ansonsten hätte ich mir das sofort bestellt.
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haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 4639
| Beitrag No.1687, eingetragen 2019-02-03
|
mit magnetstäben/kugeln kannst du auch keine spitzen winkel erstellen max 10° schätze ich
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Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9212
Wohnort: Pferdehof
| Beitrag No.1688, vom Themenstarter, eingetragen 2019-02-04
|
In 13 Tagen haben wir unserer 3-jähriges Thread-Jubiläum. Fangt schon mal an Konfetti zu lochen. 8-)
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Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9212
Wohnort: Pferdehof
| Beitrag No.1689, vom Themenstarter, eingetragen 2019-02-04
|
Doppelpost gelöscht, siehe nächsten Beitrag.
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Slash
Aktiv
Dabei seit: 23.03.2005
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Wohnort: Pferdehof
| Beitrag No.1690, vom Themenstarter, eingetragen 2019-02-04
|
68 Knoten doppelt spiegelsymmetrisch.
68 Knoten, 68×Grad 3, 0 Dreiecke,
102 Kanten, minimal 0.99999999999999855671, maximal 1.00000000000000155431
einzustellende Kanten, Abstände und Winkel:
|P17-P67|=1.00000000000000000000
|P15-P31|=1.00000000000000133227
\geo
ebene(690.65,555)
x(8.9,14.63)
y(8.59,13.19)
form(.)
#//Eingabe war:
#
#3-reg. girth 5 mit 68 Knoten doppelt spiegelsymmetrisch
#
#
#
#
#
#
#
#
#
#
#P[1]=[200.00000000000006,-155.4710137753338];
#P[2]=[200.00000000000003,-34.88601701070155]; D=ab(1,2);
#A(2,1,Bew(1)); M(3,1,2,blauerWinkel); M(4,3,1,gruenerWinkel);
#M(5,3,4,orangerWinkel);
#M(6,5,3,360-36-blauerWinkel-gruenerWinkel-orangerWinkel);N(7,2,4); N(8,4,6);
#M(9,8,4,vierterWinkel); N(10,9,7);
#M(11,5,6,fuenfterWinkel); M(12,11,5,sechsterWinkel); N(13,6,12); N(14,13,9);
#M(15,10,9,siebenterWinkel); N(16,15,14);
#M(17,11,12,achterWinkel); N(18,12,16);
#A(1,2,ab(1,2,[1,18],"gespiegelt"));
#A(17,33,ab(17,33,[1,34],"gespiegelt"));
#N(67,18,51); N(68,66,34);
#RA(17,67); A(33,68);
#RA(15,31); A(49,64);
#
#
#//Ende der Eingabe, weiter mit fedgeo:
p(11.65858112838346372087,8.71069355270793010959,P1)
p(11.65858112838346372087,9.71069355270793010959,P2)
p(10.66586578260321438449,8.59021018351367438015,P3)
p(10.94301274408645419101,9.55103772357516156433,P4)
p(9.77509708941102672952,9.04466715092498496631,P5)
p(10.36288234170350008867,9.85368414529993152939,P6)
p(11.50340061560083526615,8.72280742138887887904,P7)
p(10.21587213452658460255,8.86454917018996191302,P8)
p(10.53245641674336319227,9.81311355506496241219,P9)
p(11.52834221279075244126,9.72249633136518554011,P10)
p(9.23985067375369695242,9.88936311665820610983,P11)
p(9.90988061523016305898,10.63169719072799068726,P12)
p(9.36470247598852978399,9.79337696760735632040,P13)
p(9.93486121217407180950,10.61491151682078104557,P14)
p(11.15858112838346194451,10.65162320131241990850,P15)
p(10.57043315126037974494,9.84286986623056314727,P16)
p(8.89847640206187762146,10.82929056419172653136,P17)
p(10.89761657292450891532,10.78783071652445357813,P18)
p(12.65129647416371305724,8.59021018351367615651,P19)
p(12.37414951268047325073,9.55103772357516156433,P20)
p(13.54206516735590071221,9.04466715092498496631,P21)
p(12.95427991506342557670,9.85368414529993152939,P22)
p(11.81376164116609217558,8.72280742138887887904,P23)
p(13.10129012224034106282,8.86454917018996191302,P24)
p(12.78470584002356247311,9.81311355506496241219,P25)
p(11.78882004397617322411,9.72249633136518554011,P26)
p(14.07731158301322871296,9.88936311665820788619,P27)
p(13.40728164153676260639,10.63169719072799068726,P28)
p(13.95245978077839588138,9.79337696760735632040,P29)
p(13.38230104459285563223,10.61491151682078282192,P30)
p(12.15858112838346372087,10.65162320131241990850,P31)
p(12.74672910550654592043,9.84286986623056314727,P32)
p(14.41868585470504626755,10.82929056419172830772,P33)
p(12.41954568384241852641,10.78783071652445357813,P34)
p(11.65858112838346194451,12.94788757567552650585,P35)
p(11.65858112838346372087,11.94788757567552650585,P36)
p(10.66586578260321260814,13.06837094486978223529,P37)
p(10.94301274408645241465,12.10754340480829505111,P38)
p(9.77509708941102672952,12.61391397745847164913,P39)
p(10.36288234170350008867,11.80489698308352330969,P40)
p(11.50340061560083526615,12.93577370699457773640,P41)
p(10.21587213452658460255,12.79403195819349292606,P42)
p(10.53245641674336141591,11.84546757331849420325,P43)
p(11.52834221279075244126,11.93608479701827107533,P44)
p(9.23985067375369695242,11.76921801172524872925,P45)
p(9.90988061523016305898,11.02688393765546592817,P46)
p(9.36470247598852978399,11.86520416077609851868,P47)
p(9.93486121217407003314,11.04366961156267379351,P48)
p(11.15858112838346194451,11.00695792707103670693,P49)
p(10.57043315126037974494,11.81571126215289169181,P50)
p(10.89761657292450891532,10.87075041185900126095,P51)
p(12.65129647416371305724,13.06837094486978223529,P52)
p(12.37414951268047147437,12.10754340480829505111,P53)
p(13.54206516735589893585,12.61391397745847342549,P54)
p(12.95427991506342557670,11.80489698308352508604,P55)
p(11.81376164116609039922,12.93577370699457773640,P56)
p(13.10129012224033928646,12.79403195819349470241,P57)
p(12.78470584002356247311,11.84546757331849242689,P58)
p(11.78882004397617322411,11.93608479701826929897,P59)
p(14.07731158301322871296,11.76921801172524872925,P60)
p(13.40728164153676260639,11.02688393765546592817,P61)
p(13.95245978077839588138,11.86520416077610029504,P62)
p(13.38230104459285563223,11.04366961156267379351,P63)
p(12.15858112838346372087,11.00695792707103670693,P64)
p(12.74672910550654592043,11.81571126215289346817,P65)
p(12.41954568384241852641,10.87075041185900126095,P66)
p(9.89847640206187762146,10.82929056419172830772,P67)
p(13.41868585470504804391,10.82929056419173363679,P68)
nolabel()
s(P1,P2)
s(P1,P3)
s(P3,P4)
s(P3,P5)
s(P5,P6)
s(P2,P7) s(P4,P7)
s(P4,P8) s(P6,P8)
s(P8,P9)
s(P9,P10) s(P7,P10)
s(P5,P11)
s(P11,P12)
s(P6,P13) s(P12,P13)
s(P13,P14) s(P9,P14)
s(P10,P15) s(P31,P15)
s(P15,P16) s(P14,P16)
s(P11,P17) s(P45,P17) s(P67,P17)
s(P12,P18) s(P16,P18)
s(P1,P19)
s(P19,P20)
s(P19,P21)
s(P21,P22)
s(P2,P23) s(P20,P23)
s(P20,P24) s(P22,P24)
s(P24,P25)
s(P23,P26) s(P25,P26)
s(P21,P27)
s(P27,P28)
s(P22,P29) s(P28,P29)
s(P25,P30) s(P29,P30)
s(P26,P31)
s(P30,P32) s(P31,P32)
s(P27,P33) s(P60,P33) s(P68,P33)
s(P28,P34) s(P32,P34)
s(P35,P36)
s(P35,P37)
s(P37,P38)
s(P37,P39)
s(P39,P40)
s(P36,P41) s(P38,P41)
s(P38,P42) s(P40,P42)
s(P42,P43)
s(P41,P44) s(P43,P44)
s(P39,P45)
s(P45,P46)
s(P40,P47) s(P46,P47)
s(P43,P48) s(P47,P48)
s(P44,P49) s(P64,P49)
s(P48,P50) s(P49,P50)
s(P46,P51) s(P50,P51)
s(P35,P52)
s(P52,P53)
s(P52,P54)
s(P54,P55)
s(P36,P56) s(P53,P56)
s(P53,P57) s(P55,P57)
s(P57,P58)
s(P56,P59) s(P58,P59)
s(P54,P60)
s(P60,P61)
s(P55,P62) s(P61,P62)
s(P58,P63) s(P62,P63)
s(P59,P64)
s(P63,P65) s(P64,P65)
s(P61,P66) s(P65,P66)
s(P18,P67) s(P51,P67)
s(P66,P68) s(P34,P68)
pen(2)
color(#0000FF) m(P2,P1,MA10) m(P1,P3,MB10) b(P1,MA10,MB10)
color(#008000) m(P1,P3,MA11) m(P3,P4,MB11) b(P3,MA11,MB11)
color(#FFA500) m(P4,P3,MA12) m(P3,P5,MB12) b(P3,MA12,MB12)
color(#EE82EE) m(P4,P8,MA13) m(P8,P9,MB13) f(P8,MA13,MB13)
color(#00FFFF) m(P6,P5,MA14) m(P5,P11,MB14) b(P5,MA14,MB14)
color(#32CD32) m(P5,P11,MA15) m(P11,P12,MB15) b(P11,MA15,MB15)
color(#ADD8E6) m(P9,P10,MA16) m(P10,P15,MB16) b(P10,MA16,MB16)
color(#F08080) m(P12,P11,MA17) m(P11,P17,MB17) b(P11,MA17,MB17)
pen(2)
color(green) s(P17,P67)
color(green) s(P15,P31)
color(blue)
color(orange)
color(red)
\geooff
\geoprint()
|
Profil
|
Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9212
Wohnort: Pferdehof
| Beitrag No.1691, vom Themenstarter, eingetragen 2019-02-04
|
Hier noch ein punktsymmetrischer mit 66 Knoten. Einen Schönheitspreis gewinnt er natürlich nicht.
66 Knoten, 66×Grad 3, 0 Dreiecke,
99 Kanten, minimal 0.99999999999999800160, maximal 1.00000000000000532907
einzustellende Kanten, Abstände und Winkel:
|P32-P66|=0.99999999999999900080
|P33-P64|=1.00000000000000532907
\geo
ebene(569.43,555)
x(9.35,14.47)
y(8.47,13.46)
form(.)
#//Eingabe war:
#
#3-reg. girth 5 mit 66 Knoten punktsymmetrisch
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#P[1]=[186.1624120200521,-169.9999843749734];
#P[2]=[192.61120880856384,-58.83275167558662]; D=ab(1,2);
#A(2,1,Bew(1)); M(3,1,2,blauerWinkel); M(4,3,1,gruenerWinkel);
#M(5,3,4,orangerWinkel);
#M(6,5,3,360-36-blauerWinkel-gruenerWinkel-orangerWinkel);N(7,2,4); N(8,4,6);
#M(9,8,4,vierterWinkel); N(10,9,7);
#M(11,5,6,fuenfterWinkel); M(12,11,5,sechsterWinkel); N(13,6,12); N(14,13,9);
#M(15,10,9,siebenterWinkel); N(16,15,14);
#M(17,11,12,achterWinkel); N(18,12,16); N(19,17,18);
#M(20,1,2,neunterWinkel); M(21,20,1,zehnterWinkel); N(22,21,2); N(23,15,22);
#M(24,20,21,elfterWinkel); M(25,24,20,zwölfterWinkel); N(26,25,21); N(27,23,26);
#M(28,24,25,dreizehnterWinkel); M(29,28,24,vierzehnterWinkel); N(30,25,29);
#M(31,28,29,fuenfzehnterWinkel); M(32,27,23,sechzehnterWinkel); N(33,32,30);
#A(17,31,ab(31,17,[1,33]));
#N(65,29,51); N(66,61,19);
#RA(32,66); A(63,65);
#RA(33,64);
#
#
#//Ende der Eingabe, weiter mit fedgeo:
p(11.67180529807183830826,8.47333910499828846241,P1)
p(11.72971780855253243203,9.47166076715424054555,P2)
p(10.67180529807183830826,8.47333910499828846241,P3)
p(11.13988935140525882161,9.35702305246760523971,P4)
p(9.79591936103727611851,8.95585731740595214490,P5)
p(10.42957031626245267830,9.72947638835897699039,P6)
p(11.61677739157345534693,8.47805900477023932638,P7)
p(10.35932583228182757296,8.73194658305474646909,P8)
p(10.71906426119206834358,9.66499977701808710151,P9)
p(11.70075664367864476390,9.47452650811184504676,P10)
p(9.35148232562010051083,9.85166740975231114419,P11)
p(10.11800530468702064013,10.49388429100223163459,P12)
p(9.43030825744337342087,9.76788651468857871407,P13)
p(10.13540451749717163921,10.47699811666540803401,P14)
p(11.56297335263901970848,10.46498890755479749259,P15)
p(10.84329764031173581884,9.77067855253607930877,P16)
p(9.55140904677058699690,10.83147826199370911127,P17)
p(11.08711898466905765304,10.74049871732736249896,P18)
p(10.35705420943704524461,11.42387666836575377260,P19)
p(12.66689547654301506441,8.57231150877935377252,P20)
p(12.31374718585816729899,9.50787886861314390785,P21)
p(12.08091938168620060878,8.53536089263302955032,P22)
p(11.86585536657119810400,9.51196084624894666604,P23)
p(13.52692590884887913205,9.08255425052859877155,P24)
p(12.93801162906163959576,9.89074975352442642418,P25)
p(13.11238782083662890443,8.90607064653471702798,P26)
p(12.80428749103125163344,9.85742451696034116537,P27)
p(13.99624336105891231341,9.96558376818420121879,P28)
p(13.00367595432204304018,10.08727987775080947586,P29)
p(12.02748820801168605499,10.30420724797759390867,P30)
p(14.04073456574720069057,10.96459354426518828518,P31)
p(11.85046509483862742229,10.15779568155734402524,P32)
p(11.30586057166991764689,10.99648866074828923445,P33)
p(11.92033831444594937921,13.32273270126060893404,P34)
p(11.86242580396525525543,12.32441103910465685090,P35)
p(12.92033831444594937921,13.32273270126060715768,P36)
p(12.45225426111252886585,12.43904875379129215673,P37)
p(13.79622425148051334531,12.84021448885294702791,P38)
p(13.16257329625533500916,12.06659541789992040606,P39)
p(11.97536622094433056418,13.31801280148865807007,P40)
p(13.23281778023596011451,13.06412522320415092736,P41)
p(12.87307935132571934389,12.13107202924081029494,P42)
p(11.89138696883914292357,12.32154529814705234969,P43)
p(14.24066128689768717663,11.94440439650658625226,P44)
p(13.47413830783076704734,11.30218751525666576185,P45)
p(14.16183535507441426660,12.02818529157031868237,P46)
p(13.45673909502061604826,11.31907368959348936244,P47)
p(12.02917025987876797899,11.33108289870409990385,P48)
p(12.74884597220605186862,12.02539325372281808768,P49)
p(12.50502462784873003443,11.05557308893153667384,P50)
p(13.23508940308074244285,10.37219513789314362384,P51)
p(10.92524813597477439941,13.22376029747954362392,P52)
p(11.27839642665962038848,12.28819293764575348860,P53)
p(11.51122423083158707868,13.26071091362586784612,P54)
p(11.72628824594658958347,12.28411096000995073041,P55)
p(10.06521770366890855541,12.71351755573029684854,P56)
p(10.65413198345614809170,11.90532205273447097227,P57)
p(10.47975579168115878304,12.89000115972418036847,P58)
p(10.78785612148653605402,11.93864728929855623107,P59)
p(9.59590025145887537406,11.83048803807469795402,P60)
p(10.58846765819574464729,11.70879192850808792059,P61)
p(11.56465540450609985612,11.49186455828130526413,P62)
p(11.74167851767916026517,11.63827612470155337121,P63)
p(12.28628304084787004058,10.79958314551060816200,P64)
p(12.35634614872124004137,10.84948990312493677379,P65)
p(11.23579746379654764610,10.94658190313396062265,P66)
nolabel()
s(P1,P2)
s(P1,P3)
s(P3,P4)
s(P3,P5)
s(P5,P6)
s(P2,P7) s(P4,P7)
s(P4,P8) s(P6,P8)
s(P8,P9)
s(P9,P10) s(P7,P10)
s(P5,P11)
s(P11,P12)
s(P6,P13) s(P12,P13)
s(P13,P14) s(P9,P14)
s(P10,P15)
s(P15,P16) s(P14,P16)
s(P11,P17) s(P60,P17)
s(P12,P18) s(P16,P18)
s(P17,P19) s(P18,P19)
s(P1,P20)
s(P20,P21)
s(P21,P22) s(P2,P22)
s(P15,P23) s(P22,P23)
s(P20,P24)
s(P24,P25)
s(P25,P26) s(P21,P26)
s(P23,P27) s(P26,P27)
s(P24,P28)
s(P28,P29)
s(P25,P30) s(P29,P30)
s(P28,P31) s(P44,P31)
s(P27,P32) s(P66,P32)
s(P32,P33) s(P30,P33) s(P64,P33)
s(P34,P35)
s(P34,P36)
s(P36,P37)
s(P36,P38)
s(P38,P39)
s(P35,P40) s(P37,P40)
s(P37,P41) s(P39,P41)
s(P41,P42)
s(P40,P43) s(P42,P43)
s(P38,P44)
s(P44,P45)
s(P39,P46) s(P45,P46)
s(P42,P47) s(P46,P47)
s(P43,P48)
s(P47,P49) s(P48,P49)
s(P45,P50) s(P49,P50)
s(P31,P51) s(P50,P51)
s(P34,P52)
s(P52,P53)
s(P35,P54) s(P53,P54)
s(P48,P55) s(P54,P55)
s(P52,P56)
s(P56,P57)
s(P53,P58) s(P57,P58)
s(P55,P59) s(P58,P59)
s(P56,P60)
s(P60,P61)
s(P57,P62) s(P61,P62)
s(P59,P63) s(P65,P63)
s(P62,P64) s(P63,P64)
s(P29,P65) s(P51,P65)
s(P61,P66) s(P19,P66)
pen(2)
color(#0000FF) m(P2,P1,MA10) m(P1,P3,MB10) b(P1,MA10,MB10)
color(#008000) m(P1,P3,MA11) m(P3,P4,MB11) b(P3,MA11,MB11)
color(#FFA500) m(P4,P3,MA12) m(P3,P5,MB12) b(P3,MA12,MB12)
color(#EE82EE) m(P4,P8,MA13) m(P8,P9,MB13) f(P8,MA13,MB13)
color(#00FFFF) m(P6,P5,MA14) m(P5,P11,MB14) b(P5,MA14,MB14)
color(#32CD32) m(P5,P11,MA15) m(P11,P12,MB15) b(P11,MA15,MB15)
color(#ADD8E6) m(P9,P10,MA16) m(P10,P15,MB16) b(P10,MA16,MB16)
color(#F08080) m(P12,P11,MA17) m(P11,P17,MB17) b(P11,MA17,MB17)
color(#E0FFFF) m(P2,P1,MA18) m(P1,P20,MB18) b(P1,MA18,MB18)
color(#FAFAD2) m(P1,P20,MA19) m(P20,P21,MB19) b(P20,MA19,MB19)
color(#90EE90) m(P21,P20,MA110) m(P20,P24,MB110) b(P20,MA110,MB110)
color(#D3D3D3) m(P20,P24,MA111) m(P24,P25,MB111) b(P24,MA111,MB111)
color(#FFB6C1) m(P25,P24,MA112) m(P24,P28,MB112) b(P24,MA112,MB112)
color(#FFA07A) m(P24,P28,MA113) m(P28,P29,MB113) b(P28,MA113,MB113)
color(#20B2AA) m(P29,P28,MA114) m(P28,P31,MB114) b(P28,MA114,MB114)
color(#87CEFA) m(P23,P27,MA115) m(P27,P32,MB115) b(P27,MA115,MB115)
pen(2)
color(green) s(P32,P66)
color(green) s(P33,P64)
color(blue)
color(orange)
color(red)
\geooff
\geoprint()
Und etwas anders.
66 Knoten, 66×Grad 3, 0 Dreiecke,
99 Kanten, minimal 0.99999999999998456790, maximal 1.00000000000000222045
einzustellende Kanten, Abstände und Winkel:
|P32-P66|=0.99999999999998456790
|P33-P64|=0.99999999999999023004
\geo
ebene(631.65,555)
x(9.09,14.67)
y(8.5,13.4)
form(.)
#//Eingabe war:
#
#3-reg. girth 5 mit 66 Knoten punktsymmetrisch
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#P[1]=[190.96569555183112,-169.99950000000024];
#P[2]=[196.92978464788712,-56.952937535673186]; D=ab(1,2);
#A(2,1,Bew(1)); M(3,1,2,blauerWinkel); M(4,3,1,gruenerWinkel);
#M(5,3,4,orangerWinkel);
#M(6,5,3,360-36-blauerWinkel-gruenerWinkel-orangerWinkel);N(7,2,4); N(8,4,6);
#M(9,8,4,vierterWinkel); N(10,9,7);
#M(11,5,6,fuenfterWinkel); M(12,11,5,sechsterWinkel); N(13,6,12); N(14,13,9);
#M(15,10,9,siebenterWinkel); N(16,15,14);
#M(17,11,12,achterWinkel); N(18,12,16); N(19,18,17);
#M(20,1,2,neunterWinkel); M(21,20,1,zehnterWinkel); N(22,21,2); N(23,15,22);
#M(24,20,21,elfterWinkel); M(25,24,20,zwölfterWinkel); N(26,25,21); N(27,23,26);
#M(28,24,25,dreizehnterWinkel); M(29,28,24,vierzehnterWinkel); N(30,25,29);
#M(31,28,29,fuenfzehnterWinkel); M(32,27,23,sechzehnterWinkel); N(33,32,30);
#A(17,31,ab(31,17,[1,33]));
#N(65,29,51); N(66,61,19);
#RA(32,66); A(63,65);
#RA(33,64);
#
#
#//Ende der Eingabe, weiter mit fedgeo:
p(11.68691978980647583342,8.49828776849938982707,P1)
p(11.73960433032163486189,9.49689897371927216341,P2)
p(10.68691978980647583342,8.49828776849938982707,P3)
p(11.15346081154728885565,9.38278733041733659093,P4)
p(9.81019303409896892276,8.97927653741877662696,P5)
p(10.43978466191882681358,9.75620277727629492404,P6)
p(11.62891050311092833169,8.50304441865729287997,P7)
p(10.37227887357112443567,8.75848389475499367052,P8)
p(10.70391178787220454183,9.70189240126326701841,P9)
p(11.68363687306206522010,9.50154580795626202416,P10)
p(9.32862928467481467010,9.85568760263906007424,P11)
p(10.06758362174963927771,10.52944311298261759191,P12)
p(9.43979790201156632179,9.75105690415505144131,P13)
p(10.10195554326168476678,10.50042147372988665666,P14)
p(11.56449166985268028895,10.49442264853226980392,P15)
p(10.83042595545557418291,9.81534420906694116127,P16)
p(9.08725640756120611741,10.82612004964085805625,P17)
p(11.03171281008957826941,10.79487654755891057334,P18)
p(10.05573301023894394746,10.57701551321932598171,P19)
p(12.67624305509510662660,8.64402546698074658593,P20)
p(12.28583326721347468435,9.56466665524369652474,P21)
p(12.13108513797587129091,8.57671270059932133734,P22)
p(11.86547440727639113334,9.54079306018418904500,P23)
p(13.51510368682985507860,9.18837171756540627143,P24)
p(12.85536429972682803680,9.93986618933810284204,P25)
p(13.08776054693019830211,8.96724499674265551619,P26)
p(12.79001002226202743373,9.92188871303676478419,P27)
p(13.87004748597037817603,10.12325935757980488461,P28)
p(12.87949010588098630592,9.98616057293735082112,P29)
p(11.98092632207428209767,10.42500351344224185368,P30)
p(14.44619452964886185953,10.94060541896417682040,P31)
p(11.90210175356079069786,10.38190926298206129275,P32)
p(11.46229670937816713661,11.28000253381283712883,P33)
p(11.84653114740359036716,13.26843770010564682593,P34)
p(11.79384660688843311505,12.26982649488576271324,P35)
p(12.84653114740359214352,13.26843770010564682593,P36)
p(12.37999012566277912128,12.38393813818770006208,P37)
p(13.72325790311109727782,12.78744893118625824968,P38)
p(13.09366627529124116336,12.01052269132873995261,P39)
p(11.90454043409913964524,13.26368104994774199668,P40)
p(13.16117206363894176491,13.00824157385004298249,P41)
p(12.82953914933786165875,12.06483306734176785824,P42)
p(11.84981406414800275684,12.26517966064877285248,P43)
p(14.20482165253525330684,11.91103786596597657876,P44)
p(13.46586731546042869923,11.23728235562241906109,P45)
p(14.09365303519850165515,12.01566856444998521170,P46)
p(13.43149539394838143380,11.26630399487514821999,P47)
p(11.96895926735738591162,11.27230282007276684908,P48)
p(12.70302498175449201767,11.95138125953809549173,P49)
p(12.50173812712048970752,10.97184892104612430330,P50)
p(13.47771792697112402948,11.18970995538571067129,P51)
p(10.85720788211496135034,13.12270000162428829071,P52)
p(11.24761766999659329258,12.20205881336133835191,P53)
p(11.40236579923419668603,13.19001276800571531567,P54)
p(11.66797652993367684360,12.22593240842084583164,P55)
p(10.01834725038021289834,12.57835375103962860521,P56)
p(10.67808663748323994014,11.82685927926693203460,P57)
p(10.44569039027986789847,12.79948047186237936046,P58)
p(10.74344091494804054321,11.84483675556827009245,P59)
p(9.66340345123968980090,11.64346611102522999204,P60)
p(10.65396083132908167102,11.78056489566768405552,P61)
p(11.55252461513578587926,11.34172195516279302296,P62)
p(11.63134918364927727907,11.38481620562297358390,P63)
p(12.07115422783190084033,10.48672293479219952417,P64)
p(12.51546588680405136529,10.91755005533739897317,P65)
p(11.01798505040601661165,10.84917541326763767984,P66)
nolabel()
s(P1,P2)
s(P1,P3)
s(P3,P4)
s(P3,P5)
s(P5,P6)
s(P2,P7) s(P4,P7)
s(P4,P8) s(P6,P8)
s(P8,P9)
s(P9,P10) s(P7,P10)
s(P5,P11)
s(P11,P12)
s(P6,P13) s(P12,P13)
s(P13,P14) s(P9,P14)
s(P10,P15)
s(P15,P16) s(P14,P16)
s(P11,P17) s(P60,P17)
s(P12,P18) s(P16,P18)
s(P18,P19) s(P17,P19)
s(P1,P20)
s(P20,P21)
s(P21,P22) s(P2,P22)
s(P15,P23) s(P22,P23)
s(P20,P24)
s(P24,P25)
s(P25,P26) s(P21,P26)
s(P23,P27) s(P26,P27)
s(P24,P28)
s(P28,P29)
s(P25,P30) s(P29,P30)
s(P28,P31) s(P44,P31)
s(P27,P32) s(P66,P32)
s(P32,P33) s(P30,P33) s(P64,P33)
s(P34,P35)
s(P34,P36)
s(P36,P37)
s(P36,P38)
s(P38,P39)
s(P35,P40) s(P37,P40)
s(P37,P41) s(P39,P41)
s(P41,P42)
s(P40,P43) s(P42,P43)
s(P38,P44)
s(P44,P45)
s(P39,P46) s(P45,P46)
s(P42,P47) s(P46,P47)
s(P43,P48)
s(P47,P49) s(P48,P49)
s(P45,P50) s(P49,P50)
s(P31,P51) s(P50,P51)
s(P34,P52)
s(P52,P53)
s(P35,P54) s(P53,P54)
s(P48,P55) s(P54,P55)
s(P52,P56)
s(P56,P57)
s(P53,P58) s(P57,P58)
s(P55,P59) s(P58,P59)
s(P56,P60)
s(P60,P61)
s(P57,P62) s(P61,P62)
s(P59,P63) s(P65,P63)
s(P62,P64) s(P63,P64)
s(P29,P65) s(P51,P65)
s(P61,P66) s(P19,P66)
pen(2)
color(#0000FF) m(P2,P1,MA10) m(P1,P3,MB10) b(P1,MA10,MB10)
color(#008000) m(P1,P3,MA11) m(P3,P4,MB11) b(P3,MA11,MB11)
color(#FFA500) m(P4,P3,MA12) m(P3,P5,MB12) b(P3,MA12,MB12)
color(#EE82EE) m(P4,P8,MA13) m(P8,P9,MB13) b(P8,MA13,MB13)
color(#00FFFF) m(P6,P5,MA14) m(P5,P11,MB14) b(P5,MA14,MB14)
color(#32CD32) m(P5,P11,MA15) m(P11,P12,MB15) b(P11,MA15,MB15)
color(#ADD8E6) m(P9,P10,MA16) m(P10,P15,MB16) b(P10,MA16,MB16)
color(#F08080) m(P12,P11,MA17) m(P11,P17,MB17) b(P11,MA17,MB17)
color(#E0FFFF) m(P2,P1,MA18) m(P1,P20,MB18) b(P1,MA18,MB18)
color(#FAFAD2) m(P1,P20,MA19) m(P20,P21,MB19) b(P20,MA19,MB19)
color(#90EE90) m(P21,P20,MA110) m(P20,P24,MB110) b(P20,MA110,MB110)
color(#D3D3D3) m(P20,P24,MA111) m(P24,P25,MB111) b(P24,MA111,MB111)
color(#FFB6C1) m(P25,P24,MA112) m(P24,P28,MB112) b(P24,MA112,MB112)
color(#FFA07A) m(P24,P28,MA113) m(P28,P29,MB113) b(P28,MA113,MB113)
color(#20B2AA) m(P29,P28,MA114) m(P28,P31,MB114) b(P28,MA114,MB114)
color(#87CEFA) m(P23,P27,MA115) m(P27,P32,MB115) b(P27,MA115,MB115)
pen(2)
color(green) s(P32,P66)
color(green) s(P33,P64)
color(blue)
color(orange)
color(red)
\geooff
\geoprint()
|
Profil
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Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9212
Wohnort: Pferdehof
| Beitrag No.1692, vom Themenstarter, eingetragen 2019-02-04
|
\quoteon(2019-02-03 19:38 - haribo in Beitrag No. 1685)
für mich völlig unerwartet hat dieser graph sowohl innen als auch aussenherum jeweils die gleiche länge, 15
unerwartet ist die gleichheit
\quoteoff
Gut beobachtet. Ist mir zunächst gar nicht aufgefallen.
\quoteon(2019-02-03 19:38 - haribo in Beitrag No. 1685)
und die daraus resultierende fragen:
-könnte er innen auch ne längere kante haben als aussen?
\quoteoff
Wenn man keinen Wert auf Minimalität legt, ist es möglich einen 3-reg girth 5 zu konstruieren, dessen innerer Kreis größer ist als sein äußerer Kreis.
https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/8038_3reg_girth5_inkreis.png
Zunächst einen kleinen Graph mit zwei äußeren 2er Knoten konstruiert (Mitte). Dann zwei davon zu einer "Erdnuss" verbunden, so dass zwischen den 2er Knoten eine Seite 13 und die andere Seite 11 Kanten besitzt. Dann 2 dieser Erdnüsse mit 4 der kleinen Graphen so zu einem 3-reg girth 5 verbunden, dass die 13er Seiten innen liegen. Der innere Kreis besitzt hier 4 Kanten mehr als der äußere.
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haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 4639
| Beitrag No.1693, eingetragen 2019-02-04
|
ok, und den kann man auch von innen nach aussen stülpen, wie ein armband, da man die doppel nuss ja um ihre zwei haltepunkte innen-aussen spiegeln kann
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| Beitrag No.1694, vom Themenstarter, eingetragen 2019-02-05
|
Und jetzt auch einen 64er mit Punksymmetrie und nur einer Einstellkante.
64 Knoten, 64×Grad 3, 0 Dreiecke,
96 Kanten, minimal 0.99999999999999478195, maximal 1.00000000000000643929
einzustellende Kanten, Abstände und Winkel:
|P32-P64|=1.00000000000000643929
\geo
ebene(619.29,555)
x(9.13,14.68)
y(8.47,13.45)
form(.)
#//Eingabe war:
#
#3-reg. girth 5 mit 64 Knoten punktsymmetrisch
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#P[1]=[179.45810194107628,-169.9995000009115];
#P[2]=[187.27182905401378,-58.81573921577825]; D=ab(1,2);
#A(2,1,Bew(1)); M(3,1,2,blauerWinkel); M(4,3,1,gruenerWinkel);
#M(5,3,4,orangerWinkel);
#M(6,5,3,360-36-blauerWinkel-gruenerWinkel-orangerWinkel);N(7,2,4); N(8,4,6);
#M(9,8,4,vierterWinkel); N(10,9,7);
#M(11,5,6,fuenfterWinkel); M(12,11,5,sechsterWinkel); N(13,6,12); N(14,13,9);
#M(15,10,9,siebenterWinkel); N(16,15,14);
#M(17,11,12,achterWinkel); N(18,12,16); N(19,18,17);
#M(20,1,2,neunterWinkel); M(21,20,1,zehnterWinkel); N(22,21,2); N(23,15,22);
#M(24,20,21,elfterWinkel); M(25,24,20,zwölfterWinkel); N(26,25,21); N(27,23,26);
#M(28,24,25,dreizehnterWinkel); M(29,28,24,vierzehnterWinkel); N(30,25,29);
#M(31,28,29,fuenfzehnterWinkel); N(32,27,30);
#A(17,31,ab(31,17,[1,32]));
#N(63,29,50); N(64,60,19);
#RA(32,64); A(62,63);
#
#
#//Ende der Eingabe, weiter mit fedgeo:
p(11.61009637666636251652,8.47476610960460519095,P1)
p(11.68020106169714011912,9.47230574948702042093,P2)
p(10.61009637666636251652,8.47476610960460519095,P3)
p(11.07663739840717553875,9.35926567152255195481,P4)
p(9.81940680292252032757,9.08698338963905527521,P5)
p(10.46246177339774874326,9.85280341088889244361,P6)
p(11.55361484939233918112,8.48035014017059296521,P7)
p(10.19381130037950100586,8.88956568148505077431,P8)
p(10.69357204821660545235,9.75572917351256307938,P9)
p(11.65346222320219737867,9.47535290496236726199,P10)
p(9.35302566866257478750,9.97156726785886959874,P11)
p(10.10348701140995331116,10.63248161408067993250,P12)
p(9.46253494833074704218,9.86490070444671296457,P13)
p(10.14750580396224677315,10.59347117251102510238,P14)
p(11.49500538160509499619,10.46271880945323573542,P15)
p(10.75016693860030514429,9.79547395647780660966,P16)
p(9.12842081278737715877,10.94601719408252193944,P17)
p(11.09843546183374307645,10.73286876963008928954,P18)
p(10.09883583166180187618,10.70457425849949295582,P19)
p(12.60181243677692641825,8.60321553980490882907,P20)
p(12.22752951439744961704,9.53053010025086599910,P21)
p(12.05556278009169446364,8.54542734302590822892,P22)
p(11.82271707279963024462,9.51794103269596192263,P23)
p(13.45004545798216355479,9.13283874712973364751,P24)
p(12.84433476725680201014,9.92852370937358941205,P25)
p(13.04027220821488342040,8.94790731177930176443,P26)
p(12.74542096219093423315,9.90345047810833989388,P27)
p(14.03712448603940288194,9.94236837278611851332,P28)
p(13.49953051128046865870,10.78557221427576173767,P29)
p(12.50297121265609767704,10.86845504920133009819,P30)
p(14.46037536693601310844,10.84838089577917585871,P31)
p(11.78287756937337604768,10.17457815456956815581,P32)
p(11.97869980305702952705,13.31963198025708905448,P33)
p(11.90859511802624837173,12.32209234037467915357,P34)
p(12.97869980305702952705,13.31963198025708905448,P35)
p(12.51215878131621472846,12.43513241833914406698,P36)
p(13.76938937680086993964,12.70741470022264429929,P37)
p(13.12633440632563974759,11.94159467897280357818,P38)
p(12.03518133033104930973,13.31404794969110838565,P39)
p(13.39498487934389103771,12.90483240837664524747,P40)
p(12.89522413150678481486,12.03866891634913471876,P41)
p(11.93533395652119466490,12.31904518489932875980,P42)
p(14.23577051106081370335,11.82283082200283175212,P43)
p(13.48530916831343695605,11.16191647578101431293,P44)
p(14.12626123139264322504,11.92949738541498483357,P45)
p(13.44129037576114349406,11.20092691735067091940,P46)
p(12.09379079811829527102,11.33167928040846206272,P47)
p(12.83862924112308512292,11.99892413338388941213,P48)
p(12.49036071788964719076,11.06152932023161028496,P49)
p(13.48996034806158839103,11.08982383136220484232,P50)
p(10.98698374294646562532,13.19118255005678719272,P51)
p(11.36126666532593887382,12.26386798961083357540,P52)
p(11.53323339963169757993,13.24897074683578956922,P53)
p(11.76607910692376002260,12.27645705716573587551,P54)
p(10.13875072174122848878,12.66155934273196415063,P55)
p(10.74446141246658825708,11.86587438048811016245,P56)
p(10.54852397150850507046,12.84649077808239781007,P57)
p(10.84337521753245425771,11.89094761175335790426,P58)
p(9.55167169368398560891,11.85202971707557928482,P59)
p(10.08926566844291983216,11.00882587558593606047,P60)
p(11.08582496706729259017,10.92594304066036947631,P61)
p(11.80591861035001244318,11.61981993529213141869,P62)
p(12.50688445055407171935,10.90662508753520221205,P63)
p(11.08191172916931677150,10.88777300232649736245,P64)
nolabel()
s(P1,P2)
s(P1,P3)
s(P3,P4)
s(P3,P5)
s(P5,P6)
s(P2,P7) s(P4,P7)
s(P4,P8) s(P6,P8)
s(P8,P9)
s(P9,P10) s(P7,P10)
s(P5,P11)
s(P11,P12)
s(P6,P13) s(P12,P13)
s(P13,P14) s(P9,P14)
s(P10,P15)
s(P15,P16) s(P14,P16)
s(P11,P17) s(P59,P17)
s(P12,P18) s(P16,P18)
s(P18,P19) s(P17,P19)
s(P1,P20)
s(P20,P21)
s(P21,P22) s(P2,P22)
s(P15,P23) s(P22,P23)
s(P20,P24)
s(P24,P25)
s(P25,P26) s(P21,P26)
s(P23,P27) s(P26,P27)
s(P24,P28)
s(P28,P29)
s(P25,P30) s(P29,P30)
s(P28,P31) s(P43,P31)
s(P27,P32) s(P30,P32) s(P64,P32)
s(P33,P34)
s(P33,P35)
s(P35,P36)
s(P35,P37)
s(P37,P38)
s(P34,P39) s(P36,P39)
s(P36,P40) s(P38,P40)
s(P40,P41)
s(P39,P42) s(P41,P42)
s(P37,P43)
s(P43,P44)
s(P38,P45) s(P44,P45)
s(P41,P46) s(P45,P46)
s(P42,P47)
s(P46,P48) s(P47,P48)
s(P44,P49) s(P48,P49)
s(P31,P50) s(P49,P50)
s(P33,P51)
s(P51,P52)
s(P34,P53) s(P52,P53)
s(P47,P54) s(P53,P54)
s(P51,P55)
s(P55,P56)
s(P52,P57) s(P56,P57)
s(P54,P58) s(P57,P58)
s(P55,P59)
s(P59,P60)
s(P56,P61) s(P60,P61)
s(P58,P62) s(P61,P62) s(P63,P62)
s(P29,P63) s(P50,P63)
s(P60,P64) s(P19,P64)
pen(2)
color(#0000FF) m(P2,P1,MA10) m(P1,P3,MB10) b(P1,MA10,MB10)
color(#008000) m(P1,P3,MA11) m(P3,P4,MB11) b(P3,MA11,MB11)
color(#FFA500) m(P4,P3,MA12) m(P3,P5,MB12) b(P3,MA12,MB12)
color(#EE82EE) m(P4,P8,MA13) m(P8,P9,MB13) b(P8,MA13,MB13)
color(#00FFFF) m(P6,P5,MA14) m(P5,P11,MB14) b(P5,MA14,MB14)
color(#32CD32) m(P5,P11,MA15) m(P11,P12,MB15) b(P11,MA15,MB15)
color(#ADD8E6) m(P9,P10,MA16) m(P10,P15,MB16) b(P10,MA16,MB16)
color(#F08080) m(P12,P11,MA17) m(P11,P17,MB17) b(P11,MA17,MB17)
color(#E0FFFF) m(P2,P1,MA18) m(P1,P20,MB18) b(P1,MA18,MB18)
color(#FAFAD2) m(P1,P20,MA19) m(P20,P21,MB19) b(P20,MA19,MB19)
color(#90EE90) m(P21,P20,MA110) m(P20,P24,MB110) b(P20,MA110,MB110)
color(#D3D3D3) m(P20,P24,MA111) m(P24,P25,MB111) b(P24,MA111,MB111)
color(#FFB6C1) m(P25,P24,MA112) m(P24,P28,MB112) b(P24,MA112,MB112)
color(#FFA07A) m(P24,P28,MA113) m(P28,P29,MB113) b(P28,MA113,MB113)
color(#20B2AA) m(P29,P28,MA114) m(P28,P31,MB114) b(P28,MA114,MB114)
pen(2)
color(green) s(P32,P64)
color(blue)
color(orange)
color(red)
\geooff
\geoprint()
Wenn Stefan Zeit und Lust hat, kann er die letzten unschönen Graphen noch zurechtziehen. Da geht bestimmt noch was.
|
Profil
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Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9212
Wohnort: Pferdehof
| Beitrag No.1695, vom Themenstarter, eingetragen 2019-02-05
|
Rekord! :-) 58 Knoten punktsymmetrisch, eine Einstellkante. Der erste im Vierzehneck. Geht vielleicht sogar regelmäßig außen.
58 Knoten, 58×Grad 3, 0 Dreiecke,
87 Kanten, minimal 0.99999999999999822364, maximal 1.00000000000000155431
einzustellende Kanten, Abstände und Winkel:
|P57-P58|=1.00000000000000155431
\geo
ebene(613.93,555)
x(9.25,14.12)
y(8.65,13.06)
form(.)
#//Eingabe war:
#
#3-reg. girth 5 mit 58 Knoten punktsymmetrisch
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#P[1]=[373.7187162730806,-107.49366233473879];
#P[2]=[308.03352894745615,-0.010641771958560753]; D=ab(1,2);
#A(2,1,Bew(1)); M(3,1,2,blauerWinkel); M(4,3,1,gruenerWinkel);
#M(5,3,4,orangerWinkel);
#M(6,5,3,360-36-blauerWinkel-gruenerWinkel-orangerWinkel);N(7,2,4); N(8,4,6);
#M(9,8,4,vierterWinkel); N(10,9,7);
#M(11,5,6,fuenfterWinkel); M(12,11,5,sechsterWinkel); N(13,6,12); N(14,13,9);
#M(15,10,9,siebenterWinkel); N(16,15,14);
#M(17,11,12,achterWinkel); N(18,12,16); N(19,18,17);
#M(20,1,2,neunterWinkel); M(21,20,1,zehnterWinkel); N(22,21,2); N(23,15,22);
#M(24,20,21,elfterWinkel); M(25,24,20,zwölfterWinkel); N(26,25,21); N(27,23,26);
#M(28,24,25,dreizehnterWinkel);
#A(17,28,ab(28,17,[1,28]));
#N(55,52,19); N(56,25,46);
#N(57,54,56); N(58,27,55);
#RA(57,58);
#
#
#//Ende der Eingabe, weiter mit fedgeo:
p(12.96684920439172294948,9.14663763764527182332,P1)
p(12.44539272583807587580,9.99991551792486177419,P2)
p(12.09865038990258057083,8.65042113397006318110,P3)
p(11.90886945654357909063,9.63224759385662920863,P4)
p(11.09865038990258057083,8.65042113397006495745,P5)
p(11.17832739106149020358,9.64724186784668447103,P6)
p(12.71168786821363028139,9.03602397986304062272,P7)
p(11.52449644897795266729,8.70906971768381055199,P8)
p(11.41484577807287692508,9.70303990353953693671,P9)
p(12.37627425808846659550,9.97809494860308454633,P10)
p(10.20233806557856937047,9.09384442752249988473,P11)
p(10.43837078049294930793,10.06558953684394452921,P12)
p(10.36285572301225954561,9.06844487527587972409,P13)
p(10.48126603260038613996,10.06140962720982656720,P14)
p(11.68835918602491119600,10.70388614008159322566,P15)
p(11.42768220847201732226,9.73846006141275566392,P16)
p(9.45968984749722174854,9.76352616102028569856,P17)
p(11.20099758697135960972,10.71242827566571698128,P18)
p(10.39247162883386899068,10.12396776295662093048,P19)
p(13.63688723382578515952,9.88896441145322135924,P20)
p(12.81843655651877789126,10.46354120250529895486,P21)
p(13.37573807659371993850,9.63323101003373949425,P22)
p(12.55356268926548324316,10.20246526099871964277,P23)
p(13.92541773985654174339,10.84643511444607888450,P24)
p(12.98554616656157278953,11.18796318900516695294,P25)
p(13.80657886304604886618,10.61708201809178930830,P26)
p(12.94404233676652538065,11.12307682126041008530,P27)
p(13.71579917695272143874,11.82421835120468500691,P28)
p(10.20863982005822023780,12.44110687457969888214,P29)
p(10.73009629861186731148,11.58782899430010715491,P30)
p(11.07683863454736261644,12.93732337825490574801,P31)
p(11.26661956790636232029,11.95549691836833972047,P32)
p(12.07683863454736261644,12.93732337825490574801,P33)
p(11.99716163338845120734,11.94050264437828623443,P34)
p(10.46380115623631290589,12.55172053236193008274,P35)
p(11.65099257547198874363,12.87867479454115837711,P36)
p(11.76064324637706626220,11.88470460868543376876,P37)
p(10.79921476636147481543,11.60964956362188438277,P38)
p(12.97315095887137204045,12.49390008470247082073,P39)
p(12.73711824395699210299,11.52215497538102617625,P40)
p(12.81263330143768186531,12.51929963694909098137,P41)
p(12.69422299184955704732,11.52633488501514236191,P42)
p(11.48712983842503199128,10.88385837214337747980,P43)
p(11.74780681597792408866,11.84928445081221504154,P44)
p(11.97449143747858357756,10.87531623655925194782,P45)
p(12.78301739561607419660,11.46377674926834799862,P46)
p(9.53860179062415802775,11.69878010077174756987,P47)
p(10.35705246793116351967,11.12420330971967175060,P48)
p(9.79975094785622147242,11.95451350219122943486,P49)
p(10.62192633518445994412,11.38527925122624928633,P50)
p(9.25007128459339966753,10.74130939777889182096,P51)
p(10.18994285788837039775,10.39978132321980375252,P52)
p(9.36891016140389254474,10.97066249413318139716,P53)
p(10.23144668768341780662,10.46466769096456062016,P54)
p(11.08535702943770751006,10.84501548788892932862,P55)
p(12.09013199501223390087,10.74272902433604315320,P56)
p(11.11018266068762905263,10.94197586159265789263,P57)
p(12.06530636376231235829,10.64576865063231281283,P58)
nolabel()
s(P1,P2)
s(P1,P3)
s(P3,P4)
s(P3,P5)
s(P5,P6)
s(P2,P7) s(P4,P7)
s(P4,P8) s(P6,P8)
s(P8,P9)
s(P9,P10) s(P7,P10)
s(P5,P11)
s(P11,P12)
s(P6,P13) s(P12,P13)
s(P13,P14) s(P9,P14)
s(P10,P15)
s(P15,P16) s(P14,P16)
s(P11,P17) s(P51,P17)
s(P12,P18) s(P16,P18)
s(P18,P19) s(P17,P19)
s(P1,P20)
s(P20,P21)
s(P21,P22) s(P2,P22)
s(P15,P23) s(P22,P23)
s(P20,P24)
s(P24,P25)
s(P25,P26) s(P21,P26)
s(P23,P27) s(P26,P27)
s(P24,P28) s(P39,P28)
s(P29,P30)
s(P29,P31)
s(P31,P32)
s(P31,P33)
s(P33,P34)
s(P30,P35) s(P32,P35)
s(P32,P36) s(P34,P36)
s(P36,P37)
s(P35,P38) s(P37,P38)
s(P33,P39)
s(P39,P40)
s(P34,P41) s(P40,P41)
s(P37,P42) s(P41,P42)
s(P38,P43)
s(P42,P44) s(P43,P44)
s(P40,P45) s(P44,P45)
s(P28,P46) s(P45,P46)
s(P29,P47)
s(P47,P48)
s(P30,P49) s(P48,P49)
s(P43,P50) s(P49,P50)
s(P47,P51)
s(P51,P52)
s(P48,P53) s(P52,P53)
s(P50,P54) s(P53,P54)
s(P52,P55) s(P19,P55)
s(P25,P56) s(P46,P56)
s(P54,P57) s(P56,P57) s(P58,P57)
s(P27,P58) s(P55,P58)
pen(2)
color(#0000FF) m(P2,P1,MA10) m(P1,P3,MB10) b(P1,MA10,MB10)
color(#008000) m(P1,P3,MA11) m(P3,P4,MB11) b(P3,MA11,MB11)
color(#FFA500) m(P4,P3,MA12) m(P3,P5,MB12) b(P3,MA12,MB12)
color(#EE82EE) m(P4,P8,MA13) m(P8,P9,MB13) f(P8,MA13,MB13)
color(#00FFFF) m(P6,P5,MA14) m(P5,P11,MB14) b(P5,MA14,MB14)
color(#32CD32) m(P5,P11,MA15) m(P11,P12,MB15) b(P11,MA15,MB15)
color(#ADD8E6) m(P9,P10,MA16) m(P10,P15,MB16) b(P10,MA16,MB16)
color(#F08080) m(P12,P11,MA17) m(P11,P17,MB17) b(P11,MA17,MB17)
color(#E0FFFF) m(P2,P1,MA18) m(P1,P20,MB18) b(P1,MA18,MB18)
color(#FAFAD2) m(P1,P20,MA19) m(P20,P21,MB19) b(P20,MA19,MB19)
color(#90EE90) m(P21,P20,MA110) m(P20,P24,MB110) b(P20,MA110,MB110)
color(#D3D3D3) m(P20,P24,MA111) m(P24,P25,MB111) b(P24,MA111,MB111)
color(#FFB6C1) m(P25,P24,MA112) m(P24,P28,MB112) b(P24,MA112,MB112)
pen(2)
color(green) s(P57,P58)
color(blue)
color(orange)
color(red)
\geooff
\geoprint()
Dieser Graph ist aus dem #1694 und #1691 entstanden. Der #1694 besitzt einen breiten Querstreifen mit viel Freiraum (wenig Kanten). Diesen Freiraum konnte man einfach weglassen und ihn mittig wie im #1691 füllen.
Meine Vermutung ist, dass jetzt wohl eine erste Minimalitätsgrenze erreicht ist. Mit weniger Kanten geht es wohl nur, wenn neue Konstruktionsideen vorhanden sind.
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haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 4639
| Beitrag No.1696, eingetragen 2019-02-05
|
als gratulation zum 14eckigen mit 87 stiches möchte ich auf die 5/siebtel ähnlichkeit mit dem #1603er hinweisen... ok der hatte noch 91 hölzer, war aber ja damals, also vor drei wochen, durchaus völlig klar wie man das unterbieten könnte... haribo
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Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9212
Wohnort: Pferdehof
| Beitrag No.1697, vom Themenstarter, eingetragen 2019-02-08
|
Doppelpost gelöscht. Siehe nächsten Beitrag.
Passiert mir oft, wenn ich statt ändern auf quote gekommen bin.
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Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9212
Wohnort: Pferdehof
| Beitrag No.1698, vom Themenstarter, eingetragen 2019-02-08
|
Rekord mit 54 Knoten. :-)
54 Knoten, 54×Grad 3, 0 Dreiecke,
81 Kanten, minimal 0.99999999999999900080, maximal 1.00000000000000133227
einzustellende Kanten, Abstände und Winkel:
|P52-P54|=0.99999999999999977796
\geo
ebene(556.67,555)
x(9.47,13.92)
y(8.64,13.07)
form(.)
#//Eingabe war:
#
#3-regular matchstick graph with girth 5 with 54 vertices.
#This graph is flexible and has a point symmetry.
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#P[1]=[369.2027248616914,-81.79871027158092];
#P[2]=[298.3711202642901,21.538658258257342]; D=ab(1,2);
#A(2,1,Bew(1)); M(3,1,2,blauerWinkel); M(4,3,1,gruenerWinkel);
#M(5,3,4,orangerWinkel);
#M(6,5,3,360-36-blauerWinkel-gruenerWinkel-orangerWinkel); N(7,2,4); N(8,4,6);
#M(9,8,4,vierterWinkel); N(10,9,7);
#M(11,5,6,fuenfterWinkel); M(12,11,5,sechsterWinkel); N(13,6,12); N(14,13,9);
#M(15,14,9,siebenterWinkel); M(16,11,12,achterWinkel); N(17,12,15); N(18,17,16);
#M(19,1,2,neunterWinkel); M(20,19,1,zehnterWinkel);
#N(21,20,2); N(22,10,21); N(23,15,22); N(24,18,23);
#M(25,19,20,elfterWinkel); M(26,25,19,zwölfterWinkel);
#A(16,26,ab(26,16,[1,26]));
#N(51,24,50); N(52,45,51); N(53,49,25); N(54,20,53);
#RA(52,54);
#
#
#
#
#
#
#//Ende der Eingabe, weiter mit fedgeo:
p(12.94695949335866913543,9.34708638494032229005,P1)
p(12.38158482101209934001,10.17192059850630236895,P2)
p(12.23677411773538281636,8.64307166048435426831,P3)
p(11.83099436006918381281,9.55704255075841579981,P4)
p(11.23677411773538281636,8.64307166048435604466,P5)
p(11.26420178593818377522,9.64269545122613003230,P6)
p(12.78487209608829111573,9.25684717316731919823,P7)
p(11.40444483473933523499,8.65257834337324815976,P8)
p(11.39953668828552935111,9.65256629834989965389,P9)
p(12.28270692028298860521,10.12161889807998704782,P10)
p(10.31303949892790683407,9.02610475829263592118,P11)
p(10.43233917669878785262,10.01896304973394968840,P12)
p(10.48159671197280928823,9.02017693888802440938,P13)
p(10.46952810954721080350,10.02010411065379535955,P14)
p(11.41525192277627454018,9.69513262099435024766,P15)
p(9.50342470017976914676,9.61306632232218305489,P16)
p(11.19156260776689393310,10.66979312104071730971,P17)
p(10.39606439899865719667,10.06383718217508693726,P18)
p(13.71826965826183908348,9.98354583338699619333,P19)
p(13.09536836415902349984,10.76584627299126672995,P20)
p(13.30497618076139687560,9.78806073248701835610,P21)
p(13.05538834303754214261,10.75641289531846034322,P22)
p(12.11891959591962475429,10.40566186442703688897,P23)
p(11.16441688471532245330,10.70386410168161894774,P24)
p(13.70730374274217489017,10.98348570592774819943,P25)
p(13.68935725392161906200,11.98332465472850927313,P26)
p(10.24582246074272084968,12.24930459211037181433,P27)
p(10.81119713308929064510,11.42447037854438995907,P28)
p(10.95600783636600716875,12.95331931656633983607,P29)
p(11.36178759403220439594,12.03934842629227830457,P30)
p(11.95600783636600539239,12.95331931656633983607,P31)
p(11.92858016816320443354,11.95369552582456229572,P32)
p(10.40790985801309886938,12.33954380388337312979,P33)
p(11.78833711936205475013,12.94381263367744594461,P34)
p(11.79324526581586063401,11.94382467870079267414,P35)
p(10.91007503381840137990,11.47477207897070705656,P36)
p(12.87974245517348137469,12.57028621875805640684,P37)
p(12.76044277740260213250,11.57742792731674441598,P38)
p(12.71118524212857892053,12.57621403816266791864,P39)
p(12.72325384455417918161,11.57628686639689696847,P40)
p(11.77753003132511366857,11.90125835605634208036,P41)
p(12.00121934633449605201,10.92659785600997501831,P42)
p(12.79671755510273278844,11.53255379487560539076,P43)
p(9.47451229583954912528,11.61284514366369791105,P44)
p(10.09741358994236648527,10.83054470405942559807,P45)
p(9.88780577333999310952,11.80833024456367397192,P46)
p(10.13739361106384784250,10.83997808173223376116,P47)
p(11.07386235818176523082,11.19072911262365721541,P48)
p(12.02836506938606575545,10.89252687536907338028,P49)
p(9.48547821135921331859,10.61290527112294590495,P50)
p(10.35424113362312681375,10.11767705615587864543,P51)
p(11.09649923893315204282,10.78779115472534755327,P52)
p(12.83854082047826139501,11.47871392089481368259,P53)
p(12.09628271516823794229,10.80859982232534477475,P54)
nolabel()
s(P1,P2)
s(P1,P3)
s(P3,P4)
s(P3,P5)
s(P5,P6)
s(P2,P7) s(P4,P7)
s(P4,P8) s(P6,P8)
s(P8,P9)
s(P9,P10) s(P7,P10)
s(P5,P11)
s(P11,P12)
s(P6,P13) s(P12,P13)
s(P13,P14) s(P9,P14)
s(P14,P15)
s(P11,P16) s(P50,P16)
s(P12,P17) s(P15,P17)
s(P17,P18) s(P16,P18)
s(P1,P19)
s(P19,P20)
s(P20,P21) s(P2,P21)
s(P10,P22) s(P21,P22)
s(P15,P23) s(P22,P23)
s(P18,P24) s(P23,P24)
s(P19,P25)
s(P25,P26) s(P37,P26)
s(P27,P28)
s(P27,P29)
s(P29,P30)
s(P29,P31)
s(P31,P32)
s(P28,P33) s(P30,P33)
s(P30,P34) s(P32,P34)
s(P34,P35)
s(P33,P36) s(P35,P36)
s(P31,P37)
s(P37,P38)
s(P32,P39) s(P38,P39)
s(P35,P40) s(P39,P40)
s(P40,P41)
s(P38,P42) s(P41,P42)
s(P26,P43) s(P42,P43)
s(P27,P44)
s(P44,P45)
s(P28,P46) s(P45,P46)
s(P36,P47) s(P46,P47)
s(P41,P48) s(P47,P48)
s(P43,P49) s(P48,P49)
s(P44,P50)
s(P24,P51) s(P50,P51)
s(P45,P52) s(P51,P52) s(P54,P52)
s(P49,P53) s(P25,P53)
s(P20,P54) s(P53,P54)
pen(2)
color(#0000FF) m(P2,P1,MA10) m(P1,P3,MB10) b(P1,MA10,MB10)
color(#008000) m(P1,P3,MA11) m(P3,P4,MB11) b(P3,MA11,MB11)
color(#FFA500) m(P4,P3,MA12) m(P3,P5,MB12) b(P3,MA12,MB12)
color(#EE82EE) m(P4,P8,MA13) m(P8,P9,MB13) f(P8,MA13,MB13)
color(#00FFFF) m(P6,P5,MA14) m(P5,P11,MB14) b(P5,MA14,MB14)
color(#32CD32) m(P5,P11,MA15) m(P11,P12,MB15) b(P11,MA15,MB15)
color(#ADD8E6) m(P9,P14,MA16) m(P14,P15,MB16) f(P14,MA16,MB16)
color(#F08080) m(P12,P11,MA17) m(P11,P16,MB17) b(P11,MA17,MB17)
color(#E0FFFF) m(P2,P1,MA18) m(P1,P19,MB18) b(P1,MA18,MB18)
color(#FAFAD2) m(P1,P19,MA19) m(P19,P20,MB19) b(P19,MA19,MB19)
color(#90EE90) m(P20,P19,MA110) m(P19,P25,MB110) b(P19,MA110,MB110)
color(#D3D3D3) m(P19,P25,MA111) m(P25,P26,MB111) b(P25,MA111,MB111)
pen(2)
color(green) s(P52,P54)
color(blue)
color(orange)
color(red)
\geooff
\geoprint()
|
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haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 4639
| Beitrag No.1699, eingetragen 2019-02-08
|
in jedem fall capeaux!!! mit teilweise konkaven aussenrändern, das ist was neues, und die fünffach zickezackezickezackezicke is auch neu
ich kann keinen unterschied feststellen in den beiden 81hölzers, siehst du doppelt inzwischen ??
haribo
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Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9212
Wohnort: Pferdehof
| Beitrag No.1700, vom Themenstarter, eingetragen 2019-02-08
|
\quoteon(2019-02-08 20:54 - haribo in Beitrag No. 1699)
ich kann keinen unterschied feststellen in den beiden 81hölzers, siehst du doppelt inzwischen ??
\quoteoff
Wollte was ändern und habe ausversehen gequotet. 8-)
Keine Ahnung, ob man den neuen noch groß verziehen kann. Hab mich auch schon an einem asymmetrischen mit 13 Außenkanten versucht - erfolglos.
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Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9212
Wohnort: Pferdehof
| Beitrag No.1701, vom Themenstarter, eingetragen 2019-02-09
|
Bei P50 und P52 sind jetzt jeweils (fast) 180 Grad Winkel.
@Stefan: Schaffst du es mit der neuen Abstandsmethode zusätzlich bei P1 und P11 180 Grad Winkel hinzubekommen? Bei P52 könnte man auch drauf verzichten. Aber außen sechs 2er Kanten wäre schon was.
54 Knoten, 54×Grad 3, 0 Dreiecke,
81 Kanten, minimal 0.99999999999999833467, maximal 1.00000000000000111022
einzustellende Kanten, Abstände und Winkel:
|P52-P54|=1.00000000000000044409
\geo
ebene(469.77,461.28)
x(9.76,14.33)
y(8.35,12.84)
form(.)
#//Eingabe war:
#
#Fig.1 3-regular matchstick graph with girth 5 with 54 vertices.
#This graph is flexible and has a point symmetry.
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#P[1]=[343.9930651376141,-92.7666922497696];
#P[2]=[282.6697669242336,-10.198871534013676]; D=ab(1,2);
#A(2,1,Bew(1)); M(3,1,2,blauerWinkel); M(4,3,1,gruenerWinkel);
#M(5,3,4,orangerWinkel);
#M(6,5,3,360-36-blauerWinkel-gruenerWinkel-orangerWinkel); N(7,2,4); N(8,4,6);
#M(9,8,4,vierterWinkel); N(10,9,7);
#M(11,5,6,fuenfterWinkel); M(12,11,5,sechsterWinkel); N(13,6,12); N(14,13,9);
#M(15,14,9,siebenterWinkel); M(16,11,12,achterWinkel); N(17,12,15); N(18,17,16);
#M(19,1,2,neunterWinkel); M(20,19,1,zehnterWinkel);
#N(21,20,2); N(22,10,21); N(23,15,22); N(24,18,23);
#M(25,19,20,elfterWinkel); M(26,25,19,zwölfterWinkel);
#A(16,26,ab(26,16,[1,26]));
#N(51,24,50); N(52,45,51); N(53,49,25); N(54,20,53);
#RA(52,54);
#
#
#
#
#
#//Ende der Eingabe, weiter mit fedgeo:
p(13.34462993016291321169,9.09803339989814041644,P1)
p(12.74838611187917258860,9.90083680619287420654,P2)
p(12.65276782989031012505,8.37600373692965582961,P3)
p(12.22363864978926883964,9.27924686410295862515,P4)
p(11.65309797010490378000,8.35030993540817334519,P5)
p(11.64260259103255634727,9.35025485740044359773,P6)
p(13.18407236889284916970,9.00073820856625061992,P7)
p(11.81712580514419208555,8.36560179782253143799,P8)
p(11.77273859893833396484,9.36461620008369877155,P9)
p(12.64937002833271861846,9.84577868511132159313,P10)
p(10.73498776495967632627,8.74663511907455060168,P11)
p(10.77300318397012723892,9.74591227177917396318,P12)
p(10.84397169206462052671,8.74843371518818457844,P13)
p(10.84932368192484730685,9.74841939318789307833,P14)
p(11.79891638401685582949,9.43493302963503133185,P15)
p(9.88480685163416339378,9.27312577864696585550,P16)
p(11.53085786684248148504,10.39833566164839417922,P17)
p(10.75192490347195040101,9.77122846301740821673,P18)
p(14.08471482763903992463,9.77054685294406333185,P19)
p(13.42246934198588625975,10.51983379179460698083,P20)
p(13.68683196829418946550,9.55541043983169657849,P21)
p(13.39518175107971664772,10.51193547912693126989,P22)
p(12.44593310370802186071,10.19740884199899255691,P23)
p(11.48010959063595493035,10.45660942378292368460,P24)
p(14.02242333181984790258,10.76860485203460093828,P25)
p(13.96013183600065232781,11.76666285112513854472,P26)
p(10.50030875747190250991,11.94175522987396220742,P27)
p(11.09655257575564135664,11.13895182357923019367,P28)
p(11.19217085774450559654,12.66378489284244679425,P29)
p(11.62130003784554688195,11.76054176566914222235,P30)
p(12.19184071752991371795,12.68947869436392927867,P31)
p(12.20233609660225937432,11.68953377237165902613,P32)
p(10.66086631874196832825,12.03905042120585200394,P33)
p(12.02781288249062363604,12.67418683194957296223,P34)
p(12.07220008869648353311,11.67517242968840385231,P35)
p(11.19556865930209710314,11.19400994466078280709,P36)
p(13.10995092267513939532,12.29315351069755202218,P37)
p(13.07193550366468848267,11.29387635799292866068,P38)
p(13.00096699557019519489,12.29135491458391626907,P39)
p(12.99561500570996841475,11.29136923658420954553,P40)
p(12.04602230361795989211,11.60485560013707129201,P41)
p(12.31408082079233423656,10.64145296812371022099,P42)
p(13.09301378416286709694,11.26856016675469440713,P43)
p(9.76022385999577579696,11.26924177682803929201,P44)
p(10.42246934564892946185,10.51995483797749564303,P45)
p(10.15810671934062625610,11.48437818994040604537,P46)
p(10.44975693655509907387,10.52785315064517313033,P47)
p(11.39900558392679386088,10.84237978777311006695,P48)
p(12.36482909699886079125,10.58317920598917893926,P49)
p(9.82251535581496781901,10.27118377773750346194,P50)
p(10.71265823287697926958,9.81550224594609233009,P51)
p(11.42246934381740786080,10.51989431488605220011,P52)
p(13.13228045475783645202,11.22428638382601029377,P53)
p(12.42246934381740786080,10.51989431488605042375,P54)
nolabel()
s(P1,P2)
s(P1,P3)
s(P3,P4)
s(P3,P5)
s(P5,P6)
s(P2,P7) s(P4,P7)
s(P4,P8) s(P6,P8)
s(P8,P9)
s(P9,P10) s(P7,P10)
s(P5,P11)
s(P11,P12)
s(P6,P13) s(P12,P13)
s(P13,P14) s(P9,P14)
s(P14,P15)
s(P11,P16) s(P50,P16)
s(P12,P17) s(P15,P17)
s(P17,P18) s(P16,P18)
s(P1,P19)
s(P19,P20)
s(P20,P21) s(P2,P21)
s(P10,P22) s(P21,P22)
s(P15,P23) s(P22,P23)
s(P18,P24) s(P23,P24)
s(P19,P25)
s(P25,P26) s(P37,P26)
s(P27,P28)
s(P27,P29)
s(P29,P30)
s(P29,P31)
s(P31,P32)
s(P28,P33) s(P30,P33)
s(P30,P34) s(P32,P34)
s(P34,P35)
s(P33,P36) s(P35,P36)
s(P31,P37)
s(P37,P38)
s(P32,P39) s(P38,P39)
s(P35,P40) s(P39,P40)
s(P40,P41)
s(P38,P42) s(P41,P42)
s(P26,P43) s(P42,P43)
s(P27,P44)
s(P44,P45)
s(P28,P46) s(P45,P46)
s(P36,P47) s(P46,P47)
s(P41,P48) s(P47,P48)
s(P43,P49) s(P48,P49)
s(P44,P50)
s(P24,P51) s(P50,P51)
s(P45,P52) s(P51,P52) s(P54,P52)
s(P49,P53) s(P25,P53)
s(P20,P54) s(P53,P54)
pen(2)
color(#0000FF) m(P2,P1,MA10) m(P1,P3,MB10) b(P1,MA10,MB10)
color(#008000) m(P1,P3,MA11) m(P3,P4,MB11) b(P3,MA11,MB11)
color(#FFA500) m(P4,P3,MA12) m(P3,P5,MB12) b(P3,MA12,MB12)
color(#EE82EE) m(P4,P8,MA13) m(P8,P9,MB13) f(P8,MA13,MB13)
color(#00FFFF) m(P6,P5,MA14) m(P5,P11,MB14) b(P5,MA14,MB14)
color(#32CD32) m(P5,P11,MA15) m(P11,P12,MB15) b(P11,MA15,MB15)
color(#ADD8E6) m(P9,P14,MA16) m(P14,P15,MB16) f(P14,MA16,MB16)
color(#F08080) m(P12,P11,MA17) m(P11,P16,MB17) b(P11,MA17,MB17)
color(#E0FFFF) m(P2,P1,MA18) m(P1,P19,MB18) b(P1,MA18,MB18)
color(#FAFAD2) m(P1,P19,MA19) m(P19,P20,MB19) b(P19,MA19,MB19)
color(#90EE90) m(P20,P19,MA110) m(P19,P25,MB110) b(P19,MA110,MB110)
color(#D3D3D3) m(P19,P25,MA111) m(P25,P26,MB111) b(P25,MA111,MB111)
pen(2)
color(green) s(P52,P54)
color(blue)
color(orange)
color(red)
\geooff
\geoprint()
Fast geschafft.
54 Knoten, 54×Grad 3, 0 Dreiecke,
81 Kanten, minimal 0.99999999999999789058, maximal 1.00000000000000133227
einzustellende Kanten, Abstände und Winkel:
|P52-P54|=1.00000000000000044409
\geo
ebene(514.11,461.28)
x(9.29,14.18)
y(8.74,13.12)
form(.)
#//Eingabe war:
#
#Fig.1 3-regular matchstick graph with girth 5 with 54 vertices.
#This graph is flexible and has a point symmetry.
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#P[1]=[275.69278641157115,-85.10589969422061];
#P[2]=[237.49217748119543,12.839964137903763]; D=ab(1,2);
#A(2,1,Bew(1)); M(3,1,2,blauerWinkel); M(4,3,1,gruenerWinkel);
#M(5,3,4,orangerWinkel);
#M(6,5,3,360-36-blauerWinkel-gruenerWinkel-orangerWinkel); N(7,2,4); N(8,4,6);
#M(9,8,4,vierterWinkel); N(10,9,7);
#M(11,5,6,fuenfterWinkel); M(12,11,5,sechsterWinkel); N(13,6,12); N(14,13,9);
#M(15,14,9,siebenterWinkel); M(16,11,12,achterWinkel); N(17,12,15); N(18,17,16);
#M(19,1,2,neunterWinkel); M(20,19,1,zehnterWinkel);
#N(21,20,2); N(22,10,21); N(23,15,22); N(24,18,23);
#M(25,19,20,elfterWinkel); M(26,25,19,zwölfterWinkel);
#A(16,26,ab(26,16,[1,26]));
#N(51,24,50); N(52,45,51); N(53,49,25); N(54,20,53);
#RA(52,54);
#
#
#
#
#
#//Ende der Eingabe, weiter mit fedgeo:
p(12.62235587640624245864,9.19048314943283983780,P1)
p(12.25899638262058033433,10.12213215966997204021,P2)
p(11.73095351008861264575,8.73727037233655146053,P3)
p(11.64484102758712147363,9.73355579346717902922,P4)
p(10.73095351008861264575,8.73727037233655146053,P5)
p(10.98459905307879935776,9.70456760613866187271,P6)
p(12.45003961484462884357,9.14055053625733471279,P7)
p(11.35611927334449511307,8.77614274330175447858,P8)
p(11.15763127481124605822,9.75624606154849161044,P9)
p(12.10417095290777389494,10.07883347263101114777,P10)
p(10.00923365554350752404,9.42945564490119636503,P11)
p(10.25002654462580764516,10.40003216664865703933,P12)
p(10.02422326735575630607,9.42585924566691168991,P13)
p(10.36503377476786802447,10.36599125663000009467,P14)
p(11.18944573974324008248,9.80000105176295122078,P15)
p(9.28751380099840062599,10.12164091746584126952,P16)
p(11.16666843579242041073,10.79974161532168430710,P17)
p(10.24315348816412196697,10.41617918036864942621,P18)
p(13.51370557180246656515,9.64379950752844194994,P19)
p(13.07381878414275533373,10.54185274316785658755,P20)
p(13.07341390079505316635,9.54185282513312138519,P21)
p(12.99223542254077301550,10.53855240608433341265,P22)
p(12.00512632175610328034,10.37850359119312315670,P23)
p(11.13424657736989864532,10.86999974663873835823,P24)
p(13.72679294823864459829,10.62083265435793855147,P25)
p(13.93988032467482085508,11.59786580118743515300,P26)
p(10.60503824926697902242,12.52902356922043480836,P27)
p(10.96839774305264292309,11.59737455898330438231,P28)
p(11.49644061558461061168,12.98223634631672318562,P29)
p(11.58255309808610000744,11.98595092518609561694,P30)
p(12.49644061558461061168,12.98223634631672318562,P31)
p(12.24279507259442389966,12.01493911251461277345,P32)
p(10.77735451082859441385,12.57895618239593993337,P33)
p(11.87127485232872636800,12.94336397535152016758,P34)
p(12.06976285086197719920,11.96326065710478303572,P35)
p(11.12322317276544936249,11.64067324602226349839,P36)
p(13.21816047012971573338,12.29005107375207828113,P37)
p(12.97736758104741561226,11.31947455200461760683,P38)
p(13.20317085831746517499,12.29364747298636473261,P39)
p(12.86236035090535523295,11.35351546202327455148,P40)
p(12.03794838592998317495,11.91950566689032342538,P41)
p(12.06072568988080107033,10.91976510333159211541,P42)
p(12.98424063750910129045,11.30332753828462521994,P43)
p(9.71368855387075669228,12.07570721112483269621,P44)
p(10.15357534153046792369,11.17765397548541983497,P45)
p(10.15398022487816831472,12.17765389352015326097,P46)
p(10.23515870313245024192,11.18095431256894300986,P47)
p(11.22226780391711997709,11.34100312746015148946,P48)
p(12.09314754830332461211,10.84950697201453628793,P49)
p(9.50060117743457865913,11.09867406429533609469,P50)
p(10.23903830659052616170,10.42435173314804153222,P51)
p(11.11577751039868644511,10.90531781147980083801,P52)
p(12.98835581908269709572,11.29515498550523489030,P53)
p(12.11161661527453503595,10.81418890717347558450,P54)
nolabel()
s(P1,P2)
s(P1,P3)
s(P3,P4)
s(P3,P5)
s(P5,P6)
s(P2,P7) s(P4,P7)
s(P4,P8) s(P6,P8)
s(P8,P9)
s(P9,P10) s(P7,P10)
s(P5,P11)
s(P11,P12)
s(P6,P13) s(P12,P13)
s(P13,P14) s(P9,P14)
s(P14,P15)
s(P11,P16) s(P50,P16)
s(P12,P17) s(P15,P17)
s(P17,P18) s(P16,P18)
s(P1,P19)
s(P19,P20)
s(P20,P21) s(P2,P21)
s(P10,P22) s(P21,P22)
s(P15,P23) s(P22,P23)
s(P18,P24) s(P23,P24)
s(P19,P25)
s(P25,P26) s(P37,P26)
s(P27,P28)
s(P27,P29)
s(P29,P30)
s(P29,P31)
s(P31,P32)
s(P28,P33) s(P30,P33)
s(P30,P34) s(P32,P34)
s(P34,P35)
s(P33,P36) s(P35,P36)
s(P31,P37)
s(P37,P38)
s(P32,P39) s(P38,P39)
s(P35,P40) s(P39,P40)
s(P40,P41)
s(P38,P42) s(P41,P42)
s(P26,P43) s(P42,P43)
s(P27,P44)
s(P44,P45)
s(P28,P46) s(P45,P46)
s(P36,P47) s(P46,P47)
s(P41,P48) s(P47,P48)
s(P43,P49) s(P48,P49)
s(P44,P50)
s(P24,P51) s(P50,P51)
s(P45,P52) s(P51,P52) s(P54,P52)
s(P49,P53) s(P25,P53)
s(P20,P54) s(P53,P54)
pen(2)
color(#0000FF) m(P2,P1,MA10) m(P1,P3,MB10) b(P1,MA10,MB10)
color(#008000) m(P1,P3,MA11) m(P3,P4,MB11) b(P3,MA11,MB11)
color(#FFA500) m(P4,P3,MA12) m(P3,P5,MB12) b(P3,MA12,MB12)
color(#EE82EE) m(P4,P8,MA13) m(P8,P9,MB13) f(P8,MA13,MB13)
color(#00FFFF) m(P6,P5,MA14) m(P5,P11,MB14) b(P5,MA14,MB14)
color(#32CD32) m(P5,P11,MA15) m(P11,P12,MB15) b(P11,MA15,MB15)
color(#ADD8E6) m(P9,P14,MA16) m(P14,P15,MB16) f(P14,MA16,MB16)
color(#F08080) m(P12,P11,MA17) m(P11,P16,MB17) b(P11,MA17,MB17)
color(#E0FFFF) m(P2,P1,MA18) m(P1,P19,MB18) b(P1,MA18,MB18)
color(#FAFAD2) m(P1,P19,MA19) m(P19,P20,MB19) b(P19,MA19,MB19)
color(#90EE90) m(P20,P19,MA110) m(P19,P25,MB110) b(P19,MA110,MB110)
color(#D3D3D3) m(P19,P25,MA111) m(P25,P26,MB111) b(P25,MA111,MB111)
pen(2)
color(green) s(P52,P54)
color(blue)
color(orange)
color(red)
\geooff
\geoprint()
Noch besser, aber Abstände werden leider geringer. Man kann nicht alles haben. Oder doch?
54 Knoten, 54×Grad 3, 0 Dreiecke,
81 Kanten, minimal 0.99999999999999866773, maximal 1.00000000000000155431
einzustellende Kanten, Abstände und Winkel:
|P52-P54|=0.99999999999999944489
\geo
ebene(481.49,461.28)
x(9.98,14.61)
y(8.48,12.92)
form(.)
#//Eingabe war:
#
#Fig.1 3-regular matchstick graph with girth 5 with 54 vertices.
#This graph is flexible and has a point symmetry.
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#P[1]=[358.1201383848009,-98.31034074023287];
#P[2]=[307.4641703085309,-7.457569584317724]; D=ab(1,2);
#A(2,1,Bew(1)); M(3,1,2,blauerWinkel); M(4,3,1,gruenerWinkel);
#M(5,3,4,orangerWinkel);
#M(6,5,3,360-36-blauerWinkel-gruenerWinkel-orangerWinkel); N(7,2,4); N(8,4,6);
#M(9,8,4,vierterWinkel); N(10,9,7);
#M(11,5,6,fuenfterWinkel); M(12,11,5,sechsterWinkel); N(13,6,12); N(14,13,9);
#M(15,14,9,siebenterWinkel); M(16,11,12,achterWinkel); N(17,12,15); N(18,17,16);
#M(19,1,2,neunterWinkel); M(20,19,1,zehnterWinkel);
#N(21,20,2); N(22,10,21); N(23,15,22); N(24,18,23);
#M(25,19,20,elfterWinkel); M(26,25,19,zwölfterWinkel);
#A(16,26,ab(26,16,[1,26]));
#N(51,24,50); N(52,45,51); N(53,49,25); N(54,20,53);
#RA(52,54);
#
#
#
#
#
#//Ende der Eingabe, weiter mit fedgeo:
p(13.44278603975380548263,9.05489406378974415190,P1)
p(12.95580516090748268709,9.92830669458807690830,P2)
p(12.62363399546481268487,8.48131762743869899168,P3)
p(12.50193788589820442780,9.47388503417556648856,P4)
p(11.62363399546481268487,8.48131762743869899168,P5)
p(11.74303725209172277744,9.47416346759057681481,P6)
p(13.39893540154967510603,9.03184945086231394384,P7)
p(12.12214811750823884040,8.54881220902811023166,P8)
p(11.88854426471116454422,9.52114406593621609431,P9)
p(12.83115734869040913679,9.85503113353712834055,P10)
p(10.80415837336885864772,9.05443166913585351097,P11)
p(10.89301206217900030992,10.05047635788472248919,P12)
p(10.83648240270334284219,9.05207543761292754425,P13)
p(11.02962022378594930672,10.03324707502784107760,P14)
p(11.92684767645321386453,9.59167839613382078312,P15)
p(9.98468275127290283422,9.62754571083300803025,P16)
p(11.74446575084725630234,10.57490615876680450924,P17)
p(10.88242393727205481468,10.06806899394167231776,P18)
p(14.26191469900302877249,9.62850389598979283790,P19)
p(13.66551698940008563454,10.43119298398112704263,P20)
p(13.83127049249505624573,9.44502576884378264310,P21)
p(13.65036617429076670760,10.42852646922738735213,P22)
p(12.66330893597117857041,10.26815811735923311687,P23)
p(11.72329739567746464957,10.60930076217901962821,P24)
p(14.31752123610015914323,10.62695665552930357478,P25)
p(14.37312777319728951397,11.62540941506881608802,P26)
p(10.91502448471638686556,12.19806106211207819001,P27)
p(11.40200536356270788474,11.32464843131374720997,P28)
p(11.73417652900537966332,12.77163749846312512659,P29)
p(11.85587263857198792039,11.77907009172625762972,P30)
p(12.73417652900538143967,12.77163749846312512659,P31)
p(12.61477327237846779440,11.77879165831124730346,P32)
p(10.95887512292051546581,12.22110567503951017443,P33)
p(12.23566240696195173143,12.70414291687371388662,P34)
p(12.46926625975902602761,11.73181105996560802396,P35)
p(11.52665317577978321140,11.39792399236469577772,P36)
p(13.55365215110133547682,12.19852345676596883095,P37)
p(13.46479846229119203826,11.20247876801710162908,P38)
p(13.52132812176684950600,12.20087968828889657402,P39)
p(13.32819030068424481783,11.21970805087398304067,P40)
p(12.43096284801697848366,11.66127672976800333515,P41)
p(12.61334477362293426950,10.67804896713501960903,P42)
p(13.47538658719813575715,11.18488613196015180051,P43)
p(10.09589582546716179934,11.62445122991203128038,P44)
p(10.69229353507010671365,10.82176214192069529929,P45)
p(10.52654003197513610246,11.80792935705803969881,P46)
p(10.70744435017942564059,10.82442865667443498978,P47)
p(11.69450158849901200142,10.98479700854259100140,P48)
p(12.63451312879272592227,10.64365436372280449007,P49)
p(10.04028928837003320496,10.62599847037251876714,P50)
p(10.87643422993654596098,10.07748991374579361491,P51)
p(11.68093154623519325241,10.67144619838993691019,P52)
p(13.48137629453364638721,11.17546521215602872701,P53)
p(12.67687897823499909578,10.58150892751188720808,P54)
nolabel()
s(P1,P2)
s(P1,P3)
s(P3,P4)
s(P3,P5)
s(P5,P6)
s(P2,P7) s(P4,P7)
s(P4,P8) s(P6,P8)
s(P8,P9)
s(P9,P10) s(P7,P10)
s(P5,P11)
s(P11,P12)
s(P6,P13) s(P12,P13)
s(P13,P14) s(P9,P14)
s(P14,P15)
s(P11,P16) s(P50,P16)
s(P12,P17) s(P15,P17)
s(P17,P18) s(P16,P18)
s(P1,P19)
s(P19,P20)
s(P20,P21) s(P2,P21)
s(P10,P22) s(P21,P22)
s(P15,P23) s(P22,P23)
s(P18,P24) s(P23,P24)
s(P19,P25)
s(P25,P26) s(P37,P26)
s(P27,P28)
s(P27,P29)
s(P29,P30)
s(P29,P31)
s(P31,P32)
s(P28,P33) s(P30,P33)
s(P30,P34) s(P32,P34)
s(P34,P35)
s(P33,P36) s(P35,P36)
s(P31,P37)
s(P37,P38)
s(P32,P39) s(P38,P39)
s(P35,P40) s(P39,P40)
s(P40,P41)
s(P38,P42) s(P41,P42)
s(P26,P43) s(P42,P43)
s(P27,P44)
s(P44,P45)
s(P28,P46) s(P45,P46)
s(P36,P47) s(P46,P47)
s(P41,P48) s(P47,P48)
s(P43,P49) s(P48,P49)
s(P44,P50)
s(P24,P51) s(P50,P51)
s(P45,P52) s(P51,P52) s(P54,P52)
s(P49,P53) s(P25,P53)
s(P20,P54) s(P53,P54)
pen(2)
color(#0000FF) m(P2,P1,MA10) m(P1,P3,MB10) b(P1,MA10,MB10)
color(#008000) m(P1,P3,MA11) m(P3,P4,MB11) b(P3,MA11,MB11)
color(#FFA500) m(P4,P3,MA12) m(P3,P5,MB12) b(P3,MA12,MB12)
color(#EE82EE) m(P4,P8,MA13) m(P8,P9,MB13) b(P8,MA13,MB13)
color(#00FFFF) m(P6,P5,MA14) m(P5,P11,MB14) b(P5,MA14,MB14)
color(#32CD32) m(P5,P11,MA15) m(P11,P12,MB15) b(P11,MA15,MB15)
color(#ADD8E6) m(P9,P14,MA16) m(P14,P15,MB16) f(P14,MA16,MB16)
color(#F08080) m(P12,P11,MA17) m(P11,P16,MB17) b(P11,MA17,MB17)
color(#E0FFFF) m(P2,P1,MA18) m(P1,P19,MB18) b(P1,MA18,MB18)
color(#FAFAD2) m(P1,P19,MA19) m(P19,P20,MB19) b(P19,MA19,MB19)
color(#90EE90) m(P20,P19,MA110) m(P19,P25,MB110) b(P19,MA110,MB110)
color(#D3D3D3) m(P19,P25,MA111) m(P25,P26,MB111) b(P25,MA111,MB111)
pen(2)
color(green) s(P52,P54)
color(blue)
color(orange)
color(red)
\geooff
\geoprint()
|
Profil
|
StefanVogel
Senior
Dabei seit: 26.11.2005
Mitteilungen: 4328
Wohnort: Raun
| Beitrag No.1702, eingetragen 2019-02-10
|
Doch, mit der Abstandsmethode lassen sich die zusammengerutschten Knoten wieder etwas auseinanderbringen
$
%Eingabe war:
%
%#1701-3 3x verbessert
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%P[1]=[179.05395344548333,75.30358941332679];
%P[2]=[137.36192104455023,150.07931323413771]; D=ab(1,2);
%A(2,1,Bew(1)); M(3,1,2,blauerWinkel); M(4,3,1,gruenerWinkel);
%M(5,3,4,orangerWinkel);
%M(6,5,3,dreizehnterWinkel); N(7,2,4); N(8,4,6);
%M(9,8,4,vierterWinkel); N(10,9,7);
%M(11,5,6,fuenfterWinkel); M(12,11,5,sechsterWinkel); N(13,6,12); N(14,13,9);
%M(15,14,9,siebenterWinkel); M(16,11,12,achterWinkel); N(17,12,15); N(18,17,16);
%M(19,1,2,blauerWinkel-180); M(20,19,1,zehnterWinkel);
%N(21,20,2); N(22,10,21); N(23,15,22); N(24,18,23);
%M(25,19,20,elfterWinkel); M(26,25,19,zwölfterWinkel);
%A(16,26,ab(26,16,[1,26]));
%N(51,24,50); N(52,45,51); N(53,49,25); N(54,20,53);
%RA(52,54);
%
%RW(16,11,5,11,180);
%RW(16,18,17,18,178);
%R(50,18,"brown",1.06*D);
%R(23,20,"brown",1.06*D);
%RW(2,22,10,22,2);
%R(50,14,"brown",1.18*D);
%RW(13,12,11,12,2);
%R(15,24,"brown",1.20*D);
%RW(7,3,1,3,2);
%R(50,12,"brown",1.12*D);
%RW(8,5,3,5);
%
%
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/10.16/2.05,
2/8.70/4.67,
3/7.63/0.43,
4/7.08/3.38,
5/4.66/0.00,
6/5.237/2.944,
7/9.65/1.82,
8/6.82/0.40,
9/5.461/3.071,
10/8.14/4.42,
11/2.331/1.888,
12/2.824/4.848,
13/2.435/1.873,
14/3.020/4.815,
15/5.65/3.38,
16/0.00/3.78,
17/5.41/6.37,
18/2.728/5.025,
19/12.69/3.66,
20/10.860/6.041,
21/11.23/3.06,
22/10.682/6.014,
23/7.72/5.56,
24/5.048/6.927,
25/12.76/6.66,
26/12.83/9.66,
27/2.67/11.39,
28/4.14/8.77,
29/5.20/13.00,
30/5.75/10.05,
31/8.17/13.44,
32/7.597/10.493,
33/3.19/11.62,
34/6.01/13.04,
35/7.373/10.367,
36/4.69/9.02,
37/10.503/11.549,
38/10.009/8.590,
39/10.399/11.565,
40/9.813/8.622,
41/7.18/10.06,
42/7.42/7.07,
43/10.106/8.412,
44/0.15/9.77,
45/1.974/7.396,
46/1.60/10.37,
47/2.152/7.424,
48/5.12/7.88,
49/7.786/6.511,
50/0.07/6.78,
51/2.611/5.177,
52/4.954/7.051,
53/10.222/8.261,
54/7.880/6.387}
\coordinate (p-\i) at (\x,\y);
%Dreiecke als \fill[black!3] (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;
%Punkte als \fill[red] (p-1) circle (1.125pt)
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
%Kanten als \draw[line width=0] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1,
4/3,
5/3,
6/5,
7/2, 7/4,
8/4, 8/6,
9/8,
10/9, 10/7,
11/5,
12/11,
13/6, 13/12,
14/13, 14/9,
15/14,
16/11, 16/50,
17/12, 17/15,
18/17, 18/16,
19/1,
20/19,
21/20, 21/2,
22/10, 22/21,
23/15, 23/22,
24/18, 24/23,
25/19,
26/25, 26/37,
28/27,
29/27,
30/29,
31/29,
32/31,
33/28, 33/30,
34/30, 34/32,
35/34,
36/33, 36/35,
37/31,
38/37,
39/32, 39/38,
40/35, 40/39,
41/40,
42/38, 42/41,
43/26, 43/42,
44/27,
45/44,
46/28, 46/45,
47/36, 47/46,
48/41, 48/47,
49/43, 49/48,
50/44,
51/24, 51/50,
52/45, 52/51, 52/54,
53/49, 53/25,
54/20, 54/53}
\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);
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\end{tikzpicture}
$
Streichholzgraph-1554.htm markiert und zählt jetzt auch die Überschneidungen, mit Fragezeichen bei sehr geringen Abständen.
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Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9212
Wohnort: Pferdehof
| Beitrag No.1703, vom Themenstarter, eingetragen 2019-02-10
|
...der Stefan wird's schon richten. Sehr schön. :-)
|
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haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 4639
| Beitrag No.1704, eingetragen 2019-02-10
|
ist ja spannend mit den äusseren doppelgeraden, aber einen gewissen sinn könnte es machen den graphen auf die kleinste fläche zu bringen... bis inne nahezu wieder dreiecke entstehen... also z.B. wie weit ist es möglich in diese richtung zu drücken?
im sinne von: wenn wir verstehen welche L anordnung es geben muss, kann man evtl weitere lösungen/prinzipien finden
https://www.matheplanet.com/matheplanet/nuke/html/uploads/b/35059_81er-girth5.png
|
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Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9212
Wohnort: Pferdehof
| Beitrag No.1705, vom Themenstarter, eingetragen 2019-02-10
|
Und mit ein paar unvermeidbaren Untergraphen könnten wir den 30 Knoten Beweis hochtreiben.
Mit Handjustage.
54 Knoten, 54×Grad 3, 0 Dreiecke, 0 Überschneidungen
81 Kanten, minimal 0.99999999999999689138, maximal 1.00000000000002220446
einzustellende Kanten, Abstände und Winkel:
|P52-P54|=1.00000000000002220446
\geo
ebene(539.62,465)
x(8.61,13.38)
y(9.34,13.45)
form(.)
#//Eingabe war:
#
##1701-3 alle 180°-Außenwinkel
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#P[1]=[156.3979174920501,-67.4500012880971];
#P[2]=[160.73389266232948,45.51737930030346]; D=ab(1,2);
#A(2,1,Bew(1)); M(3,1,2,blauerWinkel); M(4,3,1,gruenerWinkel);
#M(5,3,4,orangerWinkel);
#M(6,5,3,360-36-blauerWinkel-gruenerWinkel-orangerWinkel); N(7,2,4); N(8,4,6);
#M(9,8,4,vierterWinkel); N(10,9,7);
#M(11,5,6,fuenfterWinkel); M(12,11,5,sechsterWinkel); N(13,6,12); N(14,13,9);
#M(15,14,9,siebenterWinkel); M(16,11,12,achterWinkel); N(17,12,15); N(18,17,16);
#M(19,1,2,neunterWinkel); M(20,19,1,zehnterWinkel);
#N(21,20,2); N(22,10,21); N(23,15,22); N(24,18,23);
#M(25,19,20,elfterWinkel); M(26,25,19,zwölfterWinkel);
#A(16,26,ab(26,16,[1,26]));
#N(51,24,50); N(52,45,51); N(53,49,25); N(54,20,53);
#RA(52,54);
#
#
#//Ende der Eingabe, weiter mit fedgeo:
p(11.38343333786001032593,9.40336430358545349861,P1)
p(11.42178763757760506792,10.40262850673353689501,P2)
p(10.38566565234138217022,9.33658372456129725947,P3)
p(10.63064993688443848896,10.30611077437833422721,P4)
p(9.39735971155225868756,9.48906771519940939186,P5)
p(10.01574175358537566183,10.27494534568073980552,P6)
p(11.13728848512350033673,9.44395221504123760781,P7)
p(10.37135568281820852121,9.34031240525140482589,P8)
p(10.02602783342756431750,10.27879451825901746531,P9)
p(11.01355117332452593359,10.43626722433453934968,P10)
p(8.99554104627266148952,10.40478697361484883288,P11)
p(9.60066939947313358061,11.20091490061708938697,P12)
p(9.02186590747160366277,10.38544784570509982302,P13)
p(9.61511301574948973325,11.19046826067600441945,P14)
p(10.03079569145026361809,10.28095855038026229522,P15)
p(8.60847727893390590737,11.32683992221028113079,P16)
p(10.59613718167253360036,11.10581550733295941313,P17)
p(9.60126414665442595719,11.20694732326572484737,P18)
p(12.37668130715197101210,9.51937495610235373533,P19)
p(12.03020532348954674262,10.45743379900356195833,P20)
p(11.81142425303885801213,9.48165982762881220935,P21)
p(12.01324322274471967376,10.46108266964693989109,P22)
p(11.01326313180219251819,10.46739279790021370786,P23)
p(10.58751001860194662640,11.37223216850711970949,P24)
p(12.92655107034389416754,10.35462536378094711154,P25)
p(13.16064261734646656521,11.32683992221027935443,P26)
p(10.38568655842036392301,13.25031554083510698661,P27)
p(10.34733225870276918101,12.25105133768702359021,P28)
p(11.38345424393899207871,13.31709611985926144939,P29)
p(11.13846995939593398361,12.34756907004222625801,P30)
p(12.37176018472811733773,13.16461212922114754065,P31)
p(11.75337814269500036346,12.37873449873981535063,P32)
p(10.63183141115687391220,13.20972762937932110106,P33)
p(11.39776421346216572772,13.31336743916915565933,P34)
p(11.74309206285280993143,12.37488532616154301991,P35)
p(10.75556872295584653898,12.21741262008602113553,P36)
p(12.77357885000771275941,12.24889287080570987598,P37)
p(12.16845049680723889196,11.45276494380346576918,P38)
p(12.74725398880877236252,12.26823199871545710948,P39)
p(12.15400688053088451568,11.46321158374455606577,P40)
p(11.73832420483010885448,12.37272129404029641364,P41)
p(11.17298271460784064857,11.54786433708760107208,P42)
p(12.16785574962594829174,11.44673252115483386149,P43)
p(9.39243858912840501318,13.13430488831820674989,P44)
p(9.73891457279082572995,12.19624604541699852689,P45)
p(9.95769564324151446044,13.17202001679174827586,P46)
p(9.75587667353565279882,12.19259717477362059412,P47)
p(10.75585676447818173074,12.18628704652034500100,P48)
p(11.18160987767842584617,11.28144767591344077573,P49)
p(8.84256882593647830504,12.29905448063961337368,P50)
p(9.64230073655532216037,11.69869719440254662857,P51)
p(10.64022633106313975304,11.76307504638766410210,P52)
p(12.12681915972505031220,10.95498265001801208030,P53)
p(11.12889356521723271953,10.89060479803289283041,P54)
nolabel()
s(P1,P2)
s(P1,P3)
s(P3,P4)
s(P3,P5)
s(P5,P6)
s(P2,P7) s(P4,P7)
s(P4,P8) s(P6,P8)
s(P8,P9)
s(P9,P10) s(P7,P10)
s(P5,P11)
s(P11,P12)
s(P6,P13) s(P12,P13)
s(P13,P14) s(P9,P14)
s(P14,P15)
s(P11,P16) s(P50,P16)
s(P12,P17) s(P15,P17)
s(P17,P18) s(P16,P18)
s(P1,P19)
s(P19,P20)
s(P20,P21) s(P2,P21)
s(P10,P22) s(P21,P22)
s(P15,P23) s(P22,P23)
s(P18,P24) s(P23,P24)
s(P19,P25)
s(P25,P26) s(P37,P26)
s(P27,P28)
s(P27,P29)
s(P29,P30)
s(P29,P31)
s(P31,P32)
s(P28,P33) s(P30,P33)
s(P30,P34) s(P32,P34)
s(P34,P35)
s(P33,P36) s(P35,P36)
s(P31,P37)
s(P37,P38)
s(P32,P39) s(P38,P39)
s(P35,P40) s(P39,P40)
s(P40,P41)
s(P38,P42) s(P41,P42)
s(P26,P43) s(P42,P43)
s(P27,P44)
s(P44,P45)
s(P28,P46) s(P45,P46)
s(P36,P47) s(P46,P47)
s(P41,P48) s(P47,P48)
s(P43,P49) s(P48,P49)
s(P44,P50)
s(P24,P51) s(P50,P51)
s(P45,P52) s(P51,P52) s(P54,P52)
s(P49,P53) s(P25,P53)
s(P20,P54) s(P53,P54)
pen(2)
color(#0000FF) m(P2,P1,MA10) m(P1,P3,MB10) b(P1,MA10,MB10) #blue
color(#008000) m(P1,P3,MA11) m(P3,P4,MB11) b(P3,MA11,MB11) #green
color(#FFA500) m(P4,P3,MA12) m(P3,P5,MB12) b(P3,MA12,MB12) #orange
color(#EE82EE) m(P4,P8,MA13) m(P8,P9,MB13) b(P8,MA13,MB13) #violet
color(#008080) m(P6,P5,MA14) m(P5,P11,MB14) b(P5,MA14,MB14) #teal
color(#00FF00) m(P5,P11,MA15) m(P11,P12,MB15) b(P11,MA15,MB15) #lime
color(#ADD8E6) m(P9,P14,MA16) m(P14,P15,MB16) f(P14,MA16,MB16) #LightBlue
color(#F08080) m(P12,P11,MA17) m(P11,P16,MB17) b(P11,MA17,MB17) #LightCoral
color(#E0FFFF) m(P2,P1,MA18) m(P1,P19,MB18) b(P1,MA18,MB18) #LightCyan
color(#FAFAD2) m(P1,P19,MA19) m(P19,P20,MB19) b(P19,MA19,MB19) #LightGoldenrodYellow
color(#90EE90) m(P20,P19,MA110) m(P19,P25,MB110) b(P19,MA110,MB110) #LightGreen
color(#D3D3D3) m(P19,P25,MA111) m(P25,P26,MB111) b(P25,MA111,MB111) #LightGray
pen(2)
color(#32CD32) s(P52,P54) #LimeGreen
color(blue)
color(orange)
color(red)
\geooff
\geoprint()
|
Profil
|
StefanVogel
Senior
Dabei seit: 26.11.2005
Mitteilungen: 4328
Wohnort: Raun
| Beitrag No.1706, eingetragen 2019-02-11
|
\quoteon(2019-02-10 22:20 - haribo in Beitrag No. 1704)
ist ja spannend mit den äusseren doppelgeraden, aber einen gewissen sinn könnte es machen den graphen auf die kleinste fläche zu bringen... bis inne nahezu wieder dreiecke entstehen... also z.B. wie weit ist es möglich in diese richtung zu drücken?
im sinne von: wenn wir verstehen welche L anordnung es geben muss, kann man evtl weitere lösungen/prinzipien finden
https://www.matheplanet.com/matheplanet/nuke/html/uploads/b/35059_81er-girth5.png
\quoteoff
Minimale Fläche hat den Nachteil, dass sich der Graph kaum noch übersichtlich zeichnen lässt. An gut die Hälfte der Knoten müsste Vergrößerung ran um den Kantenverlauf zu erkennen, wenn man wirklich minimalste Abstände (soweit die Rechengenauigkeit mitmacht) einsetzt.
$
%Eingabe war:
%
%#1701-3 auf minimale Fläche bringen
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%P[1]=[178.0663930604487,118.22968175109817];
%P[2]=[137.8836806041677,190.2984017431386]; D=ab(1,2);
%A(2,1,Bew(1)); M(3,1,2,blauerWinkel); M(4,3,1,gruenerWinkel);
%M(5,3,4,orangerWinkel);
%M(6,5,3,dreizehnterWinkel); N(7,2,4); N(8,4,6);
%M(9,8,4,vierterWinkel); N(10,9,7);
%M(11,5,6,fuenfterWinkel); M(12,11,5,sechsterWinkel); N(13,6,12); N(14,13,9);
%M(15,14,9,siebenterWinkel); M(16,11,12,achterWinkel); N(17,12,15); N(18,17,16);
%M(19,1,2,neunterWinkel); M(20,19,1,zehnterWinkel);
%N(21,20,2); N(22,10,21); N(23,15,22); N(24,18,23);
%M(25,19,20,elfterWinkel); M(26,25,19,zwölfterWinkel);
%A(16,26,ab(26,16,[1,26]));
%N(51,24,50); N(52,45,51); N(53,49,25); N(54,20,53);
%RA(52,54);
%
%//RW(16,11,5,11,180);
%RW(21,1,19,1,0.88358631315956026597);
%RW(16,18,17,18,178);
%R(50,18,"brown",1.02*D);
%R(23,20,"brown",1.02*D);
%RW(2,22,10,22,2);
%R(50,14,"brown",1.06*D);
%RW(13,12,11,12,2);
%R(15,24,"brown",1.12*D);
%RW(7,3,1,3,2);
%R(50,12,"brown",1.04*D);
%R(7,23,"darkred",1.02*D);
%RW(8,5,3,5,0.2);
%
%
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/11.628/3.707,
2/10.17/6.33,
3/10.40/0.97,
4/8.50/3.29,
5/7.56/0.00,
6/7.020/2.951,
7/11.484/3.632,
8/8.41/0.29,
9/7.1804/3.0291,
10/9.045/5.379,
11/4.702/0.909,
12/4.237/3.873,
13/4.805/0.927,
14/4.305/3.885,
15/7.1837/3.0405,
16/1.90/1.98,
17/6.41/5.94,
18/4.191/3.922,
19/13.81/5.76,
20/11.318/7.428,
21/12.74/4.79,
22/11.264/7.398,
23/9.005/5.425,
24/6.11/6.23,
25/12.51/8.47,
26/11.91/11.40,
27/2.185/9.682,
28/3.65/7.06,
29/3.41/12.42,
30/5.31/10.10,
31/6.25/13.39,
32/6.793/10.438,
33/2.329/9.757,
34/5.40/13.09,
35/6.6327/10.3598,
36/4.768/8.010,
37/9.111/12.480,
38/9.576/9.516,
39/9.008/12.462,
40/9.508/9.504,
41/6.6293/10.3484,
42/7.40/7.45,
43/9.622/9.467,
44/0.00/7.63,
45/2.495/5.961,
46/1.07/8.60,
47/2.549/5.991,
48/4.809/7.964,
49/7.70/7.16,
50/1.30/4.92,
51/4.142/3.964,
52/5.41/6.68,
53/9.671/9.425,
54/8.41/6.70}
\coordinate (p-\i) at (\x,\y);
%Dreiecke als \fill[black!3] (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;
%Punkte als \fill[red] (p-1) circle (1.125pt)
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
%Kanten als \draw[line width=0] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1,
4/3,
5/3,
6/5,
7/2, 7/4,
8/4, 8/6,
9/8,
10/9, 10/7,
11/5,
12/11,
13/6, 13/12,
14/13, 14/9,
15/14,
16/11, 16/50,
17/12, 17/15,
18/17, 18/16,
19/1,
20/19,
21/20, 21/2,
22/10, 22/21,
23/15, 23/22,
24/18, 24/23,
25/19,
26/25, 26/37,
28/27,
29/27,
30/29,
31/29,
32/31,
33/28, 33/30,
34/30, 34/32,
35/34,
36/33, 36/35,
37/31,
38/37,
39/32, 39/38,
40/35, 40/39,
41/40,
42/38, 42/41,
43/26, 43/42,
44/27,
45/44,
46/28, 46/45,
47/36, 47/46,
48/41, 48/47,
49/43, 49/48,
50/44,
51/24, 51/50,
52/45, 52/51, 52/54,
53/49, 53/25,
54/20, 54/53}
\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);
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\end{tikzpicture}
$
Maximale Fläche wäre für die Ansicht besser geeignet, oder noch besser eine größtmögliche Umgebung, in der von jedem Knoten aus gesehen keine weiteren Kanten liegen, außer die zum Knoten führen.
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| Beitrag No.1707, vom Themenstarter, eingetragen 2019-02-11
|
Idee für einen eng gefalteten mit 58 Knoten.
https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/8038_3reg5_idee_slash.png
[Die Antwort wurde nach Beitrag No.1705 begonnen.]
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Slash
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Wohnort: Pferdehof
| Beitrag No.1708, vom Themenstarter, eingetragen 2019-02-11
|
\quoteon(2019-02-11 00:15 - StefanVogel in Beitrag No. 1706)
Minimale Fläche hat den Nachteil, dass sich der Graph kaum noch übersichtlich zeichnen lässt. An gut die Hälfte der Knoten müsste Vergrößerung ran um den Kantenverlauf zu erkennen, wenn man wirklich minimalste Abstände (soweit die Rechengenauigkeit mitmacht) einsetzt.
Maximale Fläche wäre für die Ansicht besser geeignet, oder noch besser eine größtmögliche Umgebung, in der von jedem Knoten aus gesehen keine weiteren Kanten liegen, außer die zum Knoten führen.
\quoteoff
Ich denke da bei einer Veröffentlichung an den minimalsten Graphen mit guter Sichtbarkeit der Abstände und einem Hinweis auf die möglichen Formen mit kleinen Bildchen. Dazu würde ich ein weiteres Katalogpaper erstellen (wie auch bei den 2ern und 4ern), das alle bisherigen 11 Graphen < 70 Knoten zeigt, auch verschieden geformt - wenn sinnvoll. Das soll nicht veröffentlicht werden, aber als PDF Ergänzung dienen (wie ja auch der MGC) und je Seite einen Graphen zeigen. Ganz normale TikZ Bilder damit voll gezoomt werden kann.
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Slash
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| Beitrag No.1709, vom Themenstarter, eingetragen 2019-02-11
|
Ein (2;3)-reg. girth 5 mit 48 Knoten. Vier 2er-Knoten. Wenn man die Lücken schließen kann sind es nur 46 Knoten inkl. zwei 2er-Knoten.
https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/8038_slash_2_3reg_girth5_48.png
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haribo
Senior
Dabei seit: 25.10.2012
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| Beitrag No.1710, eingetragen 2019-02-12
|
wenn auf minimaler fläche die winkel unendlich klein werden und deswegen der graph in seiner anordnung kaum mehr erkannt werden kann, dass ist doch egal solange es funktioniert
hier ein versuch ihn abstrakt noch mehr zu komprimieren, bis nur noch möglichst wenige einfache aber verschiedene elemente enthalten sind
https://www.matheplanet.com/matheplanet/nuke/html/uploads/b/35059_dreier-girth5-abstrakt.png
die grauen dreiecke erklären ihre form selber,
gelb ist ein regelmässiges fünfeck mit einem eingespiegelten punkt,
hellblau ein regelmässiges doppel M
die vier rötlichen in dem mittelband sind noch etwas beliebig, auch ist die blaue verbindung noch nicht exakt 1, letzteres müsste aber wohl möglich sein?
ziel wäre es also: derartige abstrakte elemente zu finden welche mit minimaler auf-öffnung dann girth-5 flächen ergeben können
-aus den dreiecken werden dann beispielsweise L´s-
und dann versuchen aus diesen einfachen bestandteilen neue einfache graphen zusammenzusetzen, am besten kleinere
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Slash
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| Beitrag No.1711, vom Themenstarter, eingetragen 2019-02-13
|
Hier meine modifizierte Idee aus #1709. Wenn der existiert, dann wird's wirklich mehr als knapp.
48 Knoten, 48×Grad 3, 0 Dreiecke, 50? Überschneidungen
72 Kanten, minimal 0.90613474600472498910, maximal 1.00000000000000133227
einzustellende Kanten, Abstände und Winkel:
|P23-P48|=0.90613474600472498910
nicht passende Kanten:
|P23-P48|=0.90613474600472498910
|P46-P47|=0.90613474600480081733
\geo
ebene(729.77,506.43)
x(9.05,13.66)
y(9.15,12.35)
form(.)
#//Eingabe war:
#
#3-reg. girth 5 mit 48 Knoten Versuch
#
#
#
#
#
#
#
#
#
#
#
#
#
#P[1]=[322.95526194341767,-95.04142755871109];
#P[2]=[304.9604746669152,62.164918890134174]; D=ab(1,2);
#A(2,1,Bew(1)); M(3,1,2,blauerWinkel); M(4,3,1,gruenerWinkel);
#M(5,3,4,orangerWinkel);
#M(6,5,3,360-36-blauerWinkel-gruenerWinkel-orangerWinkel); N(7,2,4); N(8,4,6);
#M(9,8,4,vierterWinkel); N(10,9,7);
#M(11,5,6,fuenfterWinkel); M(12,11,5,sechsterWinkel); N(13,6,12); N(14,13,9);
#M(15,14,9,siebenterWinkel); M(16,11,12,achterWinkel); N(17,12,15); N(18,17,16);
#M(19,1,2,neunterWinkel); M(20,19,1,zehnterWinkel);
#N(21,20,2); N(22,10,21); N(23,15,22);
#M(24,19,20,elfterWinkel);
#A(16,24,ab(24,16,[1,24]));
#N(47,20,41); N(48,43,18);
#RA(23,48); A(46,47);
#
#
#//Ende der Eingabe, weiter mit fedgeo:
p(12.04101220863585020027,9.39935732024860115530,P1)
p(11.92728877740226600679,10.39286976666709527706,P2)
p(11.07356753512619640389,9.14627471772958600127,P3)
p(11.29017754156485331407,10.12253293414092247815,P4)
p(10.07356753512619640389,9.14627471772958600127,P5)
p(10.56553531057340222787,10.01688812672437478568,P6)
p(11.97520805131123111664,9.39401855493031412436,P7)
p(11.06210192684688387033,9.14888951174696352098,P8)
p(10.55989376847205107879,10.01363627563900671191,P9)
p(11.52221965037018236444,10.28553496454534155191,P10)
p(9.54069125905546577826,9.99246788385715056791,P11)
p(10.05168432455898752664,10.85205271795284076575,P12)
p(9.56630146100229694639,9.97775101043677636881,P13)
p(10.03178024035640802936,10.86281005138885014105,P14)
p(10.56078273143740986484,10.01418978034290496737,P15)
p(9.05146101956066395644,10.86462255635730933534,P16)
p(11.05111728364574652517,10.88572407508445394342,P17)
p(10.05145000894891360588,10.85992989162754973620,P18)
p(13.00412782540100664619,9.66844524034735641749,P19)
p(12.50609406003436951949,10.53560287800888950471,P20)
p(12.44523488456374238353,9.53745651561455787260,P21)
p(12.49023039624081121701,10.53644370468602886604,P22)
p(11.51676019796692607144,10.30762986534801584071,P23)
p(13.50548755751461271757,10.53368417787558186660,P24)
p(10.51593636843942647374,11.99894941398428649393,P25)
p(10.62965979967301066722,11.00543696756579237217,P26)
p(11.48338104194908027011,12.25203201650330342432,P27)
p(11.26677103551042158358,11.27577380009196694743,P28)
p(12.48338104194908204647,12.25203201650330164796,P29)
p(11.99141326650187444613,11.38141860750851463990,P30)
p(10.58174052576404555737,12.00428817930257707758,P31)
p(11.49484665022839280368,12.24941722248592768096,P32)
p(11.99705480860322559522,11.38467045859388449003,P33)
p(11.03472892670509430957,11.11277176968754787367,P34)
p(13.01625731801980911939,11.40583885037573708132,P35)
p(12.50526425251628914737,10.54625401628005043619,P36)
p(12.99064711607297795126,11.42055572379611660949,P37)
p(12.52516833671886686830,10.53549668284403928453,P38)
p(11.99616584563786503281,11.38411695388998445821,P39)
p(11.50583129342953014884,10.51258265914843548217,P40)
p(12.50549856812636129177,10.53837684260534146574,P41)
p(9.55282075167427002782,11.72986149388553478445,P42)
p(10.05085451704090715452,10.86270385622400169723,P43)
p(10.11171369251153429047,11.86085021861833332935,P44)
p(10.06671818083446368064,10.86186302954686233591,P45)
p(11.04018837910834882621,11.09067686888487358488,P46)
p(11.52807228420468099728,10.32710010583800297468,P47)
p(11.02887629287061166394,11.07120662839480829120,P48)
nolabel()
s(P1,P2)
s(P1,P3)
s(P3,P4)
s(P3,P5)
s(P5,P6)
s(P2,P7) s(P4,P7)
s(P4,P8) s(P6,P8)
s(P8,P9)
s(P9,P10) s(P7,P10)
s(P5,P11)
s(P11,P12)
s(P6,P13) s(P12,P13)
s(P13,P14) s(P9,P14)
s(P14,P15)
s(P11,P16) s(P42,P16)
s(P12,P17) s(P15,P17)
s(P17,P18) s(P16,P18)
s(P1,P19)
s(P19,P20)
s(P20,P21) s(P2,P21)
s(P10,P22) s(P21,P22)
s(P15,P23) s(P22,P23) s(P48,P23)
s(P19,P24) s(P35,P24)
s(P25,P26)
s(P25,P27)
s(P27,P28)
s(P27,P29)
s(P29,P30)
s(P26,P31) s(P28,P31)
s(P28,P32) s(P30,P32)
s(P32,P33)
s(P31,P34) s(P33,P34)
s(P29,P35)
s(P35,P36)
s(P30,P37) s(P36,P37)
s(P33,P38) s(P37,P38)
s(P38,P39)
s(P36,P40) s(P39,P40)
s(P24,P41) s(P40,P41)
s(P25,P42)
s(P42,P43)
s(P26,P44) s(P43,P44)
s(P34,P45) s(P44,P45)
s(P39,P46) s(P45,P46) s(P47,P46)
s(P20,P47) s(P41,P47)
s(P43,P48) s(P18,P48)
pen(2)
color(#0000FF) m(P2,P1,MA10) m(P1,P3,MB10) b(P1,MA10,MB10) #blue
color(#008000) m(P1,P3,MA11) m(P3,P4,MB11) b(P3,MA11,MB11) #green
color(#FFA500) m(P4,P3,MA12) m(P3,P5,MB12) b(P3,MA12,MB12) #orange
color(#EE82EE) m(P4,P8,MA13) m(P8,P9,MB13) b(P8,MA13,MB13) #violet
color(#008080) m(P6,P5,MA14) m(P5,P11,MB14) b(P5,MA14,MB14) #teal
color(#00FF00) m(P5,P11,MA15) m(P11,P12,MB15) b(P11,MA15,MB15) #lime
color(#ADD8E6) m(P9,P14,MA16) m(P14,P15,MB16) f(P14,MA16,MB16) #LightBlue
color(#F08080) m(P12,P11,MA17) m(P11,P16,MB17) b(P11,MA17,MB17) #LightCoral
color(#E0FFFF) m(P2,P1,MA18) m(P1,P19,MB18) b(P1,MA18,MB18) #LightCyan
color(#FAFAD2) m(P1,P19,MA19) m(P19,P20,MB19) b(P19,MA19,MB19) #LightGoldenrodYellow
color(#90EE90) m(P20,P19,MA110) m(P19,P24,MB110) b(P19,MA110,MB110) #LightGreen
pen(2)
color(#32CD32) s(P23,P48) #LimeGreen
color(blue)
color(orange)
color(red)
\geooff
\geoprint()
|
Profil
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haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 4639
| Beitrag No.1712, eingetragen 2019-02-13
|
https://www.matheplanet.com/matheplanet/nuke/html/uploads/b/35059_dreier-girth5-abstrakt-2.png
abstrakt nur noch drei elemente
das abstrakte grüne schachbrett in der mitte hat bisher noch nie bewiesen dass es aufzu-öffnen-drehen geht
explosion... ohne garantien
https://www.matheplanet.com/matheplanet/nuke/html/uploads/b/35059_dreier-girth5-explosion_-1709.png
puzzleanleitung könnte sein: jede einzelfläch hat einen konkaven aussenwinkel, zu dem müssen jeweils zwei spitzen anderer flächen hinzeigen
also liegt zumindest beim fragezeichen ein fehler vor
möglicherweise wäre es doch besser gewesen erstmal ne explosion an einem nachgewiesenen girth-5er durchzuführen...
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Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9212
Wohnort: Pferdehof
| Beitrag No.1713, vom Themenstarter, eingetragen 2019-02-13
|
Die Explosion müsste etwas anders aussehen, wenn die Teilgraphen so wie #1711 sein sollen. Einfach den Code ins Programm kopieren und zoomen. Es sei denn, ich habe dich falsch verstanden. Im unteren Bild sind 2 Knoten und 4 Kanten entfernt. Die 6 2er Knoten sind rot.
https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/8038__1171_mit_6_2er.png
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Slash
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| Beitrag No.1714, vom Themenstarter, eingetragen 2019-02-13
|
8 Überschneidungen ist bis jetzt mein bestes Ergebnis. Dazu zwei zu lange Kanten. Ich glaube nicht, dass der Graph möglich ist.
48 Knoten, 48×Grad 3, 0 Dreiecke, 8? Überschneidungen
72 Kanten, minimal 0.99999999999999666933, maximal 1.10895546651046172926
einzustellende Kanten, Abstände und Winkel:
|P20-P48|=1.10895546651046106312
nicht passende Kanten:
|P20-P48|=1.10895546651046106312
|P43-P47|=1.10895546651046172926
\geo
ebene(623.44,461.68)
x(9.32,13.85)
y(9.02,12.37)
form(.)
#//Eingabe war:
#
#3-reg. girth 5 mit 48 Knoten Versuch
#
#
#
#
#
#
#
#
#
#
#
#
#
#P[1]=[324.76642771007806,-90.71230343846872];
#P[2]=[304.731977829656,45.619252330492046]; D=ab(1,2);
#A(2,1,Bew(1)); M(3,1,2,blauerWinkel); M(4,3,1,gruenerWinkel);
#M(5,3,4,orangerWinkel);
#M(6,5,3,360-36-blauerWinkel-gruenerWinkel-orangerWinkel); N(7,2,4); N(8,4,6);
#M(9,8,4,vierterWinkel); N(10,9,7);
#M(11,5,6,fuenfterWinkel); M(12,11,5,sechsterWinkel); N(13,6,12); N(14,13,9);
#M(15,14,9,siebenterWinkel); M(16,11,12,achterWinkel); N(17,12,15); N(18,17,16);
#M(19,1,2,neunterWinkel); M(20,19,1,zehnterWinkel);
#N(21,20,2); N(22,10,21); N(23,15,22);
#M(24,19,20,elfterWinkel);
#A(16,24,ab(24,16,[1,24]));
#N(47,18,23); N(48,41,46);
#RA(20,48); A(43,47);
#
#
#//Ende der Eingabe, weiter mit fedgeo:
p(12.35686802564576147745,9.34169018326715239198,P1)
p(12.21147567500315744837,10.33106426033538660647,P2)
p(11.41078266681821595796,9.01777276506900271613,P3)
p(11.52467949695230942098,10.01126534787242050584,P4)
p(10.41078268204908674477,9.01794729799331662434,P5)
p(10.87469729102828353007,9.90382721963940326759,P6)
p(12.25874054943606417112,9.33218186903757107586,P7)
p(11.35366796999893068687,9.02599631981507144474,P8)
p(10.88014286036421474080,9.90677663893297122399,P9)
p(11.82530846293556336946,10.23336810195051427286,P10)
p(9.85840915081988455881,9.85154401223670816989,P11)
p(10.32278754182777724679,10.73718090733814811699,P12)
p(9.87659535479032335559,9.84224374070200269671,P13)
p(10.32289882821320325945,10.73712541422687216652,P14)
p(10.88043267281045700656,9.90697120437872413845,P15)
p(9.32331937488840267747,10.69633921327279146851,P16)
p(11.32048916550858486119,10.80494129476827680492,P17)
p(10.32190427019849288115,10.75064025402053502489,P18)
p(13.30921060192559401969,9.64672070207583054469,P19)
p(12.78939325930488379868,10.50099813377512525392,P20)
p(12.76943696026074803740,9.50119728054061241096,P21)
p(12.78882712034571511595,10.50100927371326875459,P22)
p(11.82396608339619170636,10.23824858529757086956,P23)
p(13.66627467838415022072,10.58080059443129705699,P24)
p(10.63272602762679142074,11.93544962443693435716,P25)
p(10.77811837826939367346,10.94607554736870191903,P26)
p(11.57881138645433516388,12.25936704263508580937,P27)
p(11.46491455632024170086,11.26587445983166801966,P28)
p(12.57881137122346615342,12.25919250971077012480,P29)
p(12.11489676224426759177,11.37331258806468348155,P30)
p(10.73085350383648872707,11.94495793866651744963,P31)
p(11.63592608327362043497,12.25114348788901885712,P32)
p(12.10945119290833638104,11.37036316877111907786,P33)
p(11.16428559033698775238,11.04377170575357247628,P34)
p(13.13118490245267011574,11.42559579546737857925,P35)
p(12.66680651144477387504,10.53995890036594040851,P36)
p(13.11299869848222954261,11.43489606700208582879,P37)
p(12.66669522505934963874,10.54001439347721635897,P38)
p(12.10916138046209411527,11.37016860332536083433,P39)
p(11.66910488776396803701,10.47219851293581172058,P40)
p(12.66768978307406001704,10.52649955368355527696,P41)
p(9.68038345134695710215,11.63041910562825798081,P42)
p(10.20020079396766732316,10.77614167392896327158,P43)
p(10.22015709301180308444,11.77594252716347789089,P44)
p(10.20076693292683600589,10.77613053399081977091,P45)
p(11.16562796987635941548,11.03889122240651765594,P46)
p(11.26940562069565388015,11.07039201837228148406,P47)
p(11.72018843257689724169,10.20674778933180704144,P48)
nolabel()
s(P1,P2)
s(P1,P3)
s(P3,P4)
s(P3,P5)
s(P5,P6)
s(P2,P7) s(P4,P7)
s(P4,P8) s(P6,P8)
s(P8,P9)
s(P9,P10) s(P7,P10)
s(P5,P11)
s(P11,P12)
s(P6,P13) s(P12,P13)
s(P13,P14) s(P9,P14)
s(P14,P15)
s(P11,P16) s(P42,P16)
s(P12,P17) s(P15,P17)
s(P17,P18) s(P16,P18)
s(P1,P19)
s(P19,P20) s(P48,P20)
s(P20,P21) s(P2,P21)
s(P10,P22) s(P21,P22)
s(P15,P23) s(P22,P23)
s(P19,P24) s(P35,P24)
s(P25,P26)
s(P25,P27)
s(P27,P28)
s(P27,P29)
s(P29,P30)
s(P26,P31) s(P28,P31)
s(P28,P32) s(P30,P32)
s(P32,P33)
s(P31,P34) s(P33,P34)
s(P29,P35)
s(P35,P36)
s(P30,P37) s(P36,P37)
s(P33,P38) s(P37,P38)
s(P38,P39)
s(P36,P40) s(P39,P40)
s(P24,P41) s(P40,P41)
s(P25,P42)
s(P42,P43) s(P47,P43)
s(P26,P44) s(P43,P44)
s(P34,P45) s(P44,P45)
s(P39,P46) s(P45,P46)
s(P18,P47) s(P23,P47)
s(P41,P48) s(P46,P48)
pen(2)
color(#0000FF) m(P2,P1,MA10) m(P1,P3,MB10) b(P1,MA10,MB10) #blue
color(#008000) m(P1,P3,MA11) m(P3,P4,MB11) b(P3,MA11,MB11) #green
color(#FFA500) m(P4,P3,MA12) m(P3,P5,MB12) b(P3,MA12,MB12) #orange
color(#EE82EE) m(P4,P8,MA13) m(P8,P9,MB13) b(P8,MA13,MB13) #violet
color(#008080) m(P6,P5,MA14) m(P5,P11,MB14) b(P5,MA14,MB14) #teal
color(#00FF00) m(P5,P11,MA15) m(P11,P12,MB15) b(P11,MA15,MB15) #lime
color(#ADD8E6) m(P9,P14,MA16) m(P14,P15,MB16) f(P14,MA16,MB16) #LightBlue
color(#F08080) m(P12,P11,MA17) m(P11,P16,MB17) b(P11,MA17,MB17) #LightCoral
color(#E0FFFF) m(P2,P1,MA18) m(P1,P19,MB18) b(P1,MA18,MB18) #LightCyan
color(#FAFAD2) m(P1,P19,MA19) m(P19,P20,MB19) b(P19,MA19,MB19) #LightGoldenrodYellow
color(#90EE90) m(P20,P19,MA110) m(P19,P24,MB110) b(P19,MA110,MB110) #LightGreen
pen(2)
color(#32CD32) s(P20,P48) #LimeGreen
color(blue)
color(orange)
color(red)
\geooff
\geoprint()
|
Profil
|
haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 4639
| Beitrag No.1715, eingetragen 2019-02-15
|
einfach nur für, wenn mans könnte, also ich gab mir mühe fehler zu finden, zur nacht
halb verstanden evtl? ich such neue ansätze um anders neu puzzlen zu können
dazu wollte ich die vorhandenen anders darstellen, das war der grund des explosionsversuch
haribo
|
Profil
|
Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9212
Wohnort: Pferdehof
| Beitrag No.1716, vom Themenstarter, eingetragen 2019-02-15
|
Hier noch eine Idee. Leider zwei 2er Knoten außen.
46 Knoten, 2×Grad 2, 44×Grad 3, 0 Dreiecke, 0 Überschneidungen
68 Kanten, minimal 0.99668447319397479589, maximal 1.00335550827739816704
einzustellende Kanten, Abstände und Winkel:
|P20-P42|=0.99668447319397490691
|P22-P39|=1.00335550827739816704
nicht passende Kanten:
|P15-P46|=1.00335550827739794499
|P18-P44|=0.99668447319397479589
|P20-P42|=0.99668447319397490691
|P22-P39|=1.00335550827739816704
\geo
ebene(671.54,420.84)
x(9.24,15.09)
y(9.02,12.69)
form(.)
#//Eingabe war:
#
#...
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#P[1]=[307.3054546377688,-76.98978680527996];
#P[2]=[265.9206209552173,30.086309471088242]; D=ab(1,2);
#A(2,1,Bew(1)); M(3,1,2,blauerWinkel); M(4,3,1,gruenerWinkel);
#M(5,3,4,orangerWinkel);
#M(6,5,3,360-36-blauerWinkel-gruenerWinkel-orangerWinkel); N(7,2,4); N(8,4,6);
#M(9,8,4,vierterWinkel); N(10,9,7);
#M(11,5,6,fuenfterWinkel); M(12,11,5,sechsterWinkel); N(13,6,12); N(14,13,9);
#M(15,14,9,siebenterWinkel); M(16,11,12,achterWinkel); N(17,12,15); N(18,17,16);
#M(19,1,2,neunterWinkel); M(20,19,1,zehnterWinkel);
#N(21,20,2); N(22,10,21);
#M(23,19,20,elfterWinkel); M(24,16,18,zwölfterWinkel);
#A(23,24,ab(24,23,[1,24]));
#RA(20,42); A(18,44);
#RA(22,39); A(15,46);
#
#
#//Ende der Eingabe, weiter mit fedgeo:
p(12.67698293205490500668,9.32933066397009547188,P1)
p(12.31647356997830655700,10.26208625889039538492,P2)
p(11.72560333545414934520,9.02130978290554530474,P3)
p(11.79640441738967382435,10.01880023739458813736,P4)
p(10.72560333545414934520,9.02130978290554530474,P5)
p(10.98220511759035389332,9.98782699713637533989,P6)
p(12.46232789260107587381,9.27278018058487241149,P7)
p(11.42402101268980629811,9.09072125373849182495,P8)
p(11.04347808848304346441,10.01548451146241625054,P9)
p(12.03070060978328292833,10.17483222383256169508,P10)
p(9.94646794075742946006,9.64816545746771225822,P11)
p(10.20947421729353976616,10.61295957980812687538,P12)
p(10.05005763562446574610,9.62574817717495889724,P13)
p(10.23788274568127754094,10.60795066547976084337,P14)
p(11.05970662488373967847,10.03820904722406659459,P15)
p(9.23983669568442067543,10.35574745518004036171,P16)
p(11.11527475318550628458,11.03666394511231807485,P17)
p(10.20112881360807932651,10.63127869482056730988,P18)
p(13.59101414555425613173,9.73497452346867397921,P19)
p(12.99996518535517608939,10.54161020743485366324,P20)
p(13.01000575520977520227,9.54166061522682973361,P21)
p(12.96145341587094179658,10.54048125495386578621,P22)
p(14.08599547242830851701,10.60387813495040987277,P23)
p(10.02576185070079262118,10.97406909535810370926,P24)
p(11.43477439107419613151,12.24861656633841988651,P25)
p(11.79528375315079458119,11.31586097141811819711,P26)
p(12.38615398767495179300,12.55663744740297005364,P27)
p(12.31535290573942553749,11.55914699291392544467,P28)
p(13.38615398767495179300,12.55663744740296827729,P29)
p(13.12955220553874724487,11.59012023317214001850,P30)
p(11.64942943052802526438,12.30516704972364294690,P31)
p(12.68773631043929484008,12.48722597657002353344,P32)
p(13.06827923464605767379,11.56246271884609910785,P33)
p(12.08105671334581643350,11.40311500647595188696,P34)
p(14.16528938237167167813,11.92978177284080310017,P35)
p(13.90228310583556137203,10.96498765050038848301,P36)
p(14.06169968750463539209,11.95219905313355646115,P37)
p(13.87387457744782359725,10.96999656482875273866,P38)
p(13.05205069824536145973,11.53973818308444876379,P39)
p(14.87192062744468046276,11.22219977512847499668,P40)
p(12.99648256994359485361,10.54128328519619728354,P41)
p(13.91062850952102181168,10.94666853548794627216,P42)
p(10.52074317757484500646,11.84297270683983960282,P43)
p(11.11179213777392327245,11.03633702287365991879,P44)
p(11.10175156791932593592,12.03628661508168384842,P45)
p(11.15030390725815934161,11.03746597535464779583,P46)
nolabel()
s(P1,P2)
s(P1,P3)
s(P3,P4)
s(P3,P5)
s(P5,P6)
s(P2,P7) s(P4,P7)
s(P4,P8) s(P6,P8)
s(P8,P9)
s(P9,P10) s(P7,P10)
s(P5,P11)
s(P11,P12)
s(P6,P13) s(P12,P13)
s(P13,P14) s(P9,P14)
s(P14,P15) s(P46,P15)
s(P11,P16)
s(P12,P17) s(P15,P17)
s(P17,P18) s(P16,P18) s(P44,P18)
s(P1,P19)
s(P19,P20) s(P42,P20)
s(P20,P21) s(P2,P21)
s(P10,P22) s(P21,P22) s(P39,P22)
s(P19,P23) s(P40,P23)
s(P16,P24) s(P43,P24)
s(P25,P26)
s(P25,P27)
s(P27,P28)
s(P27,P29)
s(P29,P30)
s(P26,P31) s(P28,P31)
s(P28,P32) s(P30,P32)
s(P32,P33)
s(P31,P34) s(P33,P34)
s(P29,P35)
s(P35,P36)
s(P30,P37) s(P36,P37)
s(P33,P38) s(P37,P38)
s(P38,P39)
s(P35,P40)
s(P36,P41) s(P39,P41)
s(P40,P42) s(P41,P42)
s(P25,P43)
s(P43,P44)
s(P26,P45) s(P44,P45)
s(P34,P46) s(P45,P46)
pen(2)
color(#0000FF) m(P2,P1,MA10) m(P1,P3,MB10) b(P1,MA10,MB10) #blue
color(#008000) m(P1,P3,MA11) m(P3,P4,MB11) b(P3,MA11,MB11) #green
color(#FFA500) m(P4,P3,MA12) m(P3,P5,MB12) b(P3,MA12,MB12) #orange
color(#EE82EE) m(P4,P8,MA13) m(P8,P9,MB13) b(P8,MA13,MB13) #violet
color(#008080) m(P6,P5,MA14) m(P5,P11,MB14) b(P5,MA14,MB14) #teal
color(#00FF00) m(P5,P11,MA15) m(P11,P12,MB15) b(P11,MA15,MB15) #lime
color(#ADD8E6) m(P9,P14,MA16) m(P14,P15,MB16) f(P14,MA16,MB16) #LightBlue
color(#F08080) m(P12,P11,MA17) m(P11,P16,MB17) b(P11,MA17,MB17) #LightCoral
color(#E0FFFF) m(P2,P1,MA18) m(P1,P19,MB18) b(P1,MA18,MB18) #LightCyan
color(#FAFAD2) m(P1,P19,MA19) m(P19,P20,MB19) b(P19,MA19,MB19) #LightGoldenrodYellow
color(#90EE90) m(P20,P19,MA110) m(P19,P23,MB110) b(P19,MA110,MB110) #LightGreen
color(#D3D3D3) m(P18,P16,MA111) m(P16,P24,MB111) f(P16,MA111,MB111) #LightGray
pen(2)
color(#32CD32) s(P20,P42) #LimeGreen
color(#32CD32) s(P22,P39) #LimeGreen
color(blue)
color(orange)
color(red)
\geooff
\geoprint()
|
Profil
|
Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9212
Wohnort: Pferdehof
| Beitrag No.1717, vom Themenstarter, eingetragen 2019-02-16
|
Hier eine Variante des #1716 mit zwei 1er oder zwei 2er außen.
50 Knoten, 2×Grad 1, 48×Grad 3, 0 Dreiecke, 0 Überschneidungen
73 Kanten, minimal 0.99999999999999733546, maximal 1.00000000000000244249
einzustellende Kanten, Abstände und Winkel:
|P49-P50|=1.00000000000000044409
|P20-P42|=0.99999999999999955591
\geo
ebene(768.8,415.72)
x(9.3,15.3)
y(9.19,12.43)
form(.)
#//Eingabe war:
#
#3-regular matchstick graph with girth 5 with 54 vertices.
#This graph is flexible and has a point symmetry.
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#P[1]=[355.58899843524534,-89.8916318376396];
#P[2]=[309.816679865233,29.977770566961574]; D=ab(1,2);
#A(2,1,Bew(1)); M(3,1,2,blauerWinkel); M(4,3,1,gruenerWinkel);
#M(5,3,4,orangerWinkel);
#M(6,5,3,360-36-blauerWinkel-gruenerWinkel-orangerWinkel); N(7,2,4); N(8,4,6);
#M(9,8,4,vierterWinkel); N(10,9,7);
#M(11,5,6,fuenfterWinkel); M(12,11,5,sechsterWinkel); N(13,6,12); N(14,13,9);
#M(15,14,9,siebenterWinkel); M(16,11,12,achterWinkel); N(17,12,15); N(18,17,16);
#M(19,1,2,neunterWinkel); M(20,19,1,zehnterWinkel);
#N(21,20,2);
#M(22,19,20,elfterWinkel); M(23,16,18,zwölfterWinkel);
#M(24,22,19,dreizehnterWinkel);
#A(23,22,ab(22,23,[1,24]));
#N(47,21,39); N(48,45,15); N(49,48,10); N(50,47,34);
#RA(49,50);
#RA(20,42); A(18,44);
#
#
#
#//Ende der Eingabe, weiter mit fedgeo:
p(12.77130008380852643768,9.29942521298025681631,P1)
p(12.41457130185132662348,10.23363320701763079512,P2)
p(11.77740582845793149147,9.18908841412744159527,P3)
p(11.68486145567486822472,10.18479697543752138245,P4)
p(10.77740582845793149147,9.18908841412744159527,P5)
p(11.03791986294078419917,10.15455847468730432581,P6)
p(12.11186790647061783943,9.28054839734695313780,P7)
p(11.40556461674528421213,9.22459216615778210269,P8)
p(11.04407417093454846224,10.15696797965122222251,P9)
p(12.03675644350759199597,10.27772354150747169399,P10)
p(10.02213048272695417040,9.84449603700876885171,P11)
p(10.26710901928430708097,10.81402453923354478604,P12)
p(10.09224962090718946683,9.82943112528076312628,P13)
p(10.28699045706491865815,10.81028585801777097686,P14)
p(11.06597587307627783559,10.18324381665083855353,P15)
p(9.30364676689150016387,10.54003981714002691206,P16)
p(11.19998432977458691084,11.17422400491563649894,P17)
p(10.25838134302516202467,10.83749887169186898461,P18)
p(13.75371975397168533561,9.48611102303691389181,P19)
p(13.20572672993470142444,10.32259392519738483429,P20)
p(12.91265411404731011658,9.36650374021642662115,P21)
p(14.38926674129830551863,10.25817321412002591785,P22)
p(10.01487515206681955249,11.24300082894715835380,P23)
p(13.42582044718516165460,9.99027166810050282209,P24)
p(11.63284180955659863343,12.20174883008692745534,P25)
p(11.98957059151379844764,11.26754083604955525288,P26)
p(12.62673606490719357964,12.31208562893974445274,P27)
p(12.71928043769025684639,11.31637706762966111285,P28)
p(13.62673606490719535600,12.31208562893974267638,P29)
p(13.36622203042434087195,11.34661556837987994584,P30)
p(12.29227398689450723168,12.22062564572022935749,P31)
p(12.99857727661984085898,12.27658187690940216896,P32)
p(13.36006772243057660887,11.34420606341596382549,P33)
p(12.36738544985753307515,11.22345050155971257766,P34)
p(14.38201141063817090071,11.65667800605841364359,P35)
p(14.13703287408081621379,10.68714950383363948561,P36)
p(14.31189227245793560428,11.67174291778641936901,P37)
p(14.11715143630020641297,10.69088818504941329479,P38)
p(13.33816602028884723552,11.31793022641634571812,P39)
p(15.10049512647362490725,10.96113422592715735959,P40)
p(13.20415756359053816027,10.32695003815154599636,P41)
p(14.14576055033996304644,10.66367517137531351068,P42)
p(10.65042213939343973550,12.01506302003027037983,P43)
p(11.19841516343042364667,11.17858011786980121371,P44)
p(11.49148777931781317818,12.13467030285075765050,P45)
p(10.97832144617996341651,11.51090237496668144956,P46)
p(13.07446715995044606018,10.35332517197373825013,P47)
p(11.32967473341467901093,11.14784887109344779788,P48)
p(12.32586818154745067488,11.23501889975777245922,P49)
p(12.07827371181767439623,10.26615514330941003607,P50)
nolabel()
s(P1,P2)
s(P1,P3)
s(P3,P4)
s(P3,P5)
s(P5,P6)
s(P2,P7) s(P4,P7)
s(P4,P8) s(P6,P8)
s(P8,P9)
s(P9,P10) s(P7,P10)
s(P5,P11)
s(P11,P12)
s(P6,P13) s(P12,P13)
s(P13,P14) s(P9,P14)
s(P14,P15)
s(P11,P16)
s(P12,P17) s(P15,P17)
s(P17,P18) s(P16,P18) s(P44,P18)
s(P1,P19)
s(P19,P20) s(P42,P20)
s(P20,P21) s(P2,P21)
s(P19,P22) s(P40,P22)
s(P16,P23) s(P43,P23)
s(P22,P24)
s(P25,P26)
s(P25,P27)
s(P27,P28)
s(P27,P29)
s(P29,P30)
s(P26,P31) s(P28,P31)
s(P28,P32) s(P30,P32)
s(P32,P33)
s(P31,P34) s(P33,P34)
s(P29,P35)
s(P35,P36)
s(P30,P37) s(P36,P37)
s(P33,P38) s(P37,P38)
s(P38,P39)
s(P35,P40)
s(P36,P41) s(P39,P41)
s(P40,P42) s(P41,P42)
s(P25,P43)
s(P43,P44)
s(P26,P45) s(P44,P45)
s(P23,P46)
s(P21,P47) s(P39,P47)
s(P45,P48) s(P15,P48)
s(P48,P49) s(P10,P49) s(P50,P49)
s(P47,P50) s(P34,P50)
pen(2)
color(#0000FF) m(P2,P1,MA10) m(P1,P3,MB10) b(P1,MA10,MB10) #blue
color(#008000) m(P1,P3,MA11) m(P3,P4,MB11) b(P3,MA11,MB11) #green
color(#FFA500) m(P4,P3,MA12) m(P3,P5,MB12) b(P3,MA12,MB12) #orange
color(#EE82EE) m(P4,P8,MA13) m(P8,P9,MB13) b(P8,MA13,MB13) #violet
color(#008080) m(P6,P5,MA14) m(P5,P11,MB14) b(P5,MA14,MB14) #teal
color(#00FF00) m(P5,P11,MA15) m(P11,P12,MB15) b(P11,MA15,MB15) #lime
color(#ADD8E6) m(P9,P14,MA16) m(P14,P15,MB16) f(P14,MA16,MB16) #LightBlue
color(#F08080) m(P12,P11,MA17) m(P11,P16,MB17) b(P11,MA17,MB17) #LightCoral
color(#E0FFFF) m(P2,P1,MA18) m(P1,P19,MB18) b(P1,MA18,MB18) #LightCyan
color(#FAFAD2) m(P1,P19,MA19) m(P19,P20,MB19) b(P19,MA19,MB19) #LightGoldenrodYellow
color(#90EE90) m(P20,P19,MA110) m(P19,P22,MB110) b(P19,MA110,MB110) #LightGreen
color(#D3D3D3) m(P18,P16,MA111) m(P16,P23,MB111) f(P16,MA111,MB111) #LightGray
color(#FFB6C1) m(P19,P22,MA112) m(P22,P24,MB112) b(P22,MA112,MB112) #LightPink
pen(2)
color(#32CD32) s(P49,P50) #LimeGreen
color(#32CD32) s(P20,P42) #LimeGreen
color(blue)
color(orange)
color(red)
\geooff
\geoprint()
|
Profil
|
StefanVogel
Senior
Dabei seit: 26.11.2005
Mitteilungen: 4328
Wohnort: Raun
| Beitrag No.1718, eingetragen 2019-02-16
|
Im #1714 (siehe nächster Graph) lassen sich die Knoten P20 und P22 nicht ohne Überschneidung auseinanderbringen, weil beide Punkte nach unten mit P21 verbunden sind. Die von P22 nach links abzweigende Kante müsste oberhalb P20 vorbeigehen, was mit dem restlichen Graph vermutlich nicht zu machen geht.
Winkel(P3,P5,P6) (Eingabe M(6,5,3...)) kann als beliebig veränderbarer Winkel eingegeben werden. Das ist ein "Dauerfehler", der schon in etlichen Graphen seit #1630-2 enthalten ist. Dort war das berechtigt, weil insgesamt ein symmetrisches 20-Eck herauskommen sollte. Bei anderen Graphen büßt man dadurch eine Bewegungsmöglichkeit ein. Beim Zurechtziehen der anderen Graphen hatte ich das ausgetauscht, aber wie das bei Kopieren so ist, der Fehler taucht immer wieder neu auf ;-)
48 Knoten, 48×Grad 3, 0 Dreiecke, 8? Überschneidungen
72 Kanten, minimal 0.99999999999999478195, maximal 1.10895546651046283948
einzustellende Kanten, Abstände und Winkel:
|P20-P48|=1.10895546651046283948
nicht passende Kanten:
|P20-P48|=1.10895546651046283948
|P43-P47|=1.10895546651046283948
$
%Eingabe war:
%
%3-reg. girth 5 mit 48 Knoten Versuch
%
%
%
%
%
%
%
%
%
%
%
%
%
%P[1]=[150.52526016508824,38.77211799907823];
%P[2]=[133.57119966293163,154.14206619609894]; D=ab(1,2);
%A(2,1,Bew(1)); M(3,1,2,blauerWinkel); M(4,3,1,gruenerWinkel);
%M(5,3,4,orangerWinkel);
%M(6,5,3,360-36-blauerWinkel-gruenerWinkel-orangerWinkel); N(7,2,4); N(8,4,6);
%M(9,8,4,vierterWinkel); N(10,9,7);
%M(11,5,6,fuenfterWinkel); M(12,11,5,sechsterWinkel); N(13,6,12); N(14,13,9);
%M(15,14,9,siebenterWinkel); M(16,11,12,achterWinkel); N(17,12,15); N(18,17,16);
%M(19,1,2,neunterWinkel); M(20,19,1,zehnterWinkel);
%N(21,20,2); N(22,10,21); N(23,15,22);
%M(24,19,20,elfterWinkel);
%A(16,24,ab(24,16,[1,24]));
%N(47,18,23); N(48,41,46);
%RA(20,48); A(43,47);
%
%
%Ende der Eingabe.
\usetikzlibrary{spy}
\tikzset{SpyStyle/.style={spy using outlines={rectangle, magnification=3, width=2cm, height=2cm, connect spies, blue!70!black}}}
\begin{tikzpicture}[SpyStyle,draw=grey,font=\sffamily\tiny]
\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{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 {
1/6.067/0.648,
2/5.78/2.63,
3/4.175/0.000,
4/4.40/1.99,
5/2.17/0.00,
6/3.1028/1.7721,
7/5.871/0.629,
8/4.061/0.016,
9/3.11365/1.77801,
10/5.0040/2.4312,
11/1.070/1.668,
12/1.99894/3.43882,
13/1.107/1.649,
14/1.99916/3.43871,
15/3.11423/1.77840,
16/0.00/3.36,
17/3.99/3.57,
18/1.997/3.466,
19/7.97/1.26,
20/6.93215/2.96645,
21/6.89/0.97,
22/6.93102/2.96647,
23/5.0013/2.4410,
24/8.69/3.13,
25/2.619/5.835,
26/2.91/3.86,
27/4.511/6.483,
28/4.28/4.50,
29/6.51/6.48,
30/5.5832/4.7111,
31/2.815/5.854,
32/4.625/6.467,
33/5.57226/4.70518,
34/3.6819/4.0520,
35/7.616/4.816,
36/6.68697/3.04437,
37/7.579/4.834,
38/6.68675/3.04448,
39/5.57168/4.70479,
40/4.69/2.91,
41/6.689/3.017,
42/0.71/5.23,
43/1.75376/3.51674,
44/1.79/5.52,
45/1.75490/3.51672,
46/3.6846/4.0422,
47/3.89/4.11,
48/4.79/2.38}
\coordinate (p-\i) at (\x,\y);
%Fläche als \fill[Yellow!3] (p-1) -- (p-2) -- (p-3) -- cycle;
%Dreiecke als \fill[black!3] (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 {
1/98.36/198.90/0.4/Blue,
3/18.90/83.46/0.4/Green,
3/83.46/179.99/0.3/Orange,
8/80.15/118.26/0.4/Violet,
5/62.36/123.53/0.4/Teal,
11/303.53/422.33/0.4/Lime,
14/303.87/303.89/0.4/LightBlue,
11/62.33/122.35/0.3/LightCoral,
1/98.36/377.76/0.3/LightCyan,
19/197.76/481.32/0.4/LightGoldenrodYellow,
19/121.32/429.08/0.3/LightGreen}
\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-48);
%Kanten als \draw[line width=0] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1,
4/3,
5/3,
6/5,
7/2, 7/4,
8/4, 8/6,
9/8,
10/9, 10/7,
11/5,
12/11,
13/6, 13/12,
14/13, 14/9,
15/14,
16/11, 16/42,
17/12, 17/15,
18/17, 18/16,
19/1,
20/19, 20/48,
21/20, 21/2,
22/10, 22/21,
23/15, 23/22,
24/19, 24/35,
26/25,
27/25,
28/27,
29/27,
30/29,
31/26, 31/28,
32/28, 32/30,
33/32,
34/31, 34/33,
35/29,
36/35,
37/30, 37/36,
38/33, 38/37,
39/38,
40/36, 40/39,
41/24, 41/40,
42/25,
43/42, 43/47,
44/26, 44/43,
45/34, 45/44,
46/39, 46/45,
47/18, 47/23,
48/41, 48/46}
\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);
%\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-20) -- (p-48);
%\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-43) -- (p-47);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/98.36/198.90/0.4/Blue,
3/18.90/83.46/0.4/Green,
3/83.46/179.99/0.3/Orange,
8/80.15/118.26/0.4/Violet,
5/62.36/123.53/0.4/Teal,
11/303.53/422.33/0.4/Lime,
14/303.87/303.89/0.4/LightBlue,
11/62.33/122.35/0.3/LightCoral,
1/98.36/377.76/0.3/LightCyan,
19/197.76/481.32/0.4/LightGoldenrodYellow,
19/121.32/429.08/0.3/LightGreen}
{
\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 {
1/241,
2/291,
3/234,
4/291,
5/275,
6/93,
7/287,
8/282,
9/161,
10/158,
11/275,
12/65,
13/216,
14/96,
15/276,
16/155,
17/36,
18/193,
19/342,
20/55,
21/109,
22/155,
23/252,
24/335,
25/61,
26/111,
27/54,
28/111,
29/95,
30/273,
31/107,
32/102,
33/341,
34/338,
35/95,
36/245,
37/36,
38/276,
39/96,
40/216,
41/13,
42/162,
43/235,
44/289,
45/235,
46/72,
47/74,
48/254}
\node[anchor=\a] (P\i) at (p-\i) {\i};
%Vergrößerungen als \spy[rectangle, magnification=3, width=2cm, h eight=2cm, blue!70!black] on (p-18) in node at (2.5 cm,-2);
\spy[magnification=300] on (p-20) in node at (11,3);
\end{tikzpicture}
$
\quoteon(2019-02-11 00:45 - Slash in Beitrag No. 1708)
Ich denke da bei einer Veröffentlichung an den minimalsten Graphen mit guter Sichtbarkeit der Abstände und einem Hinweis auf die möglichen Formen mit kleinen Bildchen.
\quoteoff
Gute Sichtbarkeit der Abstände ist akzeptabel, mit gelegentlichen \spy-Fenstern bei schwer zu vergrößernden Abständen. Auch haribo hat mit der Explosionsdarstellung #1712-2 die Abstände wieder sichtbar gemacht.
Also die neueste Version Streichholzgraph-1554.htm jetzt mit Flächenberechnung:
54 Knoten, 54×Grad 3, 0 Dreiecke, 0 Überschneidungen, Fläche=14.54
81 Kanten, minimal 0.99999999999999888978, maximal 1.00000000000000155431
$
%Eingabe war:
%
%#1701-3 3x verbessert
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%P[1]=[179.05395344548333,75.30358941332679];
%P[2]=[137.36192104455023,150.07931323413771]; D=ab(1,2);
%A(2,1,Bew(1)); M(3,1,2,blauerWinkel); M(4,3,1,gruenerWinkel);
%M(5,3,4,orangerWinkel);
%M(6,5,3,dreizehnterWinkel); N(7,2,4); N(8,4,6);
%M(9,8,4,vierterWinkel); N(10,9,7);
%M(11,5,6,fuenfterWinkel); M(12,11,5,sechsterWinkel); N(13,6,12); N(14,13,9);
%M(15,14,9,siebenterWinkel); M(16,11,12,achterWinkel); N(17,12,15); N(18,17,16);
%M(19,1,2,blauerWinkel-180); M(20,19,1,zehnterWinkel);
%N(21,20,2); N(22,10,21); N(23,15,22); N(24,18,23);
%M(25,19,20,elfterWinkel); M(26,25,19,zwölfterWinkel);
%A(16,26,ab(26,16,[1,26]));
%N(51,24,50); N(52,45,51); N(53,49,25); N(54,20,53);
%RA(52,54);
%
%RW(16,11,5,11,180);
%RW(16,18,17,18,178);
%R(50,18,"brown",1.06*D);
%R(23,20,"brown",1.06*D);
%RW(2,22,10,22,2);
%R(50,14,"brown",1.18*D);
%RW(13,12,11,12,2);
%R(15,24,"brown",1.20*D);
%RW(7,3,1,3,2);
%R(50,12,"brown",1.12*D);
%RW(8,5,3,5);
%
%
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/5.08/1.02,
2/4.35/2.33,
3/3.82/0.22,
4/3.54/1.69,
5/2.33/0.00,
6/2.618/1.472,
7/4.82/0.91,
8/3.41/0.20,
9/2.730/1.535,
10/4.07/2.21,
11/1.166/0.944,
12/1.412/2.424,
13/1.217/0.936,
14/1.510/2.408,
15/2.83/1.69,
16/0.00/1.89,
17/2.71/3.18,
18/1.364/2.513,
19/6.34/1.83,
20/5.430/3.021,
21/5.62/1.53,
22/5.341/3.007,
23/3.86/2.78,
24/2.524/3.464,
25/6.38/3.33,
26/6.42/4.83,
27/1.34/5.69,
28/2.07/4.38,
29/2.60/6.50,
30/2.87/5.03,
31/4.09/6.72,
32/3.798/5.247,
33/1.59/5.81,
34/3.01/6.52,
35/3.686/5.184,
36/2.35/4.51,
37/5.251/5.775,
38/5.005/4.295,
39/5.199/5.782,
40/4.907/4.311,
41/3.59/5.03,
42/3.71/3.53,
43/5.053/4.206,
44/0.07/4.89,
45/0.987/3.698,
46/0.80/5.19,
47/1.076/3.712,
48/2.56/3.94,
49/3.893/3.255,
50/0.04/3.39,
51/1.306/2.589,
52/2.477/3.526,
53/5.111/4.130,
54/3.940/3.193}
\coordinate (p-\i) at (\x,\y);
%Fläche als \fill[Yellow!3] (p-1) -- (p-2) -- (p-3) -- cycle;
\fill[yellow!3] (p-5) -- (p-11) -- (p-16) -- (p-50) -- (p-44) -- (p-27) -- (p-29) -- (p-31) -- (p-37) -- (p-26) -- (p-25) -- (p-19) -- (p-1) -- (p-3) -- cycle;
%Dreiecke als \fill[black!3] (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;
%Punkte als \fill[red] (p-1) circle (1.125pt)
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
%Kanten als \draw[line width=0] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1,
4/3,
5/3,
6/5,
7/2, 7/4,
8/4, 8/6,
9/8,
10/9, 10/7,
11/5,
12/11,
13/6, 13/12,
14/13, 14/9,
15/14,
16/11, 16/50,
17/12, 17/15,
18/17, 18/16,
19/1,
20/19,
21/20, 21/2,
22/10, 22/21,
23/15, 23/22,
24/18, 24/23,
25/19,
26/25, 26/37,
28/27,
29/27,
30/29,
31/29,
32/31,
33/28, 33/30,
34/30, 34/32,
35/34,
36/33, 36/35,
37/31,
38/37,
39/32, 39/38,
40/35, 40/39,
41/40,
42/38, 42/41,
43/26, 43/42,
44/27,
45/44,
46/28, 46/45,
47/36, 47/46,
48/41, 48/47,
49/43, 49/48,
50/44,
51/24, 51/50,
52/45, 52/51, 52/54,
53/49, 53/25,
54/20, 54/53}
\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);
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\end{tikzpicture}
$
54 Knoten, 54×Grad 3, 0 Dreiecke, 0 Überschneidungen, Fläche=13.84
81 Kanten, minimal 0.99999999999999811262, maximal 1.00000000000000133227
$
%Eingabe war:
%
%#1701-3 auf minimale Fläche bringen
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%P[1]=[178.0663930604487,118.22968175109817];
%P[2]=[137.8836806041677,190.2984017431386]; D=ab(1,2);
%A(2,1,Bew(1)); M(3,1,2,blauerWinkel); M(4,3,1,gruenerWinkel);
%M(5,3,4,orangerWinkel);
%M(6,5,3,dreizehnterWinkel); N(7,2,4); N(8,4,6);
%M(9,8,4,vierterWinkel); N(10,9,7);
%M(11,5,6,fuenfterWinkel); M(12,11,5,sechsterWinkel); N(13,6,12); N(14,13,9);
%M(15,14,9,siebenterWinkel); M(16,11,12,achterWinkel); N(17,12,15); N(18,17,16);
%M(19,1,2,neunterWinkel); M(20,19,1,zehnterWinkel);
%N(21,20,2); N(22,10,21); N(23,15,22); N(24,18,23);
%M(25,19,20,elfterWinkel); M(26,25,19,zwölfterWinkel);
%A(16,26,ab(26,16,[1,26]));
%N(51,24,50); N(52,45,51); N(53,49,25); N(54,20,53);
%RA(52,54);
%
%//RW(16,11,5,11,180);
%RW(21,1,19,1,0.88358631315956026597);
%RW(16,18,17,18,178);
%R(50,18,"brown",1.02*D);
%R(23,20,"brown",1.02*D);
%RW(2,22,10,22,2);
%R(50,14,"brown",1.06*D);
%RW(13,12,11,12,2);
%R(15,24,"brown",1.12*D);
%RW(7,3,1,3,2);
%R(50,12,"brown",1.04*D);
%R(7,23,"darkred",1.02*D);
%RW(8,5,3,5,0.2);
%
%
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/5.814/1.853,
2/5.08/3.16,
3/5.20/0.48,
4/4.25/1.65,
5/3.78/0.00,
6/3.510/1.475,
7/5.742/1.816,
8/4.21/0.15,
9/3.5902/1.5145,
10/4.523/2.689,
11/2.351/0.454,
12/2.119/1.936,
13/2.403/0.463,
14/2.153/1.942,
15/3.5919/1.5202,
16/0.95/0.99,
17/3.21/2.97,
18/2.095/1.961,
19/6.91/2.88,
20/5.659/3.714,
21/6.37/2.39,
22/5.632/3.699,
23/4.502/2.712,
24/3.06/3.11,
25/6.26/4.23,
26/5.96/5.70,
27/1.093/4.841,
28/1.82/3.53,
29/1.71/6.21,
30/2.65/5.05,
31/3.13/6.69,
32/3.397/5.219,
33/1.164/4.879,
34/2.70/6.55,
35/3.3163/5.1799,
36/2.384/4.005,
37/4.555/6.240,
38/4.788/4.758,
39/4.504/6.231,
40/4.754/4.752,
41/3.3147/5.1742,
42/3.70/3.72,
43/4.811/4.733,
44/0.00/3.81,
45/1.248/2.981,
46/0.54/4.30,
47/1.274/2.995,
48/2.404/3.982,
49/3.85/3.58,
50/0.65/2.46,
51/2.071/1.982,
52/2.70/3.34,
53/4.836/4.712,
54/4.20/3.35}
\coordinate (p-\i) at (\x,\y);
%Fläche als \fill[yellow!3] (p-1) -- (p-2) -- (p-3) -- cycle;
\fill[yellow!3] (p-5) -- (p-11) -- (p-16) -- (p-50) -- (p-44) -- (p-27) -- (p-29) -- (p-31) -- (p-37) -- (p-26) -- (p-25) -- (p-19) -- (p-1) -- (p-3) -- cycle;
%Dreiecke als \fill[black!3] (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;
%Punkte als \fill[red] (p-1) circle (1.125pt)
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
%Kanten als \draw[line width=0] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1,
4/3,
5/3,
6/5,
7/2, 7/4,
8/4, 8/6,
9/8,
10/9, 10/7,
11/5,
12/11,
13/6, 13/12,
14/13, 14/9,
15/14,
16/11, 16/50,
17/12, 17/15,
18/17, 18/16,
19/1,
20/19,
21/20, 21/2,
22/10, 22/21,
23/15, 23/22,
24/18, 24/23,
25/19,
26/25, 26/37,
28/27,
29/27,
30/29,
31/29,
32/31,
33/28, 33/30,
34/30, 34/32,
35/34,
36/33, 36/35,
37/31,
38/37,
39/32, 39/38,
40/35, 40/39,
41/40,
42/38, 42/41,
43/26, 43/42,
44/27,
45/44,
46/28, 46/45,
47/36, 47/46,
48/41, 48/47,
49/43, 49/48,
50/44,
51/24, 51/50,
52/45, 52/51, 52/54,
53/49, 53/25,
54/20, 54/53}
\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);
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\end{tikzpicture}
$
Außerdem neu eine geänderte Funktionsweise von Button "Feinjustieren(n)": Bisher wurden die ersten n Bedingungen mit den ersten n beweglichen Winkeln eingestellt. Gelegentlich musste man dazu die Reihenfolge der beweglichen Winkel ändern, um n geeignete Winkel bereitzustellen. Beispiel, im folgenden Graph ist als erster einzustellender Abstand |P5-P2| eingegeben und als erster Winkel der blaue Winkel. "Feinjustieren(1)" benötigt aber den grünen Winkel als ersten Winkel, weil der blaue Winkel keinen Einfluss auf |P5-P2| hat.
5 Knoten, 2×Grad 2, 2×Grad 3, 1×Grad 4, 3 Dreiecke, 0 Überschneidungen, Fläche=1.29
7 Kanten, minimal 0.84523652348139877155, maximal 1.14715287270209209680
einzustellende Kanten, Abstände und Winkel:
|P5-P2|=0.84523652348139877155
|P4-P3|=1.14715287270209209680
nicht passende Kanten:
|P4-P3|=1.14715287270209209680
|P5-P2|=0.84523652348139877155
$
%Eingabe war:
%
%Feinjustieren(w,b)
%
%
%
%
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); M(4,1,3,blauerWinkel), M(5,3,2,gruenerWinkel); RA(5,2); RA(4,3);
%
%
%
%
%
%
%
%
%
%
%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}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.93/0.00,
2/4.93/0.00,
3/3.43/2.60,
4/0.00/2.30,
5/6.38/2.08}
\coordinate (p-\i) at (\x,\y);
%Fläche als \fill[Yellow!3] (p-1) -- (p-2) -- (p-3) -- cycle;
%Dreiecke als \fill[black!3] (p-1) -- (p-2) -- (p-3) -- cycle;
\foreach \i/\j/\k in {
2/1/3,
3/1/4,
3/2/5}
\fill[black!3] (p-\i) -- (p-\j) --(p-\k) -- 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 {
1/60.00/130.00/0.4/Blue,
3/300.00/350.00/0.4/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,
4/1, 4/3,
5/3, 5/2}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,5}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-5) -- (p-2);
\draw[LimeGreen,very thick] (p-4) -- (p-3);
%Kanten als \draw[line width=0] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1, 3/2,
4/1, 4/3,
5/3, 5/2}
\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);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-4) -- (p-3);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-5) -- (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 {
1/60.00/130.00/0.4/Blue,
3/300.00/350.00/0.4/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,
2/330,
3/90,
4/338,
5/23}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
$
Bei den 4-regulären Graphen kam es eher selten zu dieser Situation, weil sowieso zuwenig einstellbare Winkel waren. Bei 3-regulären Graphen gibt es bewegliche Winkel im Überfluss, da kommt man schon ins Suchen, um einen geeigneten Winkel zu finden. Deshalb verwendet Button "Feinjustieren(n)" ab jetzt alle verfügbaren Winkel zum Einstellen, im obigen Beispiel den grünen Winkel auch mit. Klar, das hat höheren Rechenaufwand zur Folge. Dafür ist das Suchen nicht mehr notwendig.
Die alte Funktionsweise kann in der Eingabe im xml-Element Feinjustieren mit dem Attribut Anzahl="n,m" eingestellt werden. Dann werden die ersten n Bedingungen nur mit den ersten m beweglichen Winkeln eingestellt. Anzahl="n" dagegen stellt ab jetzt die ersten n Bedingungen mit allen verfügbaren beweglichen Winkeln ein.
Ein umfangreiches Testbeispiel für diese neue Funktionsweise folgt noch, dauert etwas mit dem Eintippen.
|
Profil
|
StefanVogel
Senior
Dabei seit: 26.11.2005
Mitteilungen: 4328
Wohnort: Raun
| Beitrag No.1719, eingetragen 2019-02-17
|
Testbeispiel beziehungsweise Anwendung, wo die neue Funktion recht nützlich und sogar notwendig geworden ist:
\quoteon(2019-02-03 11:47 - haribo in Beitrag No. 1683)
https://www.matheplanet.com/matheplanet/nuke/html/uploads/b/35059_dreier-girth5-1649-abgewickelt.png
gummibandtechnisch-programmatisch-a-la-vogel könnte man also doch wohl damit starten, innen die drei (bzw sechs) vermassten 1-langen gummis spannen und aussen drei 0-lange extra starke gummis obenherum zwischen A-A B-B C-C setzen und dann die innere dunklerblaue fläche nachdem sie sich aneinandergelegt hat miteinander verschmelzen, (ok diese dunkelblaue aussenkannte muss wohl dabei auch elastisch nachgeben?... also wohl auch aus gummielementen bestehen... wie lang die jetzt dann sein sollen ist entweder egal oder auch nicht...)
\quoteoff
Es ist bestimmt erlaubt, gleich mit einem regelmäßigen 16-Eck zu beginnen, abwechselnd mit je 3 M's im Inneren gefolgt von einem Haus mit Antenne auf dem Dach. Damit noch genug Platz bleibt, habe ich die Außenkanten mit Länge 2 eingegeben, und zwar so, dass Button "Feinjustieren(1)" diese Kanten nicht in einem einzigen Schritt auf Länge 1 bringt, sondern allmählich (in hundert Schritten) mit zusätzlicher Ausgabe "Ziehfaktor=0.00" bis "1.00" in 0.01 -Schritten. Die weiteren Einzelheiten zur Eingabe (jam()-Funktion) sind nicht so wichtig. Wie das gemeint ist, am besten im Streichholzprogramm anschauen (folgenden Graph ins große Eingabefenste kopieren und dann Button "neu zeichnen" gefolgt von "Feinjustieren(1)" drücken). Kleine Einschränkung noch, der Graph ist bereits symmetrisch eingegeben, die Winkel zu gegenüberliegenden Randpunkten sind gleich.
64 Knoten, 16×Grad 1, 48×Grad 3, 0 Dreiecke, 0 Überschneidungen, Fläche=80.44
80 Kanten, minimal 0.99999999999999900080, maximal 2.00000000000000266454
einzustellende Kanten, Abstände und Winkel:
|P16-P17|=2.00000000000000266454
$
%Eingabe war:
%
%#1683 symmetrisch
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%P[1]=[53.299000834421264,37.87798433201479]; P[2]=[53.299000834421264,1.0003687761555398]; D=ab(1,2); A(2,1,Bew(1));
%M(3,2,1,AW1-MW1,0,jam(2)*D);
%M(4,3,2,AW2,0,jam(2)*D);
%M(5,4,3,AW3,0,jam(2)*D);
%M(6,5,4,AW4,0,jam(2)*D);
%M(7,6,5,AW5,0,jam(2)*D);
%M(8,7,6,AW6,0,jam(2)*D);
%M(9,8,7,AW7,0,jam(2)*D);
%M(10,9,8,AW8,0,jam(2)*D);
%M(11,10,9,AW1,0,jam(2)*D);
%M(12,11,10,AW2,0,jam(2)*D);
%M(13,12,11,AW3,0,jam(2)*D);
%M(14,13,12,AW4,0,jam(2)*D);
%M(15,14,13,AW5,0,jam(2)*D);
%M(16,15,14,AW6,0,jam(2)*D);
%M(17,2,1,-MW1,0,jam(2)*D); RA(16,17,"",jam(2)*D);
%M(18,3,2,MW2);
%M(19,4,3,MW3);
%M(20,5,4,MW4);
%M(21,6,5,MW5);
%M(22,7,6,MW6);
%M(23,8,7,MW7);
%M(24,9,8,MW8);
%M(25,10,9,MW1);
%M(26,11,10,MW2);
%M(27,12,11,MW3);
%M(28,13,12,MW4);
%M(29,14,13,MW5);
%M(30,15,14,MW6);
%M(31,16,15,MW7);
%M(32,17,16,MW8);
%N(33,32,1); M(49,33,32,IW1);
%N(34,1,18); M(50,34,1,IW2);
%N(35,19,18); M(51,35,18,IW3);
%N(36,19,20); M(52,36,19,IW4);
%N(37,20,21); M(53,37,20,IW5);
%N(38,21,22); M(54,38,21,IW6);
%N(39,23,22); M(55,39,22,IW7);
%N(40,23,24); M(56,40,23,IW8);
%N(41,24,25); M(57,41,24,IW1);
%N(42,25,26); M(58,42,25,IW2);
%N(43,27,26); M(59,43,26,IW3);
%N(44,27,28); M(60,44,27,IW4);
%N(45,28,29); M(61,45,28,IW5);
%N(46,29,30); M(62,46,29,IW6);
%N(47,31,30); M(63,47,30,IW7);
%N(48,31,32); M(64,48,31,IW8);
%
%
%
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{DarkGray}{rgb}{0.66,0.66,0.66}
\definecolor{Gray}{rgb}{0.50,0.50,0.50}
\definecolor{LightGray}{rgb}{0.82,0.82,0.82}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/5.21/1.00,
2/5.21/0.00,
3/3.25/0.36,
4/1.56/1.44,
5/0.42/3.08,
6/0.00/5.04,
7/0.36/7.00,
8/1.44/8.69,
9/3.08/9.83,
10/5.04/10.25,
11/7.00/9.89,
12/8.69/8.81,
13/9.83/7.17,
14/10.25/5.21,
15/9.89/3.25,
16/8.81/1.56,
17/7.17/0.42,
18/3.63/1.28,
19/2.27/2.14,
20/1.35/3.46,
21/1.00/5.04,
22/1.28/6.62,
23/2.14/7.98,
24/3.46/8.90,
25/5.04/9.25,
26/6.62/8.97,
27/7.98/8.11,
28/8.90/6.79,
29/9.25/5.21,
30/8.97/3.63,
31/8.11/2.27,
32/6.79/1.35,
33/6.13/0.59,
34/4.32/0.56,
35/3.27/2.21,
36/1.32/2.46,
37/0.59/4.12,
38/0.56/5.93,
39/2.21/6.98,
40/2.46/8.93,
41/4.12/9.66,
42/5.93/9.69,
43/6.98/8.04,
44/8.93/7.79,
45/9.66/6.13,
46/9.69/4.32,
47/8.04/3.27,
48/7.79/1.32,
49/5.91/1.57,
50/4.49/1.54,
51/3.81/3.06,
52/2.14/3.04,
53/1.57/4.34,
54/1.54/5.76,
55/3.06/6.44,
56/3.04/8.11,
57/4.34/8.68,
58/5.76/8.71,
59/6.44/7.19,
60/8.11/7.21,
61/8.68/5.91,
62/8.71/4.49,
63/7.19/3.81,
64/7.21/2.14}
\coordinate (p-\i) at (\x,\y);
%Fläche als \fill[Yellow!3] (p-1) -- (p-2) -- (p-3) -- cycle;
%Dreiecke als \fill[black!3] (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 {
3/349.75/507.25/0.4/Gray,
4/327.25/484.75/0.4/Gray,
5/304.75/462.25/0.4/Gray,
6/282.25/439.75/0.4/Gray,
7/259.75/417.25/0.4/Gray,
8/237.25/394.75/0.4/Gray,
9/214.75/372.25/0.4/Gray,
10/192.25/349.75/0.4/Gray,
11/169.75/327.25/0.4/Gray,
12/147.25/304.75/0.4/Gray,
13/124.75/282.25/0.4/Gray,
14/102.25/259.75/0.4/Gray,
15/79.75/237.25/0.4/Gray,
3/349.75/427.50/0.3/DarkGray,
4/327.25/405.00/0.3/DarkGray,
5/304.75/382.50/0.3/DarkGray,
6/282.25/360.00/0.3/DarkGray,
7/259.75/337.50/0.3/DarkGray,
8/237.25/315.00/0.3/DarkGray,
9/214.75/292.50/0.3/DarkGray,
10/192.25/270.00/0.3/DarkGray,
11/169.75/247.50/0.3/DarkGray,
12/147.25/225.00/0.3/DarkGray,
13/124.75/202.50/0.3/DarkGray,
14/102.25/180.00/0.3/DarkGray,
15/79.75/157.50/0.3/DarkGray,
16/57.25/135.00/0.4/DarkGray,
17/34.75/112.50/0.4/DarkGray,
33/48.89/102.49/0.4/LightGray,
34/26.39/79.99/0.4/LightGray,
35/291.10/417.50/0.4/LightGray,
36/341.39/394.99/0.4/LightGray,
37/318.89/372.49/0.4/LightGray,
38/296.39/349.99/0.4/LightGray,
39/201.10/327.50/0.4/LightGray,
40/251.39/304.99/0.4/LightGray,
41/228.89/282.49/0.4/LightGray,
42/206.39/259.99/0.4/LightGray,
43/111.10/237.50/0.4/LightGray,
44/161.39/214.99/0.4/LightGray,
45/138.89/192.49/0.4/LightGray,
46/116.39/169.99/0.4/LightGray,
47/21.10/147.50/0.4/LightGray,
48/71.39/124.99/0.4/LightGray}
\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-16) -- (p-17);
%Kanten als \draw[line width=0] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/2,
4/3,
5/4,
6/5,
7/6,
8/7,
9/8,
10/9,
11/10,
12/11,
13/12,
14/13,
15/14,
16/15, 16/17,
17/2,
18/3,
19/4,
20/5,
21/6,
22/7,
23/8,
24/9,
25/10,
26/11,
27/12,
28/13,
29/14,
30/15,
31/16,
32/17,
33/32, 33/1,
34/1, 34/18,
35/19, 35/18,
36/19, 36/20,
37/20, 37/21,
38/21, 38/22,
39/23, 39/22,
40/23, 40/24,
41/24, 41/25,
42/25, 42/26,
43/27, 43/26,
44/27, 44/28,
45/28, 45/29,
46/29, 46/30,
47/31, 47/30,
48/31, 48/32,
49/33,
50/34,
51/35,
52/36,
53/37,
54/38,
55/39,
56/40,
57/41,
58/42,
59/43,
60/44,
61/45,
62/46,
63/47,
64/48}
\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 {
3/349.75/507.25/0.4/Gray,
4/327.25/484.75/0.4/Gray,
5/304.75/462.25/0.4/Gray,
6/282.25/439.75/0.4/Gray,
7/259.75/417.25/0.4/Gray,
8/237.25/394.75/0.4/Gray,
9/214.75/372.25/0.4/Gray,
10/192.25/349.75/0.4/Gray,
11/169.75/327.25/0.4/Gray,
12/147.25/304.75/0.4/Gray,
13/124.75/282.25/0.4/Gray,
14/102.25/259.75/0.4/Gray,
15/79.75/237.25/0.4/Gray,
3/349.75/427.50/0.3/DarkGray,
4/327.25/405.00/0.3/DarkGray,
5/304.75/382.50/0.3/DarkGray,
6/282.25/360.00/0.3/DarkGray,
7/259.75/337.50/0.3/DarkGray,
8/237.25/315.00/0.3/DarkGray,
9/214.75/292.50/0.3/DarkGray,
10/192.25/270.00/0.3/DarkGray,
11/169.75/247.50/0.3/DarkGray,
12/147.25/225.00/0.3/DarkGray,
13/124.75/202.50/0.3/DarkGray,
14/102.25/180.00/0.3/DarkGray,
15/79.75/157.50/0.3/DarkGray,
16/57.25/135.00/0.4/DarkGray,
17/34.75/112.50/0.4/DarkGray,
33/48.89/102.49/0.4/LightGray,
34/26.39/79.99/0.4/LightGray,
35/291.10/417.50/0.4/LightGray,
36/341.39/394.99/0.4/LightGray,
37/318.89/372.49/0.4/LightGray,
38/296.39/349.99/0.4/LightGray,
39/201.10/327.50/0.4/LightGray,
40/251.39/304.99/0.4/LightGray,
41/228.89/282.49/0.4/LightGray,
42/206.39/259.99/0.4/LightGray,
43/111.10/237.50/0.4/LightGray,
44/161.39/214.99/0.4/LightGray,
45/138.89/192.49/0.4/LightGray,
46/116.39/169.99/0.4/LightGray,
47/21.10/147.50/0.4/LightGray,
48/71.39/124.99/0.4/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 {
1/61,
2/234,
3/211,
4/189,
5/166,
6/144,
7/121,
8/99,
9/76,
10/54,
11/31,
12/9,
13/346,
14/324,
15/301,
16/279,
17/256,
18/103,
19/16,
20/353,
21/331,
22/13,
23/286,
24/263,
25/241,
26/283,
27/196,
28/173,
29/151,
30/193,
31/106,
32/83,
33/105,
34/82,
35/60,
36/37,
37/15,
38/352,
39/330,
40/307,
41/285,
42/262,
43/240,
44/217,
45/195,
46/172,
47/150,
48/127,
49/270,
50/270,
51/270,
52/270,
53/270,
54/270,
55/270,
56/270,
57/270,
58/270,
59/270,
60/270,
61/270,
62/270,
63/270,
64/270}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
$
Als nächstes setze ich die restlichen Kanten ein (Button "#1683symZ00"),
68 Knoten, 68×Grad 3, 0 Dreiecke, 0 Überschneidungen, Fläche=80.44
102 Kanten, minimal 0.99999999999999900080, maximal 3.38797928336377340841
einzustellende Kanten, Abstände und Winkel:
|P16-P17|=2.00000000000000266454
|P51-P50|=1.66380770527268406767
|P50-P49|=1.42029151629266525703
|P49-P64|=1.42029151629267502699
|P55-P54|=1.66380770527268606607
|P54-P53|=1.42029151629266880974
|P53-P52|=1.42029151629266858770
|P64-P66|=3.38797928336377340841
$
%Eingabe war:
%
%#1683 symmetrisch
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%P[1]=[53.299000834421264,37.87798433201479]; P[2]=[53.299000834421264,1.0003687761555398]; D=ab(1,2); A(2,1,Bew(1));
%M(3,2,1,AW1-MW1,0,jam(2)*D);
%M(4,3,2,AW2,0,jam(2)*D);
%M(5,4,3,AW3,0,jam(2)*D);
%M(6,5,4,AW4,0,jam(2)*D);
%M(7,6,5,AW5,0,jam(2)*D);
%M(8,7,6,AW6,0,jam(2)*D);
%M(9,8,7,AW7,0,jam(2)*D);
%M(10,9,8,AW8,0,jam(2)*D);
%M(11,10,9,AW1,0,jam(2)*D);
%M(12,11,10,AW2,0,jam(2)*D);
%M(13,12,11,AW3,0,jam(2)*D);
%M(14,13,12,AW4,0,jam(2)*D);
%M(15,14,13,AW5,0,jam(2)*D);
%M(16,15,14,AW6,0,jam(2)*D);
%M(17,2,1,-MW1,0,jam(2)*D); RA(16,17,"",jam(2)*D);
%M(18,3,2,MW2);
%M(19,4,3,MW3);
%M(20,5,4,MW4);
%M(21,6,5,MW5);
%M(22,7,6,MW6);
%M(23,8,7,MW7);
%M(24,9,8,MW8);
%M(25,10,9,MW1);
%M(26,11,10,MW2);
%M(27,12,11,MW3);
%M(28,13,12,MW4);
%M(29,14,13,MW5);
%M(30,15,14,MW6);
%M(31,16,15,MW7);
%M(32,17,16,MW8);
%N(33,32,1); M(49,33,32,IW1);
%N(34,1,18); M(50,34,1,IW2);
%N(35,19,18); M(51,35,18,IW3);
%N(36,19,20); M(52,36,19,IW4);
%N(37,20,21); M(53,37,20,IW5);
%N(38,21,22); M(54,38,21,IW6);
%N(39,23,22); M(55,39,22,IW7);
%N(40,23,24); M(56,40,23,IW8);
%N(41,24,25); M(57,41,24,IW1);
%N(42,25,26); M(58,42,25,IW2);
%N(43,27,26); M(59,43,26,IW3);
%N(44,27,28); M(60,44,27,IW4);
%N(45,28,29); M(61,45,28,IW5);
%N(46,29,30); M(62,46,29,IW6);
%N(47,31,30); M(63,47,30,IW7);
%N(48,31,32); M(64,48,31,IW8);
%RA(51,50,"green",jam(1.66380770527268428971)*D);
%RA(50,49,"green",jam(1.42029151629267658130)*D);
%RA(49,64,"green",jam(1.42029151629267658130)*D);
%A(63,62,"green",jam(1.66380770527268428971)*D);
%A(62,61,"green",jam(1.42029151629267658130)*D);
%A(61,60,"green",jam(1.42029151629267658130)*D);
%A(59,58,"green",jam(1.66380770527268428971)*D);
%A(58,57,"green",jam(1.42029151629267658130)*D);
%A(57,56,"green",jam(1.42029151629267658130)*D);
%RA(55,54,"green",jam(1.66380770527268428971)*D);
%RA(54,53,"green",jam(1.42029151629267658130)*D);
%RA(53,52,"green",jam(1.42029151629267658130)*D);
%Q(65,55,52,jam(2)*D,jam(2)*D); N(66,65,51);
%RA(64,66,"green",jam(3.38797928336377340841)*D);
%Q(67,63,60,jam(2)*D,jam(2)*D); N(68,67,59);
%A(56,68,"green",jam(3.38797928336377340841)*D);
%
%
%
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{DarkGray}{rgb}{0.66,0.66,0.66}
\definecolor{Gray}{rgb}{0.50,0.50,0.50}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LightGray}{rgb}{0.82,0.82,0.82}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/5.21/1.00,
2/5.21/0.00,
3/3.25/0.36,
4/1.56/1.44,
5/0.42/3.08,
6/0.00/5.04,
7/0.36/7.00,
8/1.44/8.69,
9/3.08/9.83,
10/5.04/10.25,
11/7.00/9.89,
12/8.69/8.81,
13/9.83/7.17,
14/10.25/5.21,
15/9.89/3.25,
16/8.81/1.56,
17/7.17/0.42,
18/3.63/1.28,
19/2.27/2.14,
20/1.35/3.46,
21/1.00/5.04,
22/1.28/6.62,
23/2.14/7.98,
24/3.46/8.90,
25/5.04/9.25,
26/6.62/8.97,
27/7.98/8.11,
28/8.90/6.79,
29/9.25/5.21,
30/8.97/3.63,
31/8.11/2.27,
32/6.79/1.35,
33/6.13/0.59,
34/4.32/0.56,
35/3.27/2.21,
36/1.32/2.46,
37/0.59/4.12,
38/0.56/5.93,
39/2.21/6.98,
40/2.46/8.93,
41/4.12/9.66,
42/5.93/9.69,
43/6.98/8.04,
44/8.93/7.79,
45/9.66/6.13,
46/9.69/4.32,
47/8.04/3.27,
48/7.79/1.32,
49/5.91/1.57,
50/4.49/1.54,
51/3.81/3.06,
52/2.14/3.04,
53/1.57/4.34,
54/1.54/5.76,
55/3.06/6.44,
56/3.04/8.11,
57/4.34/8.68,
58/5.76/8.71,
59/6.44/7.19,
60/8.11/7.21,
61/8.68/5.91,
62/8.71/4.49,
63/7.19/3.81,
64/7.21/2.14,
65/3.51/4.50,
66/4.32/3.91,
67/6.74/5.75,
68/5.93/6.34}
\coordinate (p-\i) at (\x,\y);
%Fläche als \fill[Yellow!3] (p-1) -- (p-2) -- (p-3) -- cycle;
%Dreiecke als \fill[black!3] (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 {
3/349.75/507.25/0.4/Gray,
4/327.25/484.75/0.4/Gray,
5/304.75/462.25/0.4/Gray,
6/282.25/439.75/0.4/Gray,
7/259.75/417.25/0.4/Gray,
8/237.25/394.75/0.4/Gray,
9/214.75/372.25/0.4/Gray,
10/192.25/349.75/0.4/Gray,
11/169.75/327.25/0.4/Gray,
12/147.25/304.75/0.4/Gray,
13/124.75/282.25/0.4/Gray,
14/102.25/259.75/0.4/Gray,
15/79.75/237.25/0.4/Gray,
3/349.75/427.50/0.3/DarkGray,
4/327.25/405.00/0.3/DarkGray,
5/304.75/382.50/0.3/DarkGray,
6/282.25/360.00/0.3/DarkGray,
7/259.75/337.50/0.3/DarkGray,
8/237.25/315.00/0.3/DarkGray,
9/214.75/292.50/0.3/DarkGray,
10/192.25/270.00/0.3/DarkGray,
11/169.75/247.50/0.3/DarkGray,
12/147.25/225.00/0.3/DarkGray,
13/124.75/202.50/0.3/DarkGray,
14/102.25/180.00/0.3/DarkGray,
15/79.75/157.50/0.3/DarkGray,
16/57.25/135.00/0.4/DarkGray,
17/34.75/112.50/0.4/DarkGray,
33/48.89/102.49/0.4/LightGray,
34/26.39/79.99/0.4/LightGray,
35/291.10/417.50/0.4/LightGray,
36/341.39/394.99/0.4/LightGray,
37/318.89/372.49/0.4/LightGray,
38/296.39/349.99/0.4/LightGray,
39/201.10/327.50/0.4/LightGray,
40/251.39/304.99/0.4/LightGray,
41/228.89/282.49/0.4/LightGray,
42/206.39/259.99/0.4/LightGray,
43/111.10/237.50/0.4/LightGray,
44/161.39/214.99/0.4/LightGray,
45/138.89/192.49/0.4/LightGray,
46/116.39/169.99/0.4/LightGray,
47/21.10/147.50/0.4/LightGray,
48/71.39/124.99/0.4/LightGray}
\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-16) -- (p-17);
\draw[Green,very thick] (p-51) -- (p-50);
\draw[Green,very thick] (p-50) -- (p-49);
\draw[Green,very thick] (p-49) -- (p-64);
\draw[Green,very thick] (p-55) -- (p-54);
\draw[Green,very thick] (p-54) -- (p-53);
\draw[Green,very thick] (p-53) -- (p-52);
\draw[Green,very thick] (p-64) -- (p-66);
%Kanten als \draw[line width=0] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/2,
4/3,
5/4,
6/5,
7/6,
8/7,
9/8,
10/9,
11/10,
12/11,
13/12,
14/13,
15/14,
16/15, 16/17,
17/2,
18/3,
19/4,
20/5,
21/6,
22/7,
23/8,
24/9,
25/10,
26/11,
27/12,
28/13,
29/14,
30/15,
31/16,
32/17,
33/32, 33/1,
34/1, 34/18,
35/19, 35/18,
36/19, 36/20,
37/20, 37/21,
38/21, 38/22,
39/23, 39/22,
40/23, 40/24,
41/24, 41/25,
42/25, 42/26,
43/27, 43/26,
44/27, 44/28,
45/28, 45/29,
46/29, 46/30,
47/31, 47/30,
48/31, 48/32,
49/33, 49/64,
50/34, 50/49,
51/35, 51/50,
52/36,
53/37, 53/52,
54/38, 54/53,
55/39, 55/54,
56/40, 56/68,
57/41, 57/56,
58/42, 58/57,
59/43, 59/58,
60/44,
61/45, 61/60,
62/46, 62/61,
63/47, 63/62,
64/48, 64/66,
65/55, 65/52,
66/65, 66/51,
67/63, 67/60,
68/67, 68/59}
\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);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-49) -- (p-64);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-50) -- (p-49);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-51) -- (p-50);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-53) -- (p-52);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-54) -- (p-53);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-55) -- (p-54);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-56) -- (p-68);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-57) -- (p-56);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-58) -- (p-57);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-59) -- (p-58);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-61) -- (p-60);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-62) -- (p-61);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-63) -- (p-62);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-64) -- (p-66);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
3/349.75/507.25/0.4/Gray,
4/327.25/484.75/0.4/Gray,
5/304.75/462.25/0.4/Gray,
6/282.25/439.75/0.4/Gray,
7/259.75/417.25/0.4/Gray,
8/237.25/394.75/0.4/Gray,
9/214.75/372.25/0.4/Gray,
10/192.25/349.75/0.4/Gray,
11/169.75/327.25/0.4/Gray,
12/147.25/304.75/0.4/Gray,
13/124.75/282.25/0.4/Gray,
14/102.25/259.75/0.4/Gray,
15/79.75/237.25/0.4/Gray,
3/349.75/427.50/0.3/DarkGray,
4/327.25/405.00/0.3/DarkGray,
5/304.75/382.50/0.3/DarkGray,
6/282.25/360.00/0.3/DarkGray,
7/259.75/337.50/0.3/DarkGray,
8/237.25/315.00/0.3/DarkGray,
9/214.75/292.50/0.3/DarkGray,
10/192.25/270.00/0.3/DarkGray,
11/169.75/247.50/0.3/DarkGray,
12/147.25/225.00/0.3/DarkGray,
13/124.75/202.50/0.3/DarkGray,
14/102.25/180.00/0.3/DarkGray,
15/79.75/157.50/0.3/DarkGray,
16/57.25/135.00/0.4/DarkGray,
17/34.75/112.50/0.4/DarkGray,
33/48.89/102.49/0.4/LightGray,
34/26.39/79.99/0.4/LightGray,
35/291.10/417.50/0.4/LightGray,
36/341.39/394.99/0.4/LightGray,
37/318.89/372.49/0.4/LightGray,
38/296.39/349.99/0.4/LightGray,
39/201.10/327.50/0.4/LightGray,
40/251.39/304.99/0.4/LightGray,
41/228.89/282.49/0.4/LightGray,
42/206.39/259.99/0.4/LightGray,
43/111.10/237.50/0.4/LightGray,
44/161.39/214.99/0.4/LightGray,
45/138.89/192.49/0.4/LightGray,
46/116.39/169.99/0.4/LightGray,
47/21.10/147.50/0.4/LightGray,
48/71.39/124.99/0.4/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 {
1/61,
2/234,
3/211,
4/189,
5/166,
6/144,
7/121,
8/99,
9/76,
10/54,
11/31,
12/9,
13/346,
14/324,
15/301,
16/279,
17/256,
18/103,
19/16,
20/353,
21/331,
22/13,
23/286,
24/263,
25/241,
26/283,
27/196,
28/173,
29/151,
30/193,
31/106,
32/83,
33/105,
34/82,
35/60,
36/37,
37/15,
38/352,
39/330,
40/307,
41/285,
42/262,
43/240,
44/217,
45/195,
46/172,
47/150,
48/127,
49/54,
50/133,
51/88,
52/263,
53/324,
54/43,
55/358,
56/179,
57/234,
58/313,
59/268,
60/83,
61/144,
62/223,
63/178,
64/359,
65/98,
66/106,
67/278,
68/286}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
$
auch wieder so, dass sie nicht in einem einzigen großen Schritt auf Länge 1 gebracht werden, sondern allmählich mit den hundert kleinen Schritten (Button "Feinjustieren(8)", läuft von allein bis Ziehfaktor=0.64). Bei Ziehfaktor=0.67 (noch weitere dreimal "Feinjustieren(8)" drücken) würde Überschneidung in P53 auftreten. Deshalb setze ich vorher einen festen Abstand P37-P55 ein (Button "#1683symZ64") welcher P55 von P53 weghält.
68 Knoten, 68×Grad 3, 0 Dreiecke, 0 Überschneidungen, Fläche=36.61
102 Kanten, minimal 0.99999999999999933387, maximal 1.85967254201095966160
einzustellende Kanten, Abstände und Winkel:
...zusätzlich zu den bisherigen
|P37-P55|=1.10396782836591844656
$
%Eingabe war:
%
%#1683 symmetrisch Z64
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%P[1]=[74.9531909001125,59.524198929142614]; P[2]=[74.9531909001125,2.161314244593683]; D=ab(1,2); A(2,1,Bew(1));
%M(3,2,1,AW1-MW1,0,jam(2)*D);
%M(4,3,2,AW2,0,jam(2)*D);
%M(5,4,3,AW3,0,jam(2)*D);
%M(6,5,4,AW4,0,jam(2)*D);
%M(7,6,5,AW5,0,jam(2)*D);
%M(8,7,6,AW6,0,jam(2)*D);
%M(9,8,7,AW7,0,jam(2)*D);
%M(10,9,8,AW8,0,jam(2)*D);
%M(11,10,9,AW1,0,jam(2)*D);
%M(12,11,10,AW2,0,jam(2)*D);
%M(13,12,11,AW3,0,jam(2)*D);
%M(14,13,12,AW4,0,jam(2)*D);
%M(15,14,13,AW5,0,jam(2)*D);
%M(16,15,14,AW6,0,jam(2)*D);
%M(17,2,1,-MW1,0,jam(2)*D); RA(16,17,"",jam(2)*D);
%M(18,3,2,MW2);
%M(19,4,3,MW3);
%M(20,5,4,MW4);
%M(21,6,5,MW5);
%M(22,7,6,MW6);
%M(23,8,7,MW7);
%M(24,9,8,MW8);
%M(25,10,9,MW1);
%M(26,11,10,MW2);
%M(27,12,11,MW3);
%M(28,13,12,MW4);
%M(29,14,13,MW5);
%M(30,15,14,MW6);
%M(31,16,15,MW7);
%M(32,17,16,MW8);
%N(33,32,1); M(49,33,32,IW1);
%N(34,1,18); M(50,34,1,IW2);
%N(35,19,18); M(51,35,18,IW3);
%N(36,19,20); M(52,36,19,IW4);
%N(37,20,21); M(53,37,20,IW5);
%N(38,21,22); M(54,38,21,IW6);
%N(39,23,22); M(55,39,22,IW7);
%N(40,23,24); M(56,40,23,IW8);
%N(41,24,25); M(57,41,24,IW1);
%N(42,25,26); M(58,42,25,IW2);
%N(43,27,26); M(59,43,26,IW3);
%N(44,27,28); M(60,44,27,IW4);
%N(45,28,29); M(61,45,28,IW5);
%N(46,29,30); M(62,46,29,IW6);
%N(47,31,30); M(63,47,30,IW7);
%N(48,31,32); M(64,48,31,IW8);
%RA(51,50,"green",jam(1.66380770527268428971)*D);
%RA(50,49,"green",jam(1.42029151629267658130)*D);
%RA(49,64,"green",jam(1.42029151629267658130)*D);
%A(63,62,"green",jam(1.66380770527268428971)*D);
%A(62,61,"green",jam(1.42029151629267658130)*D);
%A(61,60,"green",jam(1.42029151629267658130)*D);
%A(59,58,"green",jam(1.66380770527268428971)*D);
%A(58,57,"green",jam(1.42029151629267658130)*D);
%A(57,56,"green",jam(1.42029151629267658130)*D);
%RA(55,54,"green",jam(1.66380770527268428971)*D);
%RA(54,53,"green",jam(1.42029151629267658130)*D);
%RA(53,52,"green",jam(1.42029151629267658130)*D);
%Q(65,55,52,jam(2)*D,jam(2)*D); N(66,65,51);
%RA(64,66,"green",jam(3.38797928336377340841)*D);
%Q(67,63,60,jam(2)*D,jam(2)*D); N(68,67,59);
%A(56,68,"green",jam(3.38797928336377340841)*D);
%
%R(37,55,"brown",1.10396782836591800248*D);
%
%
%
%Ende der Eingabe.
\usetikzlibrary{spy}
\tikzset{SpyStyle/.style={spy using outlines={rectangle, magnification=3, width=2cm, height=2cm, connect spies, blue!70!black}}}
\begin{tikzpicture}[SpyStyle,draw=grey,font=\sffamily\tiny]
\definecolor{Brown}{rgb}{0.64,0.16,0.16}
\definecolor{DarkGray}{rgb}{0.66,0.66,0.66}
\definecolor{Gray}{rgb}{0.50,0.50,0.50}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LightGray}{rgb}{0.82,0.82,0.82}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/5.25/1.33,
2/5.25/0.03,
3/3.48/0.00,
4/1.97/0.91,
5/0.89/2.32,
6/0.25/3.96,
7/0.00/5.71,
8/0.88/7.25,
9/2.39/8.16,
10/4.12/8.54,
11/5.89/8.57,
12/7.40/7.65,
13/8.48/6.25,
14/9.12/4.60,
15/9.37/2.85,
16/8.49/1.32,
17/6.98/0.41,
18/3.44/1.30,
19/3.00/1.70,
20/2.10/2.79,
21/1.54/4.12,
22/1.29/5.91,
23/1.68/6.23,
24/2.78/6.92,
25/4.12/7.24,
26/5.93/7.27,
27/6.37/6.87,
28/7.27/5.77,
29/7.83/4.45,
30/8.08/2.66,
31/7.69/2.34,
32/6.59/1.65,
33/6.18/0.42,
34/4.36/0.38,
35/4.08/2.43,
36/1.71/1.55,
37/0.83/3.03,
38/0.49/4.88,
39/2.28/5.08,
40/1.63/7.53,
41/3.19/8.15,
42/5.01/8.19,
43/5.29/6.14,
44/7.66/7.01,
45/8.54/5.53,
46/8.88/3.68,
47/7.09/3.49,
48/7.74/1.04,
49/5.46/1.50,
50/3.96/1.62,
51/5.38/2.39,
52/2.53/2.57,
53/1.81/3.88,
54/1.69/5.37,
55/2.04/3.80,
56/2.51/6.56,
57/3.91/7.07,
58/5.41/6.95,
59/3.99/6.18,
60/6.84/6.00,
61/7.56/4.69,
62/7.68/3.19,
63/7.33/4.77,
64/6.86/2.00,
65/3.81/3.79,
66/5.10/3.66,
67/5.56/4.78,
68/4.27/4.91}
\coordinate (p-\i) at (\x,\y);
%Fläche als \fill[Yellow!3] (p-1) -- (p-2) -- (p-3) -- cycle;
%Dreiecke als \fill[black!3] (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 {
3/0.85/148.87/0.4/Gray,
4/328.87/487.47/0.4/Gray,
5/307.47/471.37/0.4/Gray,
6/291.37/458.11/0.4/Gray,
7/278.11/420.29/0.4/Gray,
8/240.29/390.90/0.4/Gray,
9/210.90/372.49/0.4/Gray,
10/192.49/360.85/0.4/Gray,
11/180.85/328.87/0.4/Gray,
12/148.87/307.47/0.4/Gray,
13/127.47/291.37/0.4/Gray,
14/111.37/278.11/0.4/Gray,
15/98.11/240.29/0.4/Gray,
3/0.85/91.93/0.3/DarkGray,
4/328.87/397.25/0.3/DarkGray,
5/307.47/381.50/0.3/DarkGray,
6/291.37/366.89/0.3/DarkGray,
7/278.11/368.65/0.3/DarkGray,
8/240.29/308.23/0.3/DarkGray,
9/210.90/287.33/0.3/DarkGray,
10/192.49/270.00/0.3/DarkGray,
11/180.85/271.93/0.3/DarkGray,
12/148.87/217.25/0.3/DarkGray,
13/127.47/201.50/0.3/DarkGray,
14/111.37/186.89/0.3/DarkGray,
15/98.11/188.65/0.3/DarkGray,
16/60.29/128.23/0.4/DarkGray,
17/30.90/107.33/0.4/DarkGray,
33/71.59/123.83/0.4/LightGray,
34/46.68/107.69/0.4/LightGray,
35/240.43/358.07/0.4/LightGray,
36/6.50/51.17/0.4/LightGray,
37/349.37/400.68/0.4/LightGray,
38/324.04/382.13/0.4/LightGray,
39/140.16/259.16/0.4/LightGray,
40/272.11/312.19/0.4/LightGray,
41/251.59/303.83/0.4/LightGray,
42/226.68/287.69/0.4/LightGray,
43/60.43/178.07/0.4/LightGray,
44/186.50/231.17/0.4/LightGray,
45/169.37/220.68/0.4/LightGray,
46/144.04/202.13/0.4/LightGray,
47/320.16/439.16/0.4/LightGray,
48/92.11/132.19/0.4/LightGray}
\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-16) -- (p-17);
\draw[Green,very thick] (p-51) -- (p-50);
\draw[Green,very thick] (p-50) -- (p-49);
\draw[Green,very thick] (p-49) -- (p-64);
\draw[Green,very thick] (p-55) -- (p-54);
\draw[Green,very thick] (p-54) -- (p-53);
\draw[Green,very thick] (p-53) -- (p-52);
\draw[Green,very thick] (p-64) -- (p-66);
\draw[Brown,very thick] (p-37) -- (p-55);
%Kanten als \draw[line width=0] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/2,
4/3,
5/4,
6/5,
7/6,
8/7,
9/8,
10/9,
11/10,
12/11,
13/12,
14/13,
15/14,
16/15, 16/17,
17/2,
18/3,
19/4,
20/5,
21/6,
22/7,
23/8,
24/9,
25/10,
26/11,
27/12,
28/13,
29/14,
30/15,
31/16,
32/17,
33/32, 33/1,
34/1, 34/18,
35/19, 35/18,
36/19, 36/20,
37/20, 37/21,
38/21, 38/22,
39/23, 39/22,
40/23, 40/24,
41/24, 41/25,
42/25, 42/26,
43/27, 43/26,
44/27, 44/28,
45/28, 45/29,
46/29, 46/30,
47/31, 47/30,
48/31, 48/32,
49/33, 49/64,
50/34, 50/49,
51/35, 51/50,
52/36,
53/37, 53/52,
54/38, 54/53,
55/39, 55/54,
56/40, 56/68,
57/41, 57/56,
58/42, 58/57,
59/43, 59/58,
60/44,
61/45, 61/60,
62/46, 62/61,
63/47, 63/62,
64/48, 64/66,
65/55, 65/52,
66/65, 66/51,
67/63, 67/60,
68/67, 68/59}
\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);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-3) -- (p-2);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-4) -- (p-3);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-5) -- (p-4);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-6) -- (p-5);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-7) -- (p-6);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-8) -- (p-7);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-9) -- (p-8);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-10) -- (p-9);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-11) -- (p-10);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-12) -- (p-11);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-13) -- (p-12);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-14) -- (p-13);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-15) -- (p-14);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-16) -- (p-15);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-16) -- (p-17);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-17) -- (p-2);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-49) -- (p-64);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-50) -- (p-49);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-51) -- (p-50);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-53) -- (p-52);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-54) -- (p-53);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-55) -- (p-54);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-56) -- (p-68);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-57) -- (p-56);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-58) -- (p-57);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-59) -- (p-58);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-61) -- (p-60);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-62) -- (p-61);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-63) -- (p-62);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-64) -- (p-66);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-65) -- (p-55);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-65) -- (p-52);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-67) -- (p-63);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-67) -- (p-60);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
3/0.85/148.87/0.4/Gray,
4/328.87/487.47/0.4/Gray,
5/307.47/471.37/0.4/Gray,
6/291.37/458.11/0.4/Gray,
7/278.11/420.29/0.4/Gray,
8/240.29/390.90/0.4/Gray,
9/210.90/372.49/0.4/Gray,
10/192.49/360.85/0.4/Gray,
11/180.85/328.87/0.4/Gray,
12/148.87/307.47/0.4/Gray,
13/127.47/291.37/0.4/Gray,
14/111.37/278.11/0.4/Gray,
15/98.11/240.29/0.4/Gray,
3/0.85/91.93/0.3/DarkGray,
4/328.87/397.25/0.3/DarkGray,
5/307.47/381.50/0.3/DarkGray,
6/291.37/366.89/0.3/DarkGray,
7/278.11/368.65/0.3/DarkGray,
8/240.29/308.23/0.3/DarkGray,
9/210.90/287.33/0.3/DarkGray,
10/192.49/270.00/0.3/DarkGray,
11/180.85/271.93/0.3/DarkGray,
12/148.87/217.25/0.3/DarkGray,
13/127.47/201.50/0.3/DarkGray,
14/111.37/186.89/0.3/DarkGray,
15/98.11/188.65/0.3/DarkGray,
16/60.29/128.23/0.4/DarkGray,
17/30.90/107.33/0.4/DarkGray,
33/71.59/123.83/0.4/LightGray,
34/46.68/107.69/0.4/LightGray,
35/240.43/358.07/0.4/LightGray,
36/6.50/51.17/0.4/LightGray,
37/349.37/400.68/0.4/LightGray,
38/324.04/382.13/0.4/LightGray,
39/140.16/259.16/0.4/LightGray,
40/272.11/312.19/0.4/LightGray,
41/251.59/303.83/0.4/LightGray,
42/226.68/287.69/0.4/LightGray,
43/60.43/178.07/0.4/LightGray,
44/186.50/231.17/0.4/LightGray,
45/169.37/220.68/0.4/LightGray,
46/144.04/202.13/0.4/LightGray,
47/320.16/439.16/0.4/LightGray,
48/92.11/132.19/0.4/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 {
1/274,
2/234,
3/303,
4/186,
5/167,
6/152,
7/146,
8/97,
9/72,
10/54,
11/123,
12/6,
13/347,
14/332,
15/326,
16/277,
17/252,
18/190,
19/293,
20/213,
21/193,
22/99,
23/197,
24/114,
25/94,
26/10,
27/113,
28/33,
29/13,
30/279,
31/17,
32/294,
33/106,
34/260,
35/122,
36/42,
37/26,
38/176,
39/22,
40/305,
41/286,
42/80,
43/302,
44/222,
45/206,
46/356,
47/202,
48/125,
49/164,
50/144,
51/323,
52/264,
53/82,
54/61,
55/222,
56/171,
57/344,
58/324,
59/143,
60/84,
61/262,
62/241,
63/42,
64/351,
65/111,
66/51,
67/291,
68/231}
\node[anchor=\a] (P\i) at (p-\i) {\i};
%Vergrößerungen als \spy[rectangle, magnification=3, width=2cm, h eight=2cm, blue!70!black] on (p-18) in node at (2.5 cm,-2);
\spy[magnification=2] on (p-53) in node at (2.5,-2);
\end{tikzpicture}
$
Dann weiter zusammenziehen (Button "Feinjustieren(9)", läuft bis Ziehfaktor=0.78). Bei Ziehfaktor=0.81 würde Überschneidung in P18 auftretreten, deshalb ein zusätzlicher Abstand P34-P19 und bei der Gelegenheit gleich mit ein Abstand P34-P49 gegen Überschneidung in P1 (Button " #1683symZ78").
68 Knoten, 68×Grad 3, 0 Dreiecke, 0 Überschneidungen, Fläche=29.30
102 Kanten, minimal 0.99999999999999933387, maximal 1.52535544234002973241
einzustellende Kanten, Abstände und Winkel:
...zusätzlich...
|P19-P34|=1.12542474054885333068
|P49-P34|=1.06236326562790162065
$
%Eingabe war:
%
%#1683 symmetrisch Z78
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%P[1]=[99.38901545713267,76.54308398594306]; P[2]=[99.38901545713267,13.709252345747842]; D=ab(1,2); A(2,1,Bew(1));
%M(3,2,1,AW1-MW1,0,jam(2)*D);
%M(4,3,2,AW2,0,jam(2)*D);
%M(5,4,3,AW3,0,jam(2)*D);
%M(6,5,4,AW4,0,jam(2)*D);
%M(7,6,5,AW5,0,jam(2)*D);
%M(8,7,6,AW6,0,jam(2)*D);
%M(9,8,7,AW7,0,jam(2)*D);
%M(10,9,8,AW8,0,jam(2)*D);
%M(11,10,9,AW1,0,jam(2)*D);
%M(12,11,10,AW2,0,jam(2)*D);
%M(13,12,11,AW3,0,jam(2)*D);
%M(14,13,12,AW4,0,jam(2)*D);
%M(15,14,13,AW5,0,jam(2)*D);
%M(16,15,14,AW6,0,jam(2)*D);
%M(17,2,1,-MW1,0,jam(2)*D); RA(16,17,"",jam(2)*D);
%M(18,3,2,MW2);
%M(19,4,3,MW3);
%M(20,5,4,MW4);
%M(21,6,5,MW5);
%M(22,7,6,MW6);
%M(23,8,7,MW7);
%M(24,9,8,MW8);
%M(25,10,9,MW1);
%M(26,11,10,MW2);
%M(27,12,11,MW3);
%M(28,13,12,MW4);
%M(29,14,13,MW5);
%M(30,15,14,MW6);
%M(31,16,15,MW7);
%M(32,17,16,MW8);
%N(33,32,1); M(49,33,32,IW1);
%N(34,1,18); M(50,34,1,IW2);
%N(35,19,18); M(51,35,18,IW3);
%N(36,19,20); M(52,36,19,IW4);
%N(37,20,21); M(53,37,20,IW5);
%N(38,21,22); M(54,38,21,IW6);
%N(39,23,22); M(55,39,22,IW7);
%N(40,23,24); M(56,40,23,IW8);
%N(41,24,25); M(57,41,24,IW1);
%N(42,25,26); M(58,42,25,IW2);
%N(43,27,26); M(59,43,26,IW3);
%N(44,27,28); M(60,44,27,IW4);
%N(45,28,29); M(61,45,28,IW5);
%N(46,29,30); M(62,46,29,IW6);
%N(47,31,30); M(63,47,30,IW7);
%N(48,31,32); M(64,48,31,IW8);
%RA(51,50,"green",jam(1.66380770527268428971)*D);
%RA(50,49,"green",jam(1.42029151629267658130)*D);
%RA(49,64,"green",jam(1.42029151629267658130)*D);
%A(63,62,"green",jam(1.66380770527268428971)*D);
%A(62,61,"green",jam(1.42029151629267658130)*D);
%A(61,60,"green",jam(1.42029151629267658130)*D);
%A(59,58,"green",jam(1.66380770527268428971)*D);
%A(58,57,"green",jam(1.42029151629267658130)*D);
%A(57,56,"green",jam(1.42029151629267658130)*D);
%RA(55,54,"green",jam(1.66380770527268428971)*D);
%RA(54,53,"green",jam(1.42029151629267658130)*D);
%RA(53,52,"green",jam(1.42029151629267658130)*D);
%Q(65,55,52,jam(2)*D,jam(2)*D); N(66,65,51);
%RA(64,66,"green",jam(3.38797928336377340841)*D);
%Q(67,63,60,jam(2)*D,jam(2)*D); N(68,67,59);
%A(56,68,"green",jam(3.38797928336377340841)*D);
%
%R(37,55,"brown",1.10396782836591800248*D);
%R(19,34,"brown",1.12542474054885377477*D);
%R(49,34,"brown",1.06236326562790539541*D);
%
%
%Ende der Eingabe.
\usetikzlibrary{spy}
\tikzset{SpyStyle/.style={spy using outlines={rectangle, magnification=3, width=2cm, height=2cm, connect spies, blue!70!black}}}
\begin{tikzpicture}[SpyStyle,draw=grey,font=\sffamily\tiny]
\definecolor{Brown}{rgb}{0.64,0.16,0.16}
\definecolor{DarkGray}{rgb}{0.66,0.66,0.66}
\definecolor{Gray}{rgb}{0.50,0.50,0.50}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LightGray}{rgb}{0.82,0.82,0.82}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/5.700/1.683,
2/5.70/0.28,
3/4.02/0.00,
4/2.41/0.59,
5/1.24/1.83,
6/0.50/3.37,
7/0.00/5.00,
8/0.48/6.64,
9/1.86/7.65,
10/3.50/8.14,
11/5.18/8.42,
12/6.79/7.84,
13/7.95/6.59,
14/8.70/5.05,
15/9.20/3.42,
16/8.71/1.78,
17/7.34/0.77,
18/3.65/1.35,
19/3.51/1.45,
20/2.53/2.38,
21/1.89/3.52,
22/1.32/5.46,
23/1.44/5.62,
24/2.32/6.33,
25/3.499/6.739,
26/5.54/7.07,
27/5.69/6.97,
28/6.66/6.04,
29/7.31/4.90,
30/7.87/2.97,
31/7.76/2.80,
32/6.88/2.10,
33/6.70/0.71,
34/4.83/0.59,
35/4.39/2.55,
36/2.18/1.02,
37/1.13/2.34,
38/0.67/4.22,
39/2.52/4.73,
40/1.07/6.97,
41/2.50/7.72,
42/4.37/7.83,
43/4.81/5.88,
44/7.02/7.40,
45/8.06/6.08,
46/8.52/4.21,
47/6.68/3.69,
48/8.13/1.45,
49/5.763/1.744,
50/4.24/1.86,
51/5.77/2.33,
52/3.00/2.16,
53/2.07/3.38,
54/1.90/4.90,
55/2.31/3.34,
56/2.07/5.99,
57/3.435/6.678,
58/4.96/6.56,
59/3.43/6.09,
60/6.20/6.26,
61/7.13/5.05,
62/7.30/3.53,
63/6.89/5.08,
64/7.13/2.43,
65/4.00/3.54,
66/5.40/3.68,
67/5.19/4.88,
68/3.80/4.74}
\coordinate (p-\i) at (\x,\y);
%Fläche als \fill[Yellow!3] (p-1) -- (p-2) -- (p-3) -- cycle;
%Dreiecke als \fill[black!3] (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 {
3/9.54/159.91/0.4/Gray,
4/339.91/493.09/0.4/Gray,
5/313.09/476.00/0.4/Gray,
6/296.00/466.86/0.4/Gray,
7/286.86/433.53/0.4/Gray,
8/253.53/396.24/0.4/Gray,
9/216.24/376.60/0.4/Gray,
10/196.60/369.54/0.4/Gray,
11/189.54/339.91/0.4/Gray,
12/159.91/313.09/0.4/Gray,
13/133.09/296.00/0.4/Gray,
14/116.00/286.86/0.4/Gray,
15/106.86/253.53/0.4/Gray,
3/9.54/104.95/0.3/DarkGray,
4/339.91/398.27/0.3/DarkGray,
5/313.09/382.90/0.3/DarkGray,
6/296.00/366.12/0.3/DarkGray,
7/286.86/378.87/0.3/DarkGray,
8/253.53/313.07/0.3/DarkGray,
9/216.24/288.91/0.3/DarkGray,
10/196.60/270.00/0.3/DarkGray,
11/189.54/284.95/0.3/DarkGray,
12/159.91/218.27/0.3/DarkGray,
13/133.09/202.90/0.3/DarkGray,
14/116.00/186.12/0.3/DarkGray,
15/106.86/198.87/0.3/DarkGray,
16/73.53/133.07/0.4/DarkGray,
17/36.24/108.91/0.4/DarkGray,
33/82.63/132.19/0.4/LightGray,
34/51.45/114.89/0.4/LightGray,
35/238.48/351.31/0.4/LightGray,
36/17.84/54.12/0.4/LightGray,
37/1.67/47.91/0.4/LightGray,
38/330.07/389.04/0.4/LightGray,
39/148.67/261.22/0.4/LightGray,
40/285.26/315.50/0.4/LightGray,
41/262.63/312.19/0.4/LightGray,
42/231.45/294.89/0.4/LightGray,
43/58.48/171.31/0.4/LightGray,
44/197.84/234.12/0.4/LightGray,
45/181.67/227.91/0.4/LightGray,
46/150.07/209.04/0.4/LightGray,
47/328.67/441.22/0.4/LightGray,
48/105.26/135.50/0.4/LightGray}
\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-16) -- (p-17);
\draw[Green,very thick] (p-51) -- (p-50);
\draw[Green,very thick] (p-50) -- (p-49);
\draw[Green,very thick] (p-49) -- (p-64);
\draw[Green,very thick] (p-55) -- (p-54);
\draw[Green,very thick] (p-54) -- (p-53);
\draw[Green,very thick] (p-53) -- (p-52);
\draw[Green,very thick] (p-64) -- (p-66);
\draw[Brown,very thick] (p-37) -- (p-55);
\draw[Brown,very thick] (p-19) -- (p-34);
\draw[Brown,very thick] (p-49) -- (p-34);
%Kanten als \draw[line width=0] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/2,
4/3,
5/4,
6/5,
7/6,
8/7,
9/8,
10/9,
11/10,
12/11,
13/12,
14/13,
15/14,
16/15, 16/17,
17/2,
18/3,
19/4,
20/5,
21/6,
22/7,
23/8,
24/9,
25/10,
26/11,
27/12,
28/13,
29/14,
30/15,
31/16,
32/17,
33/32, 33/1,
34/1, 34/18,
35/19, 35/18,
36/19, 36/20,
37/20, 37/21,
38/21, 38/22,
39/23, 39/22,
40/23, 40/24,
41/24, 41/25,
42/25, 42/26,
43/27, 43/26,
44/27, 44/28,
45/28, 45/29,
46/29, 46/30,
47/31, 47/30,
48/31, 48/32,
49/33, 49/64,
50/34, 50/49,
51/35, 51/50,
52/36,
53/37, 53/52,
54/38, 54/53,
55/39, 55/54,
56/40, 56/68,
57/41, 57/56,
58/42, 58/57,
59/43, 59/58,
60/44,
61/45, 61/60,
62/46, 62/61,
63/47, 63/62,
64/48, 64/66,
65/55, 65/52,
66/65, 66/51,
67/63, 67/60,
68/67, 68/59}
\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);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-3) -- (p-2);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-4) -- (p-3);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-5) -- (p-4);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-6) -- (p-5);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-7) -- (p-6);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-8) -- (p-7);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-9) -- (p-8);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-10) -- (p-9);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-11) -- (p-10);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-12) -- (p-11);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-13) -- (p-12);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-14) -- (p-13);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-15) -- (p-14);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-16) -- (p-15);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-16) -- (p-17);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-17) -- (p-2);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-49) -- (p-64);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-50) -- (p-49);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-51) -- (p-50);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-53) -- (p-52);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-54) -- (p-53);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-55) -- (p-54);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-56) -- (p-68);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-57) -- (p-56);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-58) -- (p-57);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-59) -- (p-58);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-61) -- (p-60);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-62) -- (p-61);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-63) -- (p-62);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-64) -- (p-66);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-65) -- (p-55);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-65) -- (p-52);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-67) -- (p-63);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-67) -- (p-60);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
3/9.54/159.91/0.4/Gray,
4/339.91/493.09/0.4/Gray,
5/313.09/476.00/0.4/Gray,
6/296.00/466.86/0.4/Gray,
7/286.86/433.53/0.4/Gray,
8/253.53/396.24/0.4/Gray,
9/216.24/376.60/0.4/Gray,
10/196.60/369.54/0.4/Gray,
11/189.54/339.91/0.4/Gray,
12/159.91/313.09/0.4/Gray,
13/133.09/296.00/0.4/Gray,
14/116.00/286.86/0.4/Gray,
15/106.86/253.53/0.4/Gray,
3/9.54/104.95/0.3/DarkGray,
4/339.91/398.27/0.3/DarkGray,
5/313.09/382.90/0.3/DarkGray,
6/296.00/366.12/0.3/DarkGray,
7/286.86/378.87/0.3/DarkGray,
8/253.53/313.07/0.3/DarkGray,
9/216.24/288.91/0.3/DarkGray,
10/196.60/270.00/0.3/DarkGray,
11/189.54/284.95/0.3/DarkGray,
12/159.91/218.27/0.3/DarkGray,
13/133.09/202.90/0.3/DarkGray,
14/116.00/186.12/0.3/DarkGray,
15/106.86/198.87/0.3/DarkGray,
16/73.53/133.07/0.4/DarkGray,
17/36.24/108.91/0.4/DarkGray,
33/82.63/132.19/0.4/LightGray,
34/51.45/114.89/0.4/LightGray,
35/238.48/351.31/0.4/LightGray,
36/17.84/54.12/0.4/LightGray,
37/1.67/47.91/0.4/LightGray,
38/330.07/389.04/0.4/LightGray,
39/148.67/261.22/0.4/LightGray,
40/285.26/315.50/0.4/LightGray,
41/262.63/312.19/0.4/LightGray,
42/231.45/294.89/0.4/LightGray,
43/58.48/171.31/0.4/LightGray,
44/197.84/234.12/0.4/LightGray,
45/181.67/227.91/0.4/LightGray,
46/150.07/209.04/0.4/LightGray,
47/328.67/441.22/0.4/LightGray,
48/105.26/135.50/0.4/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 {
1/115,
2/236,
3/315,
4/192,
5/170,
6/154,
7/229,
8/106,
9/75,
10/56,
11/135,
12/12,
13/350,
14/334,
15/49,
16/286,
17/255,
18/195,
19/307,
20/221,
21/34,
22/108,
23/215,
24/120,
25/295,
26/15,
27/127,
28/41,
29/214,
30/288,
31/35,
32/300,
33/112,
34/266,
35/117,
36/49,
37/32,
38/182,
39/27,
40/311,
41/292,
42/86,
43/297,
44/229,
45/212,
46/2,
47/207,
48/131,
49/172,
50/148,
51/321,
52/273,
53/90,
54/65,
55/226,
56/178,
57/352,
58/328,
59/141,
60/93,
61/270,
62/245,
63/46,
64/358,
65/122,
66/58,
67/302,
68/238}
\node[anchor=\a] (P\i) at (p-\i) {\i};
%Vergrößerungen als \spy[rectangle, magnification=3, width=2cm, h eight=2cm, blue!70!black] on (p-18) in node at (2.5 cm,-2);
\spy[magnification=2] on (p-18) in node at (4,-2);
\spy[magnification=2] on (p-1) in node at (6.5,-2);
\end{tikzpicture}
$
Und so geht das weiter (Button "Feinjustieren(11)"), als nächstes ein Abstand P46-P31 gegen Überschneidung in P30 (Button "#1683symZ81")
68 Knoten, 68×Grad 3, 0 Dreiecke, 0 Überschneidungen, Fläche=27.82
102 Kanten, minimal 0.99999999999999966693, maximal 1.45371606383912665983
einzustellende Kanten, Abstände und Winkel:
...zusätzlich...
|P31-P46|=1.05887784902094095330
$
%Eingabe war:
%
%#1683 symmetrisch Z81
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%P[1]=[99.38901545713267,76.54308398594306]; P[2]=[99.38901545713267,13.709252345747842]; D=ab(1,2); A(2,1,Bew(1));
%M(3,2,1,AW1-MW1,0,jam(2)*D);
%M(4,3,2,AW2,0,jam(2)*D);
%M(5,4,3,AW3,0,jam(2)*D);
%M(6,5,4,AW4,0,jam(2)*D);
%M(7,6,5,AW5,0,jam(2)*D);
%M(8,7,6,AW6,0,jam(2)*D);
%M(9,8,7,AW7,0,jam(2)*D);
%M(10,9,8,AW8,0,jam(2)*D);
%M(11,10,9,AW1,0,jam(2)*D);
%M(12,11,10,AW2,0,jam(2)*D);
%M(13,12,11,AW3,0,jam(2)*D);
%M(14,13,12,AW4,0,jam(2)*D);
%M(15,14,13,AW5,0,jam(2)*D);
%M(16,15,14,AW6,0,jam(2)*D);
%M(17,2,1,-MW1,0,jam(2)*D); RA(16,17,"",jam(2)*D);
%M(18,3,2,MW2);
%M(19,4,3,MW3);
%M(20,5,4,MW4);
%M(21,6,5,MW5);
%M(22,7,6,MW6);
%M(23,8,7,MW7);
%M(24,9,8,MW8);
%M(25,10,9,MW1);
%M(26,11,10,MW2);
%M(27,12,11,MW3);
%M(28,13,12,MW4);
%M(29,14,13,MW5);
%M(30,15,14,MW6);
%M(31,16,15,MW7);
%M(32,17,16,MW8);
%N(33,32,1); M(49,33,32,IW1);
%N(34,1,18); M(50,34,1,IW2);
%N(35,19,18); M(51,35,18,IW3);
%N(36,19,20); M(52,36,19,IW4);
%N(37,20,21); M(53,37,20,IW5);
%N(38,21,22); M(54,38,21,IW6);
%N(39,23,22); M(55,39,22,IW7);
%N(40,23,24); M(56,40,23,IW8);
%N(41,24,25); M(57,41,24,IW1);
%N(42,25,26); M(58,42,25,IW2);
%N(43,27,26); M(59,43,26,IW3);
%N(44,27,28); M(60,44,27,IW4);
%N(45,28,29); M(61,45,28,IW5);
%N(46,29,30); M(62,46,29,IW6);
%N(47,31,30); M(63,47,30,IW7);
%N(48,31,32); M(64,48,31,IW8);
%RA(51,50,"green",jam(1.66380770527268428971)*D);
%RA(50,49,"green",jam(1.42029151629267658130)*D);
%RA(49,64,"green",jam(1.42029151629267658130)*D);
%A(63,62,"green",jam(1.66380770527268428971)*D);
%A(62,61,"green",jam(1.42029151629267658130)*D);
%A(61,60,"green",jam(1.42029151629267658130)*D);
%A(59,58,"green",jam(1.66380770527268428971)*D);
%A(58,57,"green",jam(1.42029151629267658130)*D);
%A(57,56,"green",jam(1.42029151629267658130)*D);
%RA(55,54,"green",jam(1.66380770527268428971)*D);
%RA(54,53,"green",jam(1.42029151629267658130)*D);
%RA(53,52,"green",jam(1.42029151629267658130)*D);
%Q(65,55,52,jam(2)*D,jam(2)*D); N(66,65,51);
%RA(64,66,"green",jam(3.38797928336377340841)*D);
%Q(67,63,60,jam(2)*D,jam(2)*D); N(68,67,59);
%A(56,68,"green",jam(3.38797928336377340841)*D);
%
%R(37,55,"brown",1.10396782836591800248*D);
%R(19,34,"brown",1.12542474054885377477*D);
%R(49,34,"brown",1.06236326562790539541*D);
%R(31,46,"brown",1.05887784902094095330*D);
%
%
%Ende der Eingabe.
\usetikzlibrary{spy}
\tikzset{SpyStyle/.style={spy using outlines={rectangle, magnification=3, width=2cm, height=2cm, connect spies, blue!70!black}}}
\begin{tikzpicture}[SpyStyle,draw=grey,font=\sffamily\tiny]
\definecolor{Brown}{rgb}{0.64,0.16,0.16}
\definecolor{DarkGray}{rgb}{0.66,0.66,0.66}
\definecolor{Gray}{rgb}{0.50,0.50,0.50}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LightGray}{rgb}{0.82,0.82,0.82}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/5.777/1.746,
2/5.78/0.33,
3/4.12/0.00,
4/2.51/0.52,
5/1.33/1.73,
6/0.56/3.23,
7/0.00/4.83,
8/0.40/6.47,
9/1.74/7.50,
10/3.34/8.02,
11/5.00/8.35,
12/6.61/7.83,
13/7.79/6.62,
14/8.56/5.12,
15/9.12/3.52,
16/8.72/1.88,
17/7.38/0.85,
18/3.72/1.36,
19/3.57/1.46,
20/2.63/2.30,
21/1.97/3.40,
22/1.319/5.355,
23/1.361/5.428,
24/2.19/6.16,
25/3.343/6.604,
26/5.40/6.99,
27/5.55/6.89,
28/6.49/6.05,
29/7.15/4.95,
30/7.802/2.995,
31/7.759/2.923,
32/6.93/2.19,
33/6.81/0.78,
34/4.92/0.61,
35/4.46/2.58,
36/2.26/0.93,
37/1.22/2.19,
38/0.71/4.07,
39/2.56/4.67,
40/0.91/6.78,
41/2.31/7.57,
42/4.20/7.74,
43/4.66/5.77,
44/6.87/7.42,
45/7.90/6.16,
46/8.41/4.28,
47/6.56/3.68,
48/8.21/1.57,
49/5.840/1.810,
50/4.31/1.89,
51/5.85/2.31,
52/3.08/2.09,
53/2.12/3.29,
54/1.93/4.81,
55/2.36/3.27,
56/1.94/5.79,
57/3.281/6.541,
58/4.81/6.46,
59/3.27/6.04,
60/6.04/6.26,
61/7.00/5.06,
62/7.19/3.54,
63/6.76/5.08,
64/7.18/2.56,
65/4.03/3.49,
66/5.44/3.67,
67/5.09/4.87,
68/3.68/4.68}
\coordinate (p-\i) at (\x,\y);
%Fläche als \fill[Yellow!3] (p-1) -- (p-2) -- (p-3) -- cycle;
%Dreiecke als \fill[black!3] (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 {
3/11.14/162.04/0.4/Gray,
4/342.04/494.21/0.4/Gray,
5/314.21/477.40/0.4/Gray,
6/297.40/469.19/0.4/Gray,
7/289.19/436.39/0.4/Gray,
8/256.39/397.61/0.4/Gray,
9/217.61/378.00/0.4/Gray,
10/198.00/371.14/0.4/Gray,
11/191.14/342.04/0.4/Gray,
12/162.04/314.21/0.4/Gray,
13/134.21/297.40/0.4/Gray,
14/117.40/289.19/0.4/Gray,
15/109.19/256.39/0.4/Gray,
3/11.14/106.36/0.3/DarkGray,
4/342.04/401.64/0.3/DarkGray,
5/314.21/383.71/0.3/DarkGray,
6/297.40/366.70/0.3/DarkGray,
7/289.19/381.78/0.3/DarkGray,
8/256.39/312.73/0.3/DarkGray,
9/217.61/288.76/0.3/DarkGray,
10/198.00/270.00/0.3/DarkGray,
11/191.14/286.36/0.3/DarkGray,
12/162.04/221.64/0.3/DarkGray,
13/134.21/203.71/0.3/DarkGray,
14/117.40/186.70/0.3/DarkGray,
15/109.19/201.78/0.3/DarkGray,
16/76.39/132.73/0.4/DarkGray,
17/37.61/108.76/0.4/DarkGray,
33/85.47/133.38/0.4/LightGray,
34/53.08/115.68/0.4/LightGray,
35/238.71/349.25/0.4/LightGray,
36/21.91/54.45/0.4/LightGray,
37/4.52/50.45/0.4/LightGray,
38/331.76/391.28/0.4/LightGray,
39/151.24/261.67/0.4/LightGray,
40/288.33/316.29/0.4/LightGray,
41/265.47/313.38/0.4/LightGray,
42/233.08/295.68/0.4/LightGray,
43/58.71/169.25/0.4/LightGray,
44/201.91/234.45/0.4/LightGray,
45/184.52/230.45/0.4/LightGray,
46/151.76/211.28/0.4/LightGray,
47/331.24/441.67/0.4/LightGray,
48/108.33/136.29/0.4/LightGray}
\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-16) -- (p-17);
\draw[Green,very thick] (p-51) -- (p-50);
\draw[Green,very thick] (p-50) -- (p-49);
\draw[Green,very thick] (p-49) -- (p-64);
\draw[Green,very thick] (p-55) -- (p-54);
\draw[Green,very thick] (p-54) -- (p-53);
\draw[Green,very thick] (p-53) -- (p-52);
\draw[Green,very thick] (p-64) -- (p-66);
\draw[Brown,very thick] (p-37) -- (p-55);
\draw[Brown,very thick] (p-19) -- (p-34);
\draw[Brown,very thick] (p-49) -- (p-34);
\draw[Brown,very thick] (p-31) -- (p-46);
%Kanten als \draw[line width=0] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/2,
4/3,
5/4,
6/5,
7/6,
8/7,
9/8,
10/9,
11/10,
12/11,
13/12,
14/13,
15/14,
16/15, 16/17,
17/2,
18/3,
19/4,
20/5,
21/6,
22/7,
23/8,
24/9,
25/10,
26/11,
27/12,
28/13,
29/14,
30/15,
31/16,
32/17,
33/32, 33/1,
34/1, 34/18,
35/19, 35/18,
36/19, 36/20,
37/20, 37/21,
38/21, 38/22,
39/23, 39/22,
40/23, 40/24,
41/24, 41/25,
42/25, 42/26,
43/27, 43/26,
44/27, 44/28,
45/28, 45/29,
46/29, 46/30,
47/31, 47/30,
48/31, 48/32,
49/33, 49/64,
50/34, 50/49,
51/35, 51/50,
52/36,
53/37, 53/52,
54/38, 54/53,
55/39, 55/54,
56/40, 56/68,
57/41, 57/56,
58/42, 58/57,
59/43, 59/58,
60/44,
61/45, 61/60,
62/46, 62/61,
63/47, 63/62,
64/48, 64/66,
65/55, 65/52,
66/65, 66/51,
67/63, 67/60,
68/67, 68/59}
\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);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-3) -- (p-2);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-4) -- (p-3);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-5) -- (p-4);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-6) -- (p-5);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-7) -- (p-6);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-8) -- (p-7);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-9) -- (p-8);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-10) -- (p-9);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-11) -- (p-10);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-12) -- (p-11);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-13) -- (p-12);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-14) -- (p-13);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-15) -- (p-14);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-16) -- (p-15);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-16) -- (p-17);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-17) -- (p-2);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-49) -- (p-64);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-50) -- (p-49);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-51) -- (p-50);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-53) -- (p-52);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-54) -- (p-53);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-55) -- (p-54);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-56) -- (p-68);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-57) -- (p-56);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-58) -- (p-57);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-59) -- (p-58);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-61) -- (p-60);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-62) -- (p-61);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-63) -- (p-62);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-64) -- (p-66);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-65) -- (p-55);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-65) -- (p-52);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-67) -- (p-63);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-67) -- (p-60);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
3/11.14/162.04/0.4/Gray,
4/342.04/494.21/0.4/Gray,
5/314.21/477.40/0.4/Gray,
6/297.40/469.19/0.4/Gray,
7/289.19/436.39/0.4/Gray,
8/256.39/397.61/0.4/Gray,
9/217.61/378.00/0.4/Gray,
10/198.00/371.14/0.4/Gray,
11/191.14/342.04/0.4/Gray,
12/162.04/314.21/0.4/Gray,
13/134.21/297.40/0.4/Gray,
14/117.40/289.19/0.4/Gray,
15/109.19/256.39/0.4/Gray,
3/11.14/106.36/0.3/DarkGray,
4/342.04/401.64/0.3/DarkGray,
5/314.21/383.71/0.3/DarkGray,
6/297.40/366.70/0.3/DarkGray,
7/289.19/381.78/0.3/DarkGray,
8/256.39/312.73/0.3/DarkGray,
9/217.61/288.76/0.3/DarkGray,
10/198.00/270.00/0.3/DarkGray,
11/191.14/286.36/0.3/DarkGray,
12/162.04/221.64/0.3/DarkGray,
13/134.21/203.71/0.3/DarkGray,
14/117.40/186.70/0.3/DarkGray,
15/109.19/201.78/0.3/DarkGray,
16/76.39/132.73/0.4/DarkGray,
17/37.61/108.76/0.4/DarkGray,
33/85.47/133.38/0.4/LightGray,
34/53.08/115.68/0.4/LightGray,
35/238.71/349.25/0.4/LightGray,
36/21.91/54.45/0.4/LightGray,
37/4.52/50.45/0.4/LightGray,
38/331.76/391.28/0.4/LightGray,
39/151.24/261.67/0.4/LightGray,
40/288.33/316.29/0.4/LightGray,
41/265.47/313.38/0.4/LightGray,
42/233.08/295.68/0.4/LightGray,
43/58.71/169.25/0.4/LightGray,
44/201.91/234.45/0.4/LightGray,
45/184.52/230.45/0.4/LightGray,
46/151.76/211.28/0.4/LightGray,
47/331.24/441.67/0.4/LightGray,
48/108.33/136.29/0.4/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 {
1/116,
2/237,
3/317,
4/194,
5/171,
6/155,
7/232,
8/107,
9/76,
10/57,
11/137,
12/14,
13/351,
14/335,
15/52,
16/287,
17/256,
18/196,
19/309,
20/222,
21/35,
22/111,
23/221,
24/122,
25/296,
26/16,
27/129,
28/42,
29/215,
30/291,
31/41,
32/302,
33/114,
34/267,
35/116,
36/51,
37/34,
38/184,
39/29,
40/314,
41/294,
42/87,
43/296,
44/231,
45/214,
46/4,
47/209,
48/134,
49/174,
50/149,
51/321,
52/275,
53/92,
54/67,
55/227,
56/181,
57/354,
58/329,
59/141,
60/95,
61/272,
62/247,
63/47,
64/1,
65/124,
66/60,
67/304,
68/240}
\node[anchor=\a] (P\i) at (p-\i) {\i};
%Vergrößerungen als \spy[rectangle, magnification=3, width=2cm, h eight=2cm, blue!70!black] on (p-18) in node at (2.5 cm,-2);
\spy[magnification=2] on (p-30) in node at (9,-1);
\end{tikzpicture}
$
Dann zur Abwechslung auch mit zwei zusätzliche Winkel, damit die Spitzen in P48 und P36 nicht über die Außenkanten hinausragen (Button "##1683symZ87 ")
68 Knoten, 68×Grad 3, 0 Dreiecke, 0 Überschneidungen, Fläche=25.09
102 Kanten, minimal 0.99999999999999933387, maximal 1.31043730683729808817
einzustellende Kanten, Abstände und Winkel:
...zusätzlich...
∠(P16-P17,P48-P17)=1.19234930042722786503°
∠(P4-P5,P36-P5)=2.25589393965175233348°
|P52-P21|=1.12432169364628564701
$
%Eingabe war:
%
%#1683 symmetrisch Z87
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%P[1]=[107.2637577995421,85.27506290525736]; P[2]=[107.2637577995421,18.42393802652532]; D=ab(1,2); A(2,1,Bew(1));
%M(3,2,1,AW1-MW1,0,jam(2)*D);
%M(4,3,2,AW2,0,jam(2)*D);
%M(5,4,3,AW3,0,jam(2)*D);
%M(6,5,4,AW4,0,jam(2)*D);
%M(7,6,5,AW5,0,jam(2)*D);
%M(8,7,6,AW6,0,jam(2)*D);
%M(9,8,7,AW7,0,jam(2)*D);
%M(10,9,8,AW8,0,jam(2)*D);
%M(11,10,9,AW1,0,jam(2)*D);
%M(12,11,10,AW2,0,jam(2)*D);
%M(13,12,11,AW3,0,jam(2)*D);
%M(14,13,12,AW4,0,jam(2)*D);
%M(15,14,13,AW5,0,jam(2)*D);
%M(16,15,14,AW6,0,jam(2)*D);
%M(17,2,1,-MW1,0,jam(2)*D); RA(16,17,"",jam(2)*D);
%M(18,3,2,MW2);
%M(19,4,3,MW3);
%M(20,5,4,MW4);
%M(21,6,5,MW5);
%M(22,7,6,MW6);
%M(23,8,7,MW7);
%M(24,9,8,MW8);
%M(25,10,9,MW1);
%M(26,11,10,MW2);
%M(27,12,11,MW3);
%M(28,13,12,MW4);
%M(29,14,13,MW5);
%M(30,15,14,MW6);
%M(31,16,15,MW7);
%M(32,17,16,MW8);
%N(33,32,1); M(49,33,32,IW1);
%N(34,1,18); M(50,34,1,IW2);
%N(35,19,18); M(51,35,18,IW3);
%N(36,19,20); M(52,36,19,IW4);
%N(37,20,21); M(53,37,20,IW5);
%N(38,21,22); M(54,38,21,IW6);
%N(39,23,22); M(55,39,22,IW7);
%N(40,23,24); M(56,40,23,IW8);
%N(41,24,25); M(57,41,24,IW1);
%N(42,25,26); M(58,42,25,IW2);
%N(43,27,26); M(59,43,26,IW3);
%N(44,27,28); M(60,44,27,IW4);
%N(45,28,29); M(61,45,28,IW5);
%N(46,29,30); M(62,46,29,IW6);
%N(47,31,30); M(63,47,30,IW7);
%N(48,31,32); M(64,48,31,IW8);
%RA(51,50,"green",jam(1.66380770527268428971)*D);
%RA(50,49,"green",jam(1.42029151629267658130)*D);
%RA(49,64,"green",jam(1.42029151629267658130)*D);
%A(63,62,"green",jam(1.66380770527268428971)*D);
%A(62,61,"green",jam(1.42029151629267658130)*D);
%A(61,60,"green",jam(1.42029151629267658130)*D);
%A(59,58,"green",jam(1.66380770527268428971)*D);
%A(58,57,"green",jam(1.42029151629267658130)*D);
%A(57,56,"green",jam(1.42029151629267658130)*D);
%RA(55,54,"green",jam(1.66380770527268428971)*D);
%RA(54,53,"green",jam(1.42029151629267658130)*D);
%RA(53,52,"green",jam(1.42029151629267658130)*D);
%Q(65,55,52,jam(2)*D,jam(2)*D); N(66,65,51);
%RA(64,66,"green",jam(3.38797928336377340841)*D);
%Q(67,63,60,jam(2)*D,jam(2)*D); N(68,67,59);
%A(56,68,"green",jam(3.38797928336377340841)*D);
%
%R(37,55,"brown",1.10396782836591800248*D);
%R(19,34,"brown",1.12542474054885377477*D);
%R(49,34,"brown",1.06236326562790539541*D);
%R(31,46,"brown",1.05887784902094095330*D);
%RW(48,17,16,17,1.19234930042720232990);
%RW(36,5,4,5,2.25589393965173945489);
%R(52,21,"brown",1.12432169364628609110*D);
%
%
%Ende der Eingabe.
\usetikzlibrary{spy}
\tikzset{SpyStyle/.style={spy using outlines={rectangle, magnification=3, width=2cm, height=2cm, connect spies, blue!70!black}}}
\begin{tikzpicture}[SpyStyle,draw=grey,font=\sffamily\tiny]
\definecolor{Brown}{rgb}{0.64,0.16,0.16}
\definecolor{DarkGray}{rgb}{0.66,0.66,0.66}
\definecolor{Gray}{rgb}{0.50,0.50,0.50}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LightGray}{rgb}{0.82,0.82,0.82}
\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 {
1/5.568/1.815,
2/5.57/0.38,
3/3.99/0.00,
4/2.41/0.41,
5/1.29/1.59,
6/0.55/3.04,
7/0.00/4.57,
8/0.31/6.17,
9/1.58/7.19,
10/3.10/7.77,
11/4.68/8.14,
12/6.26/7.73,
13/7.38/6.55,
14/8.12/5.10,
15/8.67/3.57,
16/8.36/1.97,
17/7.09/0.95,
18/3.55/1.37,
19/3.39/1.47,
20/2.62/2.13,
21/1.991/3.143,
22/1.333/5.120,
23/1.372/5.195,
24/2.02/5.82,
25/3.101/6.327,
26/5.12/6.77,
27/5.28/6.67,
28/6.05/6.01,
29/6.678/4.999,
30/7.337/3.022,
31/7.297/2.947,
32/6.65/2.32,
33/6.66/0.88,
34/4.77/0.62,
35/4.24/2.63,
36/2.13/0.78,
37/1.20/1.94,
38/0.72/3.82,
39/2.62/4.48,
40/0.75/6.49,
41/2.01/7.26,
42/3.90/7.53,
43/4.43/5.51,
44/6.54/7.37,
45/7.47/6.20,
46/7.95/4.33,
47/6.05/3.66,
48/7.92/1.65,
49/5.630/1.882,
50/4.11/1.90,
51/5.63/2.26,
52/3.03/1.90,
53/2.076/3.082,
54/1.93/4.59,
55/2.31/3.08,
56/1.75/5.46,
57/3.040/6.260,
58/4.56/6.25,
59/3.04/5.88,
60/5.64/6.24,
61/6.594/5.060,
62/6.74/3.55,
63/6.36/5.07,
64/6.92/2.68,
65/3.93/3.26,
66/5.31/3.66,
67/4.74/4.88,
68/3.36/4.48}
\coordinate (p-\i) at (\x,\y);
%Fläche als \fill[Yellow!3] (p-1) -- (p-2) -- (p-3) -- cycle;
%Dreiecke als \fill[black!3] (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 {
3/13.34/165.24/0.4/Gray,
4/345.24/493.64/0.4/Gray,
5/313.64/476.81/0.4/Gray,
6/296.81/469.93/0.4/Gray,
7/289.93/438.89/0.4/Gray,
8/258.89/398.99/0.4/Gray,
9/218.99/380.59/0.4/Gray,
10/200.59/373.34/0.4/Gray,
11/193.34/345.24/0.4/Gray,
12/165.24/313.64/0.4/Gray,
13/133.64/296.81/0.4/Gray,
14/116.81/289.93/0.4/Gray,
15/109.93/258.89/0.4/Gray,
3/13.34/107.78/0.3/DarkGray,
4/345.24/407.03/0.3/DarkGray,
5/313.64/381.89/0.3/DarkGray,
6/296.81/363.92/0.3/DarkGray,
7/289.93/382.28/0.3/DarkGray,
8/258.89/317.34/0.3/DarkGray,
9/218.99/287.94/0.3/DarkGray,
10/200.59/270.00/0.3/DarkGray,
11/193.34/287.78/0.3/DarkGray,
12/165.24/227.03/0.3/DarkGray,
13/133.64/201.89/0.3/DarkGray,
14/116.81/183.92/0.3/DarkGray,
15/109.93/202.28/0.3/DarkGray,
16/78.89/137.34/0.4/DarkGray,
17/38.99/107.94/0.4/DarkGray,
33/90.53/135.76/0.4/LightGray,
34/56.40/117.30/0.4/LightGray,
35/241.14/345.08/0.4/LightGray,
36/28.71/51.33/0.4/LightGray,
37/7.46/52.38/0.4/LightGray,
38/332.07/392.66/0.4/LightGray,
39/153.70/257.44/0.4/LightGray,
40/295.81/314.22/0.4/LightGray,
41/270.53/315.76/0.4/LightGray,
42/236.40/297.30/0.4/LightGray,
43/61.14/165.08/0.4/LightGray,
44/208.71/231.33/0.4/LightGray,
45/187.46/232.38/0.4/LightGray,
46/152.07/212.66/0.4/LightGray,
47/333.70/437.44/0.4/LightGray,
48/115.81/134.22/0.4/LightGray}
\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-16) -- (p-17);
\draw[Green,very thick] (p-51) -- (p-50);
\draw[Green,very thick] (p-50) -- (p-49);
\draw[Green,very thick] (p-49) -- (p-64);
\draw[Green,very thick] (p-55) -- (p-54);
\draw[Green,very thick] (p-54) -- (p-53);
\draw[Green,very thick] (p-53) -- (p-52);
\draw[Green,very thick] (p-64) -- (p-66);
\draw[Brown,very thick] (p-37) -- (p-55);
\draw[Brown,very thick] (p-19) -- (p-34);
\draw[Brown,very thick] (p-49) -- (p-34);
\draw[Brown,very thick] (p-31) -- (p-46);
\draw[Violet,very thick] (p-48) -- (p-17);
\draw[Violet,very thick] (p-36) -- (p-5);
\draw[Brown,very thick] (p-52) -- (p-21);
%Kanten als \draw[line width=0] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/2,
4/3,
5/4,
6/5,
7/6,
8/7,
9/8,
10/9,
11/10,
12/11,
13/12,
14/13,
15/14,
16/15, 16/17,
17/2,
18/3,
19/4,
20/5,
21/6,
22/7,
23/8,
24/9,
25/10,
26/11,
27/12,
28/13,
29/14,
30/15,
31/16,
32/17,
33/32, 33/1,
34/1, 34/18,
35/19, 35/18,
36/19, 36/20,
37/20, 37/21,
38/21, 38/22,
39/23, 39/22,
40/23, 40/24,
41/24, 41/25,
42/25, 42/26,
43/27, 43/26,
44/27, 44/28,
45/28, 45/29,
46/29, 46/30,
47/31, 47/30,
48/31, 48/32,
49/33, 49/64,
50/34, 50/49,
51/35, 51/50,
52/36,
53/37, 53/52,
54/38, 54/53,
55/39, 55/54,
56/40, 56/68,
57/41, 57/56,
58/42, 58/57,
59/43, 59/58,
60/44,
61/45, 61/60,
62/46, 62/61,
63/47, 63/62,
64/48, 64/66,
65/55, 65/52,
66/65, 66/51,
67/63, 67/60,
68/67, 68/59}
\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);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-3) -- (p-2);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-4) -- (p-3);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-5) -- (p-4);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-6) -- (p-5);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-7) -- (p-6);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-8) -- (p-7);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-9) -- (p-8);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-10) -- (p-9);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-11) -- (p-10);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-12) -- (p-11);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-13) -- (p-12);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-14) -- (p-13);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-15) -- (p-14);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-16) -- (p-15);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-16) -- (p-17);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-17) -- (p-2);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-49) -- (p-64);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-50) -- (p-49);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-51) -- (p-50);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-53) -- (p-52);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-54) -- (p-53);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-55) -- (p-54);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-56) -- (p-68);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-57) -- (p-56);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-58) -- (p-57);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-59) -- (p-58);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-61) -- (p-60);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-62) -- (p-61);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-63) -- (p-62);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-64) -- (p-66);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-65) -- (p-55);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-65) -- (p-52);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-67) -- (p-63);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-67) -- (p-60);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
3/13.34/165.24/0.4/Gray,
%4/345.24/493.64/0.4/Gray,
5/313.64/476.81/0.4/Gray,
6/296.81/469.93/0.4/Gray,
7/289.93/438.89/0.4/Gray,
8/258.89/398.99/0.4/Gray,
9/218.99/380.59/0.4/Gray,
10/200.59/373.34/0.4/Gray,
11/193.34/345.24/0.4/Gray,
12/165.24/313.64/0.4/Gray,
13/133.64/296.81/0.4/Gray,
14/116.81/289.93/0.4/Gray,
15/109.93/258.89/0.4/Gray,
3/13.34/107.78/0.3/DarkGray,
4/345.24/407.03/0.3/DarkGray,
5/313.64/381.89/0.3/DarkGray,
6/296.81/363.92/0.3/DarkGray,
7/289.93/382.28/0.3/DarkGray,
8/258.89/317.34/0.3/DarkGray,
9/218.99/287.94/0.3/DarkGray,
10/200.59/270.00/0.3/DarkGray,
11/193.34/287.78/0.3/DarkGray,
12/165.24/227.03/0.3/DarkGray,
13/133.64/201.89/0.3/DarkGray,
14/116.81/183.92/0.3/DarkGray,
15/109.93/202.28/0.3/DarkGray,
16/78.89/137.34/0.4/DarkGray,
17/38.99/107.94/0.4/DarkGray,
33/90.53/135.76/0.4/LightGray,
34/56.40/117.30/0.4/LightGray,
35/241.14/345.08/0.4/LightGray,
36/28.71/51.33/0.4/LightGray,
37/7.46/52.38/0.4/LightGray,
38/332.07/392.66/0.4/LightGray,
39/153.70/257.44/0.4/LightGray,
40/295.81/314.22/0.4/LightGray,
41/270.53/315.76/0.4/LightGray,
42/236.40/297.30/0.4/LightGray,
43/61.14/165.08/0.4/LightGray,
44/208.71/231.33/0.4/LightGray,
45/187.46/232.38/0.4/LightGray,
46/152.07/212.66/0.4/LightGray,
47/333.70/437.44/0.4/LightGray,
48/115.81/134.22/0.4/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 {
1/117,
2/238,
3/319,
4/199,
5/170,
6/153,
7/233,
8/111,
9/76,
10/58,
11/139,
12/19,
13/350,
14/333,
15/53,
16/291,
17/256,
18/197,
19/314,
20/221,
21/33,
22/112,
23/226,
24/124,
25/297,
26/17,
27/134,
28/41,
29/213,
30/292,
31/46,
32/304,
33/117,
34/269,
35/116,
36/52,
37/34,
38/185,
39/28,
40/317,
41/297,
42/89,
43/296,
44/232,
45/214,
46/5,
47/208,
48/137,
49/176,
50/151,
51/317,
52/275,
53/93,
54/67,
55/224,
56/183,
57/356,
58/331,
59/137,
60/95,
61/273,
62/247,
63/44,
64/3,
65/129,
66/62,
67/309,
68/242}
\node[anchor=\a] (P\i) at (p-\i) {\i};
%Vergrößerungen als \spy[rectangle, magnification=3, width=2cm, h eight=2cm, blue!70!black] on (p-18) in node at (2.5 cm,-2);
\spy[circle,magnification=10] on (p-36) in node at (2.5,-2);
\spy[magnification=2] on (p-53) in node at (5,-2);
\spy[circle,magnification=10] on (p-48) in node at (10,0);
\end{tikzpicture}
$
Noch ein Winkel weil sich P47 einer Kante nähert (Button "##1683symZ93 ")
68 Knoten, 68×Grad 3, 0 Dreiecke, 0 Überschneidungen, Fläche=22.55
102 Kanten, minimal 0.99999999999999944489, maximal 1.16715854983546618584
einzustellende Kanten, Abstände und Winkel:
...zusätzlich...
∠(P47-P64,P66-P64)=2.61196905598772621815°
$
%Eingabe war:
%
%#1683 symmetrisch Z93
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%P[1]=[109.05820756743078,88.77618842891317]; P[2]=[109.05820756743078,18.95164382921729]; D=ab(1,2); A(2,1,Bew(1));
%M(3,2,1,AW1-MW1,0,jam(2)*D);
%M(4,3,2,AW2,0,jam(2)*D);
%M(5,4,3,AW3,0,jam(2)*D);
%M(6,5,4,AW4,0,jam(2)*D);
%M(7,6,5,AW5,0,jam(2)*D);
%M(8,7,6,AW6,0,jam(2)*D);
%M(9,8,7,AW7,0,jam(2)*D);
%M(10,9,8,AW8,0,jam(2)*D);
%M(11,10,9,AW1,0,jam(2)*D);
%M(12,11,10,AW2,0,jam(2)*D);
%M(13,12,11,AW3,0,jam(2)*D);
%M(14,13,12,AW4,0,jam(2)*D);
%M(15,14,13,AW5,0,jam(2)*D);
%M(16,15,14,AW6,0,jam(2)*D);
%M(17,2,1,-MW1,0,jam(2)*D); RA(16,17,"",jam(2)*D);
%M(18,3,2,MW2);
%M(19,4,3,MW3);
%M(20,5,4,MW4);
%M(21,6,5,MW5);
%M(22,7,6,MW6);
%M(23,8,7,MW7);
%M(24,9,8,MW8);
%M(25,10,9,MW1);
%M(26,11,10,MW2);
%M(27,12,11,MW3);
%M(28,13,12,MW4);
%M(29,14,13,MW5);
%M(30,15,14,MW6);
%M(31,16,15,MW7);
%M(32,17,16,MW8);
%N(33,32,1); M(49,33,32,IW1);
%N(34,1,18); M(50,34,1,IW2);
%N(35,19,18); M(51,35,18,IW3);
%N(36,19,20); M(52,36,19,IW4);
%N(37,20,21); M(53,37,20,IW5);
%N(38,21,22); M(54,38,21,IW6);
%N(39,23,22); M(55,39,22,IW7);
%N(40,23,24); M(56,40,23,IW8);
%N(41,24,25); M(57,41,24,IW1);
%N(42,25,26); M(58,42,25,IW2);
%N(43,27,26); M(59,43,26,IW3);
%N(44,27,28); M(60,44,27,IW4);
%N(45,28,29); M(61,45,28,IW5);
%N(46,29,30); M(62,46,29,IW6);
%N(47,31,30); M(63,47,30,IW7);
%N(48,31,32); M(64,48,31,IW8);
%RA(51,50,"green",jam(1.66380770527268428971)*D);
%RA(50,49,"green",jam(1.42029151629267658130)*D);
%RA(49,64,"green",jam(1.42029151629267658130)*D);
%A(63,62,"green",jam(1.66380770527268428971)*D);
%A(62,61,"green",jam(1.42029151629267658130)*D);
%A(61,60,"green",jam(1.42029151629267658130)*D);
%A(59,58,"green",jam(1.66380770527268428971)*D);
%A(58,57,"green",jam(1.42029151629267658130)*D);
%A(57,56,"green",jam(1.42029151629267658130)*D);
%RA(55,54,"green",jam(1.66380770527268428971)*D);
%RA(54,53,"green",jam(1.42029151629267658130)*D);
%RA(53,52,"green",jam(1.42029151629267658130)*D);
%Q(65,55,52,jam(2)*D,jam(2)*D); N(66,65,51);
%RA(64,66,"green",jam(3.38797928336377340841)*D);
%Q(67,63,60,jam(2)*D,jam(2)*D); N(68,67,59);
%A(56,68,"green",jam(3.38797928336377340841)*D);
%
%R(37,55,"brown",1.10396782836591800248*D);
%R(19,34,"brown",1.12542474054885377477*D);
%R(49,34,"brown",1.06236326562790539541*D);
%R(31,46,"brown",1.05887784902094095330*D);
%RW(48,17,16,17,1.19234930042720232990);
%RW(36,5,4,5,2.25589393965173945489);
%R(52,21,"brown",1.12432169364628609110*D);
%RW(66,64,47,64,2.61196905598767559198);
%
%
%Ende der Eingabe.
\usetikzlibrary{spy}
\tikzset{SpyStyle/.style={spy using outlines={rectangle, magnification=3, width=2cm, height=2cm, connect spies, blue!70!black}}}
\begin{tikzpicture}[SpyStyle,draw=grey,font=\sffamily\tiny]
\definecolor{Brown}{rgb}{0.64,0.16,0.16}
\definecolor{DarkGray}{rgb}{0.66,0.66,0.66}
\definecolor{Gray}{rgb}{0.50,0.50,0.50}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LightGray}{rgb}{0.82,0.82,0.82}
\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 {
1/5.324/1.823,
2/5.32/0.37,
3/3.82/0.00,
4/2.31/0.36,
5/1.25/1.49,
6/0.53/2.87,
7/0.00/4.33,
8/0.27/5.85,
9/1.44/6.87,
10/2.87/7.48,
11/4.38/7.85,
12/5.89/7.49,
13/6.95/6.36,
14/7.67/4.98,
15/8.20/3.52,
16/7.92/2.00,
17/6.75/0.98,
18/3.40/1.39,
19/3.24/1.47,
20/2.56/2.11,
21/1.973/2.990,
22/1.353/4.846,
23/1.387/4.924,
24/1.99/5.53,
25/2.871/6.027,
26/4.79/6.46,
27/4.96/6.38,
28/5.64/5.74,
29/6.222/4.859,
30/6.842/3.004,
31/6.808/2.925,
32/6.20/2.32,
33/6.43/0.89,
34/4.60/0.57,
35/3.98/2.72,
36/1.96/0.79,
37/1.14/1.80,
38/0.65/3.58,
39/2.70/4.31,
40/0.71/6.21,
41/1.76/6.96,
42/3.60/7.28,
43/4.21/5.13,
44/6.23/7.06,
45/7.06/6.05,
46/7.55/4.27,
47/5.49/3.54,
48/7.48/1.64,
49/5.386/1.891,
50/3.89/1.84,
51/5.36/2.25,
52/3.04/1.76,
53/2.084/2.904,
54/1.86/4.38,
55/2.28/2.92,
56/1.61/5.07,
57/2.809/5.958,
58/4.30/6.01,
59/2.84/5.60,
60/5.16/6.09,
61/6.111/4.945,
62/6.34/3.47,
63/5.91/4.93,
64/6.58/2.78,
65/3.83/3.09,
66/5.15/3.68,
67/4.37/4.75,
68/3.04/4.17}
\coordinate (p-\i) at (\x,\y);
%Fläche als \fill[Yellow!3] (p-1) -- (p-2) -- (p-3) -- cycle;
%Dreiecke als \fill[black!3] (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 {
3/13.90/166.56/0.4/Gray,
4/346.56/493.24/0.4/Gray,
5/313.24/477.56/0.4/Gray,
6/297.56/469.91/0.4/Gray,
7/289.91/439.86/0.4/Gray,
8/259.86/401.09/0.4/Gray,
9/221.09/382.94/0.4/Gray,
10/202.94/373.90/0.4/Gray,
11/193.90/346.56/0.4/Gray,
12/166.56/313.24/0.4/Gray,
13/133.24/297.56/0.4/Gray,
14/117.56/289.91/0.4/Gray,
15/109.91/259.86/0.4/Gray,
3/13.90/106.69/0.3/DarkGray,
4/346.56/410.11/0.3/DarkGray,
5/313.24/385.28/0.3/DarkGray,
6/297.56/364.91/0.3/DarkGray,
7/289.91/381.04/0.3/DarkGray,
8/259.86/320.21/0.3/DarkGray,
9/221.09/292.36/0.3/DarkGray,
10/202.94/270.00/0.3/DarkGray,
11/193.90/286.69/0.3/DarkGray,
12/166.56/230.11/0.3/DarkGray,
13/133.24/205.28/0.3/DarkGray,
14/117.56/184.91/0.3/DarkGray,
15/109.91/201.04/0.3/DarkGray,
16/79.86/140.21/0.4/DarkGray,
17/41.09/112.36/0.4/DarkGray,
33/99.14/136.16/0.4/LightGray,
34/59.91/118.99/0.4/LightGray,
35/246.31/341.02/0.4/LightGray,
36/28.17/41.93/0.4/LightGray,
37/12.20/49.37/0.4/LightGray,
38/336.06/393.51/0.4/LightGray,
39/158.41/253.25/0.4/LightGray,
40/297.80/308.32/0.4/LightGray,
41/279.14/316.16/0.4/LightGray,
42/239.91/298.99/0.4/LightGray,
43/66.31/161.02/0.4/LightGray,
44/208.17/221.93/0.4/LightGray,
45/192.20/229.37/0.4/LightGray,
46/156.06/213.51/0.4/LightGray,
47/338.41/433.25/0.4/LightGray,
48/117.80/128.32/0.4/LightGray}
\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-16) -- (p-17);
\draw[Green,very thick] (p-51) -- (p-50);
\draw[Green,very thick] (p-50) -- (p-49);
\draw[Green,very thick] (p-49) -- (p-64);
\draw[Green,very thick] (p-55) -- (p-54);
\draw[Green,very thick] (p-54) -- (p-53);
\draw[Green,very thick] (p-53) -- (p-52);
\draw[Green,very thick] (p-64) -- (p-66);
\draw[Brown,very thick] (p-37) -- (p-55);
\draw[Brown,very thick] (p-19) -- (p-34);
\draw[Brown,very thick] (p-49) -- (p-34);
\draw[Brown,very thick] (p-31) -- (p-46);
\draw[Violet,very thick] (p-48) -- (p-17);
\draw[Violet,very thick] (p-36) -- (p-5);
\draw[Brown,very thick] (p-52) -- (p-21);
\draw[Violet,very thick] (p-66) -- (p-64);
%Kanten als \draw[line width=0] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/2,
4/3,
5/4,
6/5,
7/6,
8/7,
9/8,
10/9,
11/10,
12/11,
13/12,
14/13,
15/14,
16/15, 16/17,
17/2,
18/3,
19/4,
20/5,
21/6,
22/7,
23/8,
24/9,
25/10,
26/11,
27/12,
28/13,
29/14,
30/15,
31/16,
32/17,
33/32, 33/1,
34/1, 34/18,
35/19, 35/18,
36/19, 36/20,
37/20, 37/21,
38/21, 38/22,
39/23, 39/22,
40/23, 40/24,
41/24, 41/25,
42/25, 42/26,
43/27, 43/26,
44/27, 44/28,
45/28, 45/29,
46/29, 46/30,
47/31, 47/30,
48/31, 48/32,
49/33, 49/64,
50/34, 50/49,
51/35, 51/50,
52/36,
53/37, 53/52,
54/38, 54/53,
55/39, 55/54,
56/40, 56/68,
57/41, 57/56,
58/42, 58/57,
59/43, 59/58,
60/44,
61/45, 61/60,
62/46, 62/61,
63/47, 63/62,
64/48, 64/66,
65/55, 65/52,
66/65, 66/51,
67/63, 67/60,
68/67, 68/59}
\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);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-3) -- (p-2);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-4) -- (p-3);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-5) -- (p-4);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-6) -- (p-5);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-7) -- (p-6);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-8) -- (p-7);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-9) -- (p-8);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-10) -- (p-9);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-11) -- (p-10);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-12) -- (p-11);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-13) -- (p-12);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-14) -- (p-13);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-15) -- (p-14);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-16) -- (p-15);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-16) -- (p-17);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-17) -- (p-2);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-49) -- (p-64);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-50) -- (p-49);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-51) -- (p-50);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-53) -- (p-52);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-54) -- (p-53);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-55) -- (p-54);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-56) -- (p-68);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-57) -- (p-56);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-58) -- (p-57);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-59) -- (p-58);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-61) -- (p-60);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-62) -- (p-61);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-63) -- (p-62);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-64) -- (p-66);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-65) -- (p-55);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-65) -- (p-52);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-67) -- (p-63);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-67) -- (p-60);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
3/13.90/166.56/0.4/Gray,
4/346.56/493.24/0.4/Gray,
5/313.24/477.56/0.4/Gray,
6/297.56/469.91/0.4/Gray,
7/289.91/439.86/0.4/Gray,
8/259.86/401.09/0.4/Gray,
9/221.09/382.94/0.4/Gray,
10/202.94/373.90/0.4/Gray,
11/193.90/346.56/0.4/Gray,
12/166.56/313.24/0.4/Gray,
13/133.24/297.56/0.4/Gray,
14/117.56/289.91/0.4/Gray,
15/109.91/259.86/0.4/Gray,
3/13.90/106.69/0.3/DarkGray,
4/346.56/410.11/0.3/DarkGray,
5/313.24/385.28/0.3/DarkGray,
6/297.56/364.91/0.3/DarkGray,
7/289.91/381.04/0.3/DarkGray,
8/259.86/320.21/0.3/DarkGray,
9/221.09/292.36/0.3/DarkGray,
10/202.94/270.00/0.3/DarkGray,
11/193.90/286.69/0.3/DarkGray,
12/166.56/230.11/0.3/DarkGray,
13/133.24/205.28/0.3/DarkGray,
14/117.56/184.91/0.3/DarkGray,
15/109.91/201.04/0.3/DarkGray,
16/79.86/140.21/0.4/DarkGray,
17/41.09/112.36/0.4/DarkGray,
33/99.14/136.16/0.4/LightGray,
34/59.91/118.99/0.4/LightGray,
35/246.31/341.02/0.4/LightGray,
36/28.17/41.93/0.4/LightGray,
37/12.20/49.37/0.4/LightGray,
38/336.06/393.51/0.4/LightGray,
39/158.41/253.25/0.4/LightGray,
40/297.80/308.32/0.4/LightGray,
41/279.14/316.16/0.4/LightGray,
42/239.91/298.99/0.4/LightGray,
43/66.31/161.02/0.4/LightGray,
44/208.17/221.93/0.4/LightGray,
45/192.20/229.37/0.4/LightGray,
46/156.06/213.51/0.4/LightGray,
47/338.41/433.25/0.4/LightGray,
48/117.80/128.32/0.4/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 {
1/117,
2/239,
3/319,
4/201,
5/172,
6/154,
7/233,
8/113,
9/79,
10/59,
11/139,
12/21,
13/352,
14/334,
15/53,
16/293,
17/259,
18/198,
19/316,
20/221,
21/32,
22/112,
23/312,
24/128,
25/297,
26/18,
27/136,
28/41,
29/212,
30/292,
31/132,
32/308,
33/122,
34/272,
35/116,
36/49,
37/36,
38/187,
39/28,
40/318,
41/302,
42/92,
43/296,
44/229,
45/216,
46/7,
47/208,
48/138,
49/179,
50/153,
51/312,
52/277,
53/92,
54/69,
55/222,
56/185,
57/359,
58/333,
59/132,
60/97,
61/272,
62/249,
63/42,
64/5,
65/134,
66/63,
67/314,
68/243}
\node[anchor=\a] (P\i) at (p-\i) {\i};
%Vergrößerungen als \spy[rectangle, magnification=3, width=2cm, h eight=2cm, blue!70!black] on (p-18) in node at (2.5 cm,-2);
\spy[circle,magnification=2] on (p-47) in node at (10,1);
\end{tikzpicture}
$
Zuallerletzt noch zwei Abstände (Button "#1683symZ98")
68 Knoten, 68×Grad 3, 0 Dreiecke, 0 Überschneidungen, Fläche=20.59
102 Kanten, minimal 0.99999999999999944489, maximal 1.04775958566727322996
einzustellende Kanten, Abstände und Winkel:
|P34-P52|=1.18641869432938884543
|P2-P51|=1.12752850231051948704
$
%Eingabe war:
%
%#1683 symmetrisch Z98
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%P[1]=[111.10343631995715,95.56933775149179]; P[2]=[111.10343631995715,21.587994810164645]; D=ab(1,2); A(2,1,Bew(1));
%M(3,2,1,AW1-MW1,0,jam(2)*D);
%M(4,3,2,AW2,0,jam(2)*D);
%M(5,4,3,AW3,0,jam(2)*D);
%M(6,5,4,AW4,0,jam(2)*D);
%M(7,6,5,AW5,0,jam(2)*D);
%M(8,7,6,AW6,0,jam(2)*D);
%M(9,8,7,AW7,0,jam(2)*D);
%M(10,9,8,AW8,0,jam(2)*D);
%M(11,10,9,AW1,0,jam(2)*D);
%M(12,11,10,AW2,0,jam(2)*D);
%M(13,12,11,AW3,0,jam(2)*D);
%M(14,13,12,AW4,0,jam(2)*D);
%M(15,14,13,AW5,0,jam(2)*D);
%M(16,15,14,AW6,0,jam(2)*D);
%M(17,2,1,-MW1,0,jam(2)*D); RA(16,17,"",jam(2)*D);
%M(18,3,2,MW2);
%M(19,4,3,MW3);
%M(20,5,4,MW4);
%M(21,6,5,MW5);
%M(22,7,6,MW6);
%M(23,8,7,MW7);
%M(24,9,8,MW8);
%M(25,10,9,MW1);
%M(26,11,10,MW2);
%M(27,12,11,MW3);
%M(28,13,12,MW4);
%M(29,14,13,MW5);
%M(30,15,14,MW6);
%M(31,16,15,MW7);
%M(32,17,16,MW8);
%N(33,32,1); M(49,33,32,IW1);
%N(34,1,18); M(50,34,1,IW2);
%N(35,19,18); M(51,35,18,IW3);
%N(36,19,20); M(52,36,19,IW4);
%N(37,20,21); M(53,37,20,IW5);
%N(38,21,22); M(54,38,21,IW6);
%N(39,23,22); M(55,39,22,IW7);
%N(40,23,24); M(56,40,23,IW8);
%N(41,24,25); M(57,41,24,IW1);
%N(42,25,26); M(58,42,25,IW2);
%N(43,27,26); M(59,43,26,IW3);
%N(44,27,28); M(60,44,27,IW4);
%N(45,28,29); M(61,45,28,IW5);
%N(46,29,30); M(62,46,29,IW6);
%N(47,31,30); M(63,47,30,IW7);
%N(48,31,32); M(64,48,31,IW8);
%RA(51,50,"green",jam(1.66380770527268428971)*D);
%RA(50,49,"green",jam(1.42029151629267658130)*D);
%RA(49,64,"green",jam(1.42029151629267658130)*D);
%A(63,62,"green",jam(1.66380770527268428971)*D);
%A(62,61,"green",jam(1.42029151629267658130)*D);
%A(61,60,"green",jam(1.42029151629267658130)*D);
%A(59,58,"green",jam(1.66380770527268428971)*D);
%A(58,57,"green",jam(1.42029151629267658130)*D);
%A(57,56,"green",jam(1.42029151629267658130)*D);
%RA(55,54,"green",jam(1.66380770527268428971)*D);
%RA(54,53,"green",jam(1.42029151629267658130)*D);
%RA(53,52,"green",jam(1.42029151629267658130)*D);
%Q(65,55,52,jam(2)*D,jam(2)*D); N(66,65,51);
%RA(64,66,"green",jam(3.38797928336377340841)*D);
%Q(67,63,60,jam(2)*D,jam(2)*D); N(68,67,59);
%A(56,68,"green",jam(3.38797928336377340841)*D);
%
%R(37,55,"brown",1.10396782836591800248*D);
%R(19,34,"brown",1.12542474054885377477*D);
%R(49,34,"brown",1.06236326562790539541*D);
%R(31,46,"brown",1.05887784902094095330*D);
%RW(48,17,16,17,1.19234930042720232990);
%RW(36,5,4,5,2.25589393965173945489);
%R(52,21,"brown",1.12432169364628609110*D);
%RW(66,64,47,64,2.61196905598767559198);
%R(34,52,"brown",1.18641869432938884543*D);
%R(2,51,"brown",1.12752850231051904295*D);
%
%
%Ende der Eingabe.
\usetikzlibrary{spy}
\tikzset{SpyStyle/.style={spy using outlines={rectangle, magnification=3, width=2cm, height=2cm, connect spies, blue!70!black}}}
\begin{tikzpicture}[SpyStyle,draw=grey,font=\sffamily\tiny]
\definecolor{Brown}{rgb}{0.64,0.16,0.16}
\definecolor{DarkGray}{rgb}{0.66,0.66,0.66}
\definecolor{Gray}{rgb}{0.50,0.50,0.50}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LightGray}{rgb}{0.82,0.82,0.82}
\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 {
1/5.150/1.854,
2/5.15/0.40,
3/3.73/0.00,
4/2.28/0.29,
5/1.18/1.29,
6/0.44/2.56,
7/0.00/3.98,
8/0.29/5.43,
9/1.41/6.40,
10/2.75/7.01,
11/4.18/7.41,
12/5.63/7.12,
13/6.72/6.12,
14/7.47/4.84,
15/7.90/3.43,
16/7.62/1.98,
17/6.50/1.01,
18/3.28/1.38,
19/3.124/1.469,
20/2.43/2.03,
21/1.88/2.67,
22/1.379/4.426,
23/1.410/4.508,
24/2.00/5.07,
25/2.755/5.555,
26/4.62/6.03,
27/4.780/5.939,
28/5.48/5.38,
29/6.02/4.74,
30/6.526/2.982,
31/6.494/2.900,
32/5.91/2.34,
33/6.27/0.93,
34/4.48/0.57,
35/3.91/2.69,
36/1.91/0.68,
37/1.10/1.45,
38/0.55/3.24,
39/2.75/3.95,
40/0.74/5.79,
41/1.63/6.48,
42/3.42/6.84,
43/3.99/4.72,
44/5.99/6.73,
45/6.81/5.96,
46/7.35/4.17,
47/5.16/3.46,
48/7.16/1.61,
49/5.211/1.923,
50/3.75/1.82,
51/5.206/2.037,
52/3.070/1.547,
53/2.02/2.57,
54/1.78/4.01,
55/2.21/2.60,
56/1.54/4.59,
57/2.693/5.485,
58/4.15/5.59,
59/2.699/5.371,
60/4.835/5.862,
61/5.88/4.84,
62/6.13/3.40,
63/5.70/4.81,
64/6.36/2.82,
65/3.65/2.91,
66/4.99/3.47,
67/4.25/4.50,
68/2.92/3.94}
\coordinate (p-\i) at (\x,\y);
%Fläche als \fill[Yellow!3] (p-1) -- (p-2) -- (p-3) -- cycle;
%Dreiecke als \fill[black!3] (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 {
3/15.83/168.59/0.4/Gray,
4/348.59/497.79/0.4/Gray,
5/317.79/480.20/0.4/Gray,
6/300.20/467.21/0.4/Gray,
7/287.21/438.73/0.4/Gray,
8/258.73/400.91/0.4/Gray,
9/220.91/384.31/0.4/Gray,
10/204.31/375.83/0.4/Gray,
11/195.83/348.59/0.4/Gray,
12/168.59/317.79/0.4/Gray,
13/137.79/300.20/0.4/Gray,
14/120.20/287.21/0.4/Gray,
15/107.21/258.73/0.4/Gray,
3/15.83/107.82/0.3/DarkGray,
4/348.59/414.26/0.3/DarkGray,
5/317.79/390.90/0.3/DarkGray,
6/300.20/364.01/0.3/DarkGray,
7/287.21/378.04/0.3/DarkGray,
8/258.73/320.65/0.3/DarkGray,
9/220.91/294.07/0.3/DarkGray,
10/204.31/270.00/0.3/DarkGray,
11/195.83/287.82/0.3/DarkGray,
12/168.59/234.26/0.3/DarkGray,
13/137.79/210.90/0.3/DarkGray,
14/120.20/184.01/0.3/DarkGray,
15/107.21/198.04/0.3/DarkGray,
16/78.73/140.65/0.4/DarkGray,
17/40.91/114.07/0.4/DarkGray,
33/104.53/136.91/0.4/LightGray,
34/62.62/120.24/0.4/LightGray,
35/244.40/333.34/0.4/LightGray,
36/33.21/36.95/0.4/LightGray,
37/23.73/50.49/0.4/LightGray,
38/336.85/392.16/0.4/LightGray,
39/160.73/248.10/0.4/LightGray,
40/297.49/303.49/0.4/LightGray,
41/284.53/316.91/0.4/LightGray,
42/242.62/300.24/0.4/LightGray,
43/64.40/153.34/0.4/LightGray,
44/213.21/216.95/0.4/LightGray,
45/203.73/230.49/0.4/LightGray,
46/156.85/212.16/0.4/LightGray,
47/340.73/428.10/0.4/LightGray,
48/117.49/123.49/0.4/LightGray}
\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-16) -- (p-17);
\draw[Green,very thick] (p-51) -- (p-50);
\draw[Green,very thick] (p-50) -- (p-49);
\draw[Green,very thick] (p-49) -- (p-64);
\draw[Green,very thick] (p-55) -- (p-54);
\draw[Green,very thick] (p-54) -- (p-53);
\draw[Green,very thick] (p-53) -- (p-52);
\draw[Green,very thick] (p-64) -- (p-66);
\draw[Brown,very thick] (p-37) -- (p-55);
\draw[Brown,very thick] (p-19) -- (p-34);
\draw[Brown,very thick] (p-49) -- (p-34);
\draw[Brown,very thick] (p-31) -- (p-46);
\draw[Violet,very thick] (p-48) -- (p-17);
\draw[Violet,very thick] (p-36) -- (p-5);
\draw[Brown,very thick] (p-52) -- (p-21);
\draw[Violet,very thick] (p-66) -- (p-64);
\draw[Brown,very thick] (p-34) -- (p-52);
\draw[Brown,very thick] (p-2) -- (p-51);
%Kanten als \draw[line width=0] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/2,
4/3,
5/4,
6/5,
7/6,
8/7,
9/8,
10/9,
11/10,
12/11,
13/12,
14/13,
15/14,
16/15, 16/17,
17/2,
18/3,
19/4,
20/5,
21/6,
22/7,
23/8,
24/9,
25/10,
26/11,
27/12,
28/13,
29/14,
30/15,
31/16,
32/17,
33/32, 33/1,
34/1, 34/18,
35/19, 35/18,
36/19, 36/20,
37/20, 37/21,
38/21, 38/22,
39/23, 39/22,
40/23, 40/24,
41/24, 41/25,
42/25, 42/26,
43/27, 43/26,
44/27, 44/28,
45/28, 45/29,
46/29, 46/30,
47/31, 47/30,
48/31, 48/32,
49/33, 49/64,
50/34, 50/49,
51/35, 51/50,
52/36,
53/37, 53/52,
54/38, 54/53,
55/39, 55/54,
56/40, 56/68,
57/41, 57/56,
58/42, 58/57,
59/43, 59/58,
60/44,
61/45, 61/60,
62/46, 62/61,
63/47, 63/62,
64/48, 64/66,
65/55, 65/52,
66/65, 66/51,
67/63, 67/60,
68/67, 68/59}
\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);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-3) -- (p-2);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-4) -- (p-3);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-5) -- (p-4);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-6) -- (p-5);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-7) -- (p-6);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-8) -- (p-7);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-9) -- (p-8);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-10) -- (p-9);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-11) -- (p-10);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-12) -- (p-11);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-13) -- (p-12);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-14) -- (p-13);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-15) -- (p-14);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-16) -- (p-15);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-16) -- (p-17);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-17) -- (p-2);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-49) -- (p-64);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-50) -- (p-49);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-51) -- (p-50);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-53) -- (p-52);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-54) -- (p-53);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-55) -- (p-54);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-56) -- (p-68);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-57) -- (p-56);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-58) -- (p-57);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-59) -- (p-58);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-61) -- (p-60);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-62) -- (p-61);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-63) -- (p-62);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-64) -- (p-66);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-65) -- (p-55);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-65) -- (p-52);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-67) -- (p-63);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-67) -- (p-60);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
3/15.83/168.59/0.4/Gray,
4/348.59/497.79/0.4/Gray,
5/317.79/480.20/0.4/Gray,
6/300.20/467.21/0.4/Gray,
7/287.21/438.73/0.4/Gray,
8/258.73/400.91/0.4/Gray,
9/220.91/384.31/0.4/Gray,
10/204.31/375.83/0.4/Gray,
11/195.83/348.59/0.4/Gray,
12/168.59/317.79/0.4/Gray,
13/137.79/300.20/0.4/Gray,
14/120.20/287.21/0.4/Gray,
15/107.21/258.73/0.4/Gray,
3/15.83/107.82/0.3/DarkGray,
4/348.59/414.26/0.3/DarkGray,
5/317.79/390.90/0.3/DarkGray,
6/300.20/364.01/0.3/DarkGray,
7/287.21/378.04/0.3/DarkGray,
8/258.73/320.65/0.3/DarkGray,
9/220.91/294.07/0.3/DarkGray,
10/204.31/270.00/0.3/DarkGray,
11/195.83/287.82/0.3/DarkGray,
12/168.59/234.26/0.3/DarkGray,
13/137.79/210.90/0.3/DarkGray,
14/120.20/184.01/0.3/DarkGray,
15/107.21/198.04/0.3/DarkGray,
16/78.73/140.65/0.4/DarkGray,
17/40.91/114.07/0.4/DarkGray,
33/104.53/136.91/0.4/LightGray,
34/62.62/120.24/0.4/LightGray,
35/244.40/333.34/0.4/LightGray,
36/33.21/36.95/0.4/LightGray,
37/23.73/50.49/0.4/LightGray,
38/336.85/392.16/0.4/LightGray,
39/160.73/248.10/0.4/LightGray,
40/297.49/303.49/0.4/LightGray,
41/284.53/316.91/0.4/LightGray,
42/242.62/300.24/0.4/LightGray,
43/64.40/153.34/0.4/LightGray,
44/213.21/216.95/0.4/LightGray,
45/203.73/230.49/0.4/LightGray,
46/156.85/212.16/0.4/LightGray,
47/340.73/428.10/0.4/LightGray,
48/117.49/123.49/0.4/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 {
1/118,
2/240,
3/321,
4/204,
5/177,
6/155,
7/231,
8/112,
9/80,
10/60,
11/141,
12/24,
13/357,
14/335,
15/51,
16/292,
17/260,
18/198,
19/46,
20/229,
21/33,
22/110,
23/312,
24/130,
25/298,
26/18,
27/226,
28/49,
29/213,
30/290,
31/132,
32/310,
33/303,
34/274,
35/111,
36/54,
37/220,
38/187,
39/27,
40/316,
41/123,
42/94,
43/291,
44/234,
45/40,
46/7,
47/207,
48/136,
49/180,
50/155,
51/308,
52/284,
53/96,
54/68,
55/222,
56/189,
57/360,
58/335,
59/128,
60/104,
61/276,
62/248,
63/42,
64/9,
65/42,
66/129,
67/222,
68/309}
\node[anchor=\a] (P\i) at (p-\i) {\i};
%Vergrößerungen als \spy[rectangle, magnification=3, width=2cm, h eight=2cm, blue!70!black] on (p-18) in node at (2.5 cm,-2);
\spy[magnification=2] on (p-49) in node at (9,0);
\spy[magnification=2] on (p-19) in node at (5,-2);
\end{tikzpicture}
$
dann endlich lässt sich der Graph ohne Überschneidung auf Kantenlänge 1 ziehen mit Button "Feinjustieren(18)"
68 Knoten, 68×Grad 3, 0 Dreiecke, 0 Überschneidungen, Fläche=19.91
102 Kanten, minimal 0.99999999999999866773, maximal 1.00000000000001110223
$
%Eingabe war:
%
%#1683 symmetrisch Z98
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%P[1]=[111.10343631995715,95.56933775149179]; P[2]=[111.10343631995715,21.587994810164645]; D=ab(1,2); A(2,1,Bew(1));
%M(3,2,1,AW1-MW1,0,jam(2)*D);
%M(4,3,2,AW2,0,jam(2)*D);
%M(5,4,3,AW3,0,jam(2)*D);
%M(6,5,4,AW4,0,jam(2)*D);
%M(7,6,5,AW5,0,jam(2)*D);
%M(8,7,6,AW6,0,jam(2)*D);
%M(9,8,7,AW7,0,jam(2)*D);
%M(10,9,8,AW8,0,jam(2)*D);
%M(11,10,9,AW1,0,jam(2)*D);
%M(12,11,10,AW2,0,jam(2)*D);
%M(13,12,11,AW3,0,jam(2)*D);
%M(14,13,12,AW4,0,jam(2)*D);
%M(15,14,13,AW5,0,jam(2)*D);
%M(16,15,14,AW6,0,jam(2)*D);
%M(17,2,1,-MW1,0,jam(2)*D); RA(16,17,"",jam(2)*D);
%M(18,3,2,MW2);
%M(19,4,3,MW3);
%M(20,5,4,MW4);
%M(21,6,5,MW5);
%M(22,7,6,MW6);
%M(23,8,7,MW7);
%M(24,9,8,MW8);
%M(25,10,9,MW1);
%M(26,11,10,MW2);
%M(27,12,11,MW3);
%M(28,13,12,MW4);
%M(29,14,13,MW5);
%M(30,15,14,MW6);
%M(31,16,15,MW7);
%M(32,17,16,MW8);
%N(33,32,1); M(49,33,32,IW1);
%N(34,1,18); M(50,34,1,IW2);
%N(35,19,18); M(51,35,18,IW3);
%N(36,19,20); M(52,36,19,IW4);
%N(37,20,21); M(53,37,20,IW5);
%N(38,21,22); M(54,38,21,IW6);
%N(39,23,22); M(55,39,22,IW7);
%N(40,23,24); M(56,40,23,IW8);
%N(41,24,25); M(57,41,24,IW1);
%N(42,25,26); M(58,42,25,IW2);
%N(43,27,26); M(59,43,26,IW3);
%N(44,27,28); M(60,44,27,IW4);
%N(45,28,29); M(61,45,28,IW5);
%N(46,29,30); M(62,46,29,IW6);
%N(47,31,30); M(63,47,30,IW7);
%N(48,31,32); M(64,48,31,IW8);
%RA(51,50,"green",jam(1.66380770527268428971)*D);
%RA(50,49,"green",jam(1.42029151629267658130)*D);
%RA(49,64,"green",jam(1.42029151629267658130)*D);
%A(63,62,"green",jam(1.66380770527268428971)*D);
%A(62,61,"green",jam(1.42029151629267658130)*D);
%A(61,60,"green",jam(1.42029151629267658130)*D);
%A(59,58,"green",jam(1.66380770527268428971)*D);
%A(58,57,"green",jam(1.42029151629267658130)*D);
%A(57,56,"green",jam(1.42029151629267658130)*D);
%RA(55,54,"green",jam(1.66380770527268428971)*D);
%RA(54,53,"green",jam(1.42029151629267658130)*D);
%RA(53,52,"green",jam(1.42029151629267658130)*D);
%Q(65,55,52,jam(2)*D,jam(2)*D); N(66,65,51);
%RA(64,66,"green",jam(3.38797928336377340841)*D);
%Q(67,63,60,jam(2)*D,jam(2)*D); N(68,67,59);
%A(56,68,"green",jam(3.38797928336377340841)*D);
%
%R(37,55,"brown",1.10396782836591800248*D);
%R(19,34,"brown",1.12542474054885377477*D);
%R(49,34,"brown",1.06236326562790539541*D);
%R(31,46,"brown",1.05887784902094095330*D);
%RW(48,17,16,17,1.19234930042720232990);
%RW(36,5,4,5,2.25589393965173945489);
%R(52,21,"brown",1.12432169364628609110*D);
%RW(66,64,47,64,2.61196905598767559198);
%R(34,52,"brown",1.18641869432938884543*D);
%R(2,51,"brown",1.12752850231051904295*D);
%
%
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/5.152/1.867,
2/5.15/0.42,
3/3.76/0.00,
4/2.34/0.30,
5/1.198/1.185,
6/0.39/2.39,
7/0.00/3.79,
8/0.27/5.21,
9/1.313/6.218,
10/2.59/6.90,
11/3.98/7.32,
12/5.40/7.02,
13/6.546/6.131,
14/7.35/4.93,
15/7.74/3.53,
16/7.47/2.11,
17/6.432/1.098,
18/3.36/1.39,
19/3.191/1.472,
20/2.41/1.98,
21/1.83/2.53,
22/1.381/4.228,
23/1.410/4.313,
24/1.95/4.92,
25/2.593/5.449,
26/4.39/5.92,
27/4.554/5.844,
28/5.33/5.34,
29/5.91/4.79,
30/6.364/3.088,
31/6.335/3.003,
32/5.79/2.40,
33/6.360/1.065,
34/4.54/0.55,
35/3.91/2.73,
36/2.05/0.57,
37/1.162/1.243,
38/0.49/3.08,
39/2.768/3.806,
40/0.65/5.55,
41/1.384/6.251,
42/3.21/6.76,
43/3.84/4.58,
44/5.69/6.74,
45/6.582/6.073,
46/7.25/4.23,
47/4.976/3.510,
48/7.10/1.77,
49/5.205/1.941,
50/3.76/1.78,
51/5.189/2.051,
52/3.132/1.543,
53/1.99/2.43,
54/1.72/3.86,
55/2.17/2.48,
56/1.494/4.370,
57/2.539/5.375,
58/3.98/5.54,
59/2.556/5.265,
60/4.613/5.773,
61/5.76/4.88,
62/6.03/3.46,
63/5.57/4.83,
64/6.251/2.946,
65/3.55/2.93,
66/4.899/3.472,
67/4.19/4.39,
68/2.846/3.844}
\coordinate (p-\i) at (\x,\y);
%Fläche als \fill[Yellow!3] (p-1) -- (p-2) -- (p-3) -- cycle;
%Dreiecke als \fill[black!3] (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;
%Punkte als \fill[red] (p-1) circle (1.125pt)
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
%Kanten als \draw[line width=0] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/2,
4/3,
5/4,
6/5,
7/6,
8/7,
9/8,
10/9,
11/10,
12/11,
13/12,
14/13,
15/14,
16/15, 16/17,
17/2,
18/3,
19/4,
20/5,
21/6,
22/7,
23/8,
24/9,
25/10,
26/11,
27/12,
28/13,
29/14,
30/15,
31/16,
32/17,
33/32, 33/1,
34/1, 34/18,
35/19, 35/18,
36/19, 36/20,
37/20, 37/21,
38/21, 38/22,
39/23, 39/22,
40/23, 40/24,
41/24, 41/25,
42/25, 42/26,
43/27, 43/26,
44/27, 44/28,
45/28, 45/29,
46/29, 46/30,
47/31, 47/30,
48/31, 48/32,
49/33, 49/64,
50/34, 50/49,
51/35, 51/50,
52/36,
53/37, 53/52,
54/38, 54/53,
55/39, 55/54,
56/40, 56/68,
57/41, 57/56,
58/42, 58/57,
59/43, 59/58,
60/44,
61/45, 61/60,
62/46, 62/61,
63/47, 63/62,
64/48, 64/66,
65/55, 65/52,
66/65, 66/51,
67/63, 67/60,
68/67, 68/59}
\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);
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\end{tikzpicture}
$
Das neue Feinjustieren war zuerst nur als Zusatzfunktion gedacht, um geeignete Winkel fürs alte Feinjustieren zu finden. Weil dann das Zusammenziehen mit dem alten Feinjustieren überhaupt nicht geklappt hat, dafür überraschenderweise das neue fast auf Anhieb, lasse ich das neue Feinjustieren so wie es ist zum weiteren Testen und Ausprobieren.
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2023-11-29 20:23 ?
Wie unterstütze ich den Matheplaneten mit Geld?
