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Summary
| Description |
English: Special orthographic projection of 120-cell making the petrie polygon |
| Date | |
| Source | Own work |
| Author | Claudio Rocchini |
/*********************************
* Drawing the 120-cell Petrie Polygon
* (C) 2008 Claudio Rocchini
* CC-BY 3.0
*********************************/
bool even_permutation( int p[], int n )
{
int i,ns;
int * pt = new int[n];
for(i=0;i<n;++i) pt[i] = p[i];
ns = 0;
for(;;) {
int j,k;
for(j=0;j<n;++j) if(pt[j]!=j) break;
if(j==n) break;
for(k=0;k<n;++k) if(pt[k]==j) break;
std::swap(pt[k],pt[j]);
++ns;
}
delete[] pt;
return ns%2==0;
}
void main()
{
const double EPS = 1e-6;
const int ND = 4;
const int NV = 600; const int NE = 1200;
const double fi = (1+sqrt(5))/2; const double fi2 = fi*fi;
const double rfi = pow(fi,-1); const double rfi2 = pow(fi,-2);
double v[NV][ND]; int e[NE][2];
double px[NV]; double py[NV];
// Magic numbers: hard to find projection directions
const double PX[ND] = {-0.11317046518674401,-0.13682953481325594,-0.09854835601535949,-0.29133803200072961};
const double PY[ND] = { 0.19601699561964564, 0.23699570627257371,-0.05689691987366302,-0.16820409120079699};
int i,j,k,l;
int i1,i2,i3,i4;
k = 0;
for(i1= 0;i1<4-1;++i1) for(i2=i1+1;i2<4 ;++i2)
for(i3=0;i3<2;++i3) for(i4=0;i4<2;++i4) {
v[k][ 0] = v[k][ 1] = v[k][ 2] = v[k][ 3] = 0;
v[k][i1] = -2+4*i3;
v[k][i2] = -2+4*i4;
++k;
}
for(i1=0;i1<2;++i1) for(i2=0;i2<2;++i2)
for(i3=0;i3<2;++i3) for(i4=0;i4<2;++i4) {
v[k][0] = -1+2*i1; v[k][1] = -1+2*i2; v[k][2] = -1+2*i3; v[k][3] = i4==0 ? -sqrt(5) : sqrt(5); ++k;
v[k][0] = -1+2*i1; v[k][1] = -1+2*i2; v[k][2] = i3==0 ? -sqrt(5) : sqrt(5); v[k][3] = -1+2*i4; ++k;
v[k][0] = -1+2*i1; v[k][1] = i2==0 ? -sqrt(5) : sqrt(5); v[k][2] = -1+2*i3; v[k][3] = -1+2*i4; ++k;
v[k][0] = i1==0 ? -sqrt(5) : sqrt(5); v[k][1] = -1+2*i2; v[k][2] = -1+2*i3; v[k][3] = -1+2*i4; ++k;;
}
for(i1=0;i1<2;++i1) for(i2=0;i2<2;++i2)
for(i3=0;i3<2;++i3) for(i4=0;i4<2;++i4) {
v[k][0] = i1==0?-fi:fi; v[k][1] = i2==0?-fi:fi; v[k][2] = i3==0?-fi:fi; v[k][3] = i4==0?-rfi2:rfi2; ++k;
v[k][0] = i1==0?-fi:fi; v[k][1] = i2==0?-fi:fi; v[k][2] = i3==0?-rfi2:rfi2; v[k][3] = i4==0?-fi:fi; ++k;
v[k][0] = i1==0?-fi:fi; v[k][1] = i2==0?-rfi2:rfi2; v[k][2] = i3==0?-fi:fi; v[k][3] = i4==0?-fi:fi; ++k;
v[k][0] = i1==0?-rfi2:rfi2; v[k][1] = i2==0?-fi:fi; v[k][2] = i3==0?-fi:fi; v[k][3] = i4==0?-fi:fi; ++k;
}
for(i1=0;i1<2;++i1) for(i2=0;i2<2;++i2)
for(i3=0;i3<2;++i3) for(i4=0;i4<2;++i4) {
v[k][0] = i1==0?-rfi:rfi; v[k][1] = i2==0?-rfi:rfi; v[k][2] = i3==0?-rfi:rfi; v[k][3] = i4==0?-fi2:fi2; ++k;
v[k][0] = i1==0?-rfi:rfi; v[k][1] = i2==0?-rfi:rfi; v[k][2] = i3==0?-fi2:fi2; v[k][3] = i4==0?-rfi:rfi; ++k;
v[k][0] = i1==0?-rfi:rfi; v[k][1] = i2==0?-fi2:fi2; v[k][2] = i3==0?-rfi:rfi; v[k][3] = i4==0?-rfi:rfi; ++k;
v[k][0] = i1==0?-fi2:fi2; v[k][1] = i2==0?-rfi:rfi; v[k][2] = i3==0?-rfi:rfi; v[k][3] = i4==0?-rfi:rfi; ++k;
}
double val[4]; int per[4];
for(i1=0;i1<2;++i1) for(i2=0;i2<2;++i2) for(i3=0;i3<2;++i3) {
val[0] = 0;
val[1] = i1==0 ? -rfi2 : rfi2;
val[2] = i2==0 ? -1 : 1;
val[3] = i3==0 ? -fi2 : fi2;
for(i=0;i<4;++i) per[i] = i;
do {
if(even_permutation(per,4)) { for(i=0;i<4;++i) v[k][i] = val[per[i]]; ++k; }
} while(std::next_permutation(per,per+4));
}
for(i1=0;i1<2;++i1) for(i2=0;i2<2;++i2) for(i3=0;i3<2;++i3) {
val[0] = 0;
val[1] = i1==0 ? -rfi : rfi;
val[2] = i2==0 ? -fi : fi;
val[3] = i3==0 ? -sqrt(5) : sqrt(5);
for(i=0;i<4;++i) per[i] = i;
do {
if(even_permutation(per,4)) { for(i=0;i<4;++i) v[k][i] = val[per[i]]; ++k; }
} while(std::next_permutation(per,per+4));
}
for(i1=0;i1<2;++i1) for(i2=0;i2<2;++i2)
for(i3=0;i3<2;++i3) for(i4=0;i4<2;++i4) {
val[0] = i1==0 ? -rfi : rfi;
val[1] = i2==0 ? -1 : 1;
val[2] = i3==0 ? -fi : fi;
val[3] = i4==0 ? -2 : 2;
for(i=0;i<4;++i) per[i] = i;
do {
if(even_permutation(per,4)) { for(i=0;i<4;++i) v[k][i] = val[per[i]]; ++k; }
} while(std::next_permutation(per,per+4));
}
assert(k==NV);
const double de = 0.76393202250021019;
k = 0;
for(i= 0;i<NV-1;++i)
for(j=i+1;j<NV ;++j) {
double d = 0;
for(l=0;l<ND;++l) d += (v[i][l]-v[j][l])*(v[i][l]-v[j][l]);
d = sqrt(d);
if( fabs(de-d)<EPS ) { e[k][0] = i; e[k][1] = j; ++k; }
}
assert(k==NE);
for(i=0;i<NV;++i){
px[i] = 0; for(l=0;l<ND;++l) px[i] += v[i][l]*PX[l];
py[i] = 0; for(l=0;l<ND;++l) py[i] += v[i][l]*PY[l];
}
const double SX = 800; const double SY = 800;
const double B = 32; const double R = 6;
const double sca = std::min((SX-2*B)/2,(SY-2*B)/2);
for(i=0;i<NV;++i) { px[i] = B+(px[i]+1)*sca; py[i] = B+(py[i]+1)*sca; }
FILE * fp = fopen("c:\\temp\\New120Cell.svg","w");
fprintf(fp,
"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n"
"<svg\n"
"xmlns:svg=\"http://www.w3.org/2000/svg\"\n"
"xmlns=\"http://www.w3.org/2000/svg\"\n"
"version=\"1.0\"\n"
"width=\"%g\"\n" "height=\"%g\"\n"
"id=\"New120Cell\">\n"
,SX,SY
);
fprintf(fp,"<g style=\"stroke:#000000;stroke-width:2;stroke-opacity:0.6;\">\n");
for(i=0;i<NE;++i)
fprintf(fp,
"<line x1=\"%5.1lf\" y1=\"%5.1lf\" x2=\"%5.1lf\" y2=\"%5.1lf\"/>\n"
,px[e[i][0]],py[e[i][0]], px[e[i][1]],py[e[i][1]]
);
fprintf(fp,"</g>\n");
fprintf(fp,"<g style=\"stroke:#000000;stroke-width:2;stroke-opacity:0.6;fill:#0080FF\">\n");
for(i=0;i<NV;++i)
fprintf(fp,"<circle cx=\"%5.1lf\" cy=\"%5.1lf\" r=\"%5.1lf\"/>\n",px[i],py[i],R);
fprintf(fp,"</g>\n");
fprintf(fp,"</svg>\n");
fclose(fp);
}
Licensing
I, the copyright holder of this work, hereby publish it under the following licenses:
|
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
This file is licensed under the Creative Commons Attribution 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
You may select the license of your choice.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 10:00, 1 August 2008 | | 800 × 800 (88 KB) | Rocchini | {{Information |Description={{en|1=Special orthographic projection of 120-cell making the petrie polygon}} |Source=Opera creata dall'uploader (own work by uploader) |Author=Claudio Rocchini |Date=2008-08-01 |Permission= |other_versions= } |
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