[edit] Summary
Great stellated dodecahedron, rendered with POVRay
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[edit] Source
//GPL
#include <stdio.h>
#include <math.h>
#include <vector>
using std::vector;
const char *theader = "//Picture *** Use flashiness=1 !!! ***\n//\n// +w1024 +h1024 +a0.3 +am2\n// +w512 +h512 +a0.3 +am2\n//\n//Movie *** Use flashiness=0.25 !!! ***\n//\n// +kc +kff120 +w256 +h256 +a0.3 +am2\n// +kc +kff60 +w256 +h256 +a0.3 +am2\n//\"Fast\" preview\n// +w128 +h128\n#declare notwireframe=1;\n#declare withreflection=0;\n#declare flashiness=1; //Still pictures use 1, animated should probably be about 0.25.\n\n#declare rotation=seed(%d);\n\n#declare rot1=rand(rotation)*pi*2;\n#declare rot2=acos(1-2*rand(rotation));\n#declare rot3=(rand(rotation)+clock)*pi*2;\n#macro dorot()\n rotate rot1*180/pi*y\n rotate rot2*180/pi*x\n rotate rot3*180/pi*y\n#end\n\n";
const char *tline = "object {\n cylinder { <%lf,%lf,%lf>, <%lf,%lf,%lf>, .01 dorot() }\n pigment { colour <.3,.3,.3> }\n finish { ambient 0 diffuse 1 phong 1 }\n}\n\n";
const char *tvertex = "object {\n sphere { <%lf,%lf,%lf>, .01 dorot() }\n pigment { colour <.3,.3,.3> }\n finish { ambient 0 diffuse 1 phong 1 }\n}\n\n";
const char *tstartmesh = "object {\n mesh {\n";
const char *ttriangle = " triangle {\n <%lf,%lf,%lf>, <%lf,%lf,%lf>, <%lf,%lf,%lf>\n }\n";
const char *tendmesh = " //sphere { <0,0,0>, 1 }\n //sphere { <0,0,0>, ld+.01 inverse }\n dorot()\n }\n pigment { colour rgbt <.8,.8,.8,.4> }\n finish { ambient 0 diffuse 1 phong flashiness #if(withreflection) reflection { .2 } #end }\n //interior { ior 1.5 }\n photons {\n target on\n refraction on\n reflection on\n collect on\n }\n}\n\n";
const char *tfooter = "// CCC Y Y PP\n// C Y Y P P\n// C Y PP\n// C Y P\n// CCC Y P\n\n#local a=0;\n#while(a<11.0001)\n light_source { <4*sin(a*pi*2/11), 5*cos(a*pi*6/11), -4*cos(a*pi*2/11)> colour (1+<sin(a*pi*2/11),sin(a*pi*2/11+pi*2/3),sin(a*pi*2/11+pi*4/3)>)*2/11 }\n #local a=a+1;\n#end\n\nbackground { color <1,1,1> }\n\ncamera {\n perspective\n location <0,0,0>\n direction <0,0,1>\n right x/2\n up y/2\n sky <0,1,0>\n location <0,0,-4.8>\n look_at <0,0,0>\n}\n\nglobal_settings {\n max_trace_level 40\n photons {\n count 200000\n autostop 0\n }\n}\n";
#define PHI ((1+sqrt(5))/2)
#define PI (3.14159265358979323846264338327)
#define SQ2 (sqrt(2))
#define SQ3 (sqrt(3))
bool eq(double a, double b)
{
return a+0.00001>=b&&b+0.00001>=a;
}
bool eqt(double a1, double a2, double a3, double b1, double b2, double b3)
{
//printf("Tri: {%lf, %lf, %lf}, {%lf, %lf, %lf}\n", a1, a2, a3, b1, b2, b3);
return eq(a1, b1)? eq(a2, b2)? eq(a3, b3):eq(a2, b3)&&eq(a3, b2):eq(a1, b2)? eq(a2, b3)? eq(a3, b1):eq(a2, b1)&&eq(a3, b3):eq(a1, b3)&&(eq(a2, b1)? eq(a3, b2):eq(a2, b3)&&eq(a3, b2));
}
class vec
{
public:
double x, y, z;
vec() : x(0), y(0), z(0) {}
vec(double nx, double ny, double nz) : x(nx), y(ny), z(nz) {}
vec operator + (vec o)
{
return vec(x+o.x, y+o.y, z+o.z);
}
vec operator - (vec o)
{
return vec(x-o.x, y-o.y, z-o.z);
}
double operator * (vec o)
{
return x*o.x+y*o.y+z*o.z;
}
vec operator * (double o)
{
return vec(x*o, y*o, z*o);
}
vec operator ^ (vec o)
{
return vec(y*o.z-z*o.y, z*o.x-x*o.z, x*o.y-y*o.x);
}
double norm()
{
return sqrt(x*x+y*y+z*z);
}
};
class vec2
{
public:
double x, y;
vec2() {}
vec2(double nx, double ny) : x(nx), y(ny) {}
vec2 operator + (vec2 o)
{
return vec2(x+o.x, y+o.y);
}
vec2 operator - (vec2 o)
{
return vec2(x-o.x, y-o.y);
}
double operator * (vec2 o)
{
return x*o.x+y*o.y;
}
vec2 operator * (double o)
{
return vec2(x*o, y*o);
}
vec2 operator ~ ()
{
return vec2(y, -x);
}
double norm()
{
return sqrt(x*x+y*y);
}
};
vector<vec> cyclicperm(vector<vec> v)
{
vector<vec> r;
vector<vec>::iterator i;
for(i = v.begin(); i!=v.end(); ++i)
{
r.push_back(*i);
r.push_back(vec(i->y, i->z, i->x));
r.push_back(vec(i->z, i->x, i->y));
}
return r;
}
vector<vec> altperm(vector<vec> v)
{
vector<vec> r;
vector<vec>::iterator i;
for(i = v.begin(); i!=v.end(); ++i)
{
r.push_back(*i);
r.push_back(vec(i->x, i->z, i->y));
}
return r;
}
vector<vec> signperm(vector<vec> v)
{
vector<vec> r;
vector<vec>::iterator i;
for( i = v.begin(); i!=v.end(); ++i )
{
int j;
for(j = 0; j<8; ++j)
if(((j&1)||i->x)&&((j&2)||i->y)&&((j&4)||i->z))
r.push_back(vec(j&1? i->x:-i->x, j&2? i->y:-i->y, j&4? i->z:-i->z));
}
return r;
}
vector<vec> mvvec(double x, double y, double z)
{
vector<vec> v;
v.push_back(vec(x, y, z));
return v;
}
vector<vec> mvvec(vec q)
{
vector<vec> v;
v.push_back(q);
return v;
}
vector<vec> concat(const vector<vec> a, const vector<vec> b)
{
vector<vec> r;
r = a;
r.insert(r.end(), b.begin(), b.end());
return r;
}
void printvvec(FILE *f, vector<vec> v)
{
vector<vec>::iterator i;
for(i = v.begin(); i!=v.end(); ++i)
fprintf(f, tvertex, i->x, i->y, i->z);
}
void printvveclines(FILE *f, vector<vec> v, double len)
{
vector<vec>::iterator i, j;
len *= len;
for(i = v.begin(); i!=v.end(); ++i)
for(j = i+1; j!=v.end(); ++j)
if(eq((*i-*j)*(*i-*j), len))
fprintf(f, tline, i->x, i->y, i->z, j->x, j->y, j->z);
}
void printvveclines(FILE *f, vector<vec> v)
{
vector<vec>::iterator i;
for(i = v.begin(); i!=v.end(); i += 2)
fprintf(f, tline, i->x, i->y, i->z, (i+1)->x, (i+1)->y, (i+1)->z);
}
void printvvecdottedlines(FILE *f, vector<vec> v)
{
vector<vec>::iterator i;
int n, m;
double s;
for(i = v.begin(); i!=v.end(); i += 2)
// for(i = v.begin(); i!=v.begin()+12; i += 2)
{
s = (*i-*(i+1)).norm();
m = (int)(s/0.04+.5);
s = 1./(double)m;
for(n = 1; n<m; ++n)
{
vec c = *i+(*(i+1)-*i)*(s*n);
fprintf(f, tvertex, c.x, c.y, c.z);
}
}
}
void printvvectriangles(FILE *f, vector<vec> v, double len1, double len2, double len3)
{
vector<vec>::iterator i, j, k;
len1 *= len1;
len2 *= len2;
len3 *= len3;
for(i = v.begin(); i!=v.end(); ++i)
for(j = i+1; j!=v.end(); ++j)
for(k = j+1; k!=v.end(); ++k)
if(eqt((*i-*j)*(*i-*j), (*j-*k)*(*j-*k), (*k-*i)*(*k-*i), len1, len2, len3))
fprintf(f, ttriangle, i->x, i->y, i->z, j->x, j->y, j->z, k->x, k->y, k->z);
}
void printvvectriangles(FILE *f, vector<vec> v)
{
vector<vec>::iterator i;
for(i = v.begin(); i!=v.end(); i += 3)
//i = v.begin();
fprintf(f, ttriangle, i->x, i->y, i->z, (i+1)->x, (i+1)->y, (i+1)->z, (i+2)->x, (i+2)->y, (i+2)->z);
/*i += 3;
fprintf(f, ttriangle, i->x, i->y, i->z, (i+1)->x, (i+1)->y, (i+1)->z, (i+2)->x, (i+2)->y, (i+2)->z);
i += 3;
fprintf(f, ttriangle, i->x, i->y, i->z, (i+1)->x, (i+1)->y, (i+1)->z, (i+2)->x, (i+2)->y, (i+2)->z);
i += 3;
fprintf(f, ttriangle, i->x, i->y, i->z, (i+1)->x, (i+1)->y, (i+1)->z, (i+2)->x, (i+2)->y, (i+2)->z);
i += 3;
fprintf(f, ttriangle, i->x, i->y, i->z, (i+1)->x, (i+1)->y, (i+1)->z, (i+2)->x, (i+2)->y, (i+2)->z);
i += 3;
fprintf(f, ttriangle, i->x, i->y, i->z, (i+1)->x, (i+1)->y, (i+1)->z, (i+2)->x, (i+2)->y, (i+2)->z);
*/}
void SmallStellatedDodecahedron()
{
vector<vec> v;
v = cyclicperm(signperm(mvvec(vec(0, PHI, 1)*(1/sqrt(PHI+2)))));
FILE *f;
f = fopen("SmallStellatedDodecahedron.pov", "wb");
fprintf(f, theader, 22491);
printvvec(f, v);
printvveclines(f, v, 2*PHI*(1/sqrt(PHI+2)));
fprintf(f, tstartmesh);
v = concat(v, cyclicperm(signperm(mvvec(vec(0, 2-PHI, 1)*(1/sqrt(PHI+2))))));
v = concat(v, signperm(mvvec(vec(PHI-1, PHI-1, PHI-1)*(1/sqrt(PHI+2)))));
printvvectriangles(f, v, (2*PHI-2)*(1/sqrt(PHI+2)), (2*PHI-2)*(1/sqrt(PHI+2)), (4-2*PHI)*(1/sqrt(PHI+2)));
fprintf(f, tendmesh);
fprintf(f, tfooter);
fclose(f);
}
void GreatStellatedDodecahedron()
{
vector<vec> v;
v = concat(signperm(mvvec(vec(1, 1, 1)*(1/SQ3))), cyclicperm(signperm(mvvec(vec(0, PHI, 1/PHI)*(1/SQ3)))));
FILE *f;
f = fopen("GreatStellatedDodecahedron.pov", "wb");
fprintf(f, theader, 7409);//7412);
printvvec(f, v);
printvveclines(f, v, 2*PHI*(1/SQ3));
fprintf(f, tstartmesh);
v = concat(v, cyclicperm(signperm(mvvec(vec(0, 2-PHI, PHI-1)*(1/SQ3)))));
printvvectriangles(f, v, (2*PHI-2)*(1/SQ3), (2*PHI-2)*(1/SQ3), (4-2*PHI)*(1/SQ3));
fprintf(f, tendmesh);
fprintf(f, tfooter);
fclose(f);
}
void GreatDodecahedron()
{
vector<vec> v;
v = cyclicperm(signperm(mvvec(vec(0, PHI, 1)*(1/sqrt(PHI+2)))));
FILE *f;
f = fopen("GreatDodecahedron.pov", "wb");
fprintf(f, theader, 11404);
printvveclines(f, v, 2*(1/sqrt(PHI+2)));
v = concat(v, concat(signperm(mvvec(vec(PHI-1, PHI-1, PHI-1)*(1/sqrt(PHI+2)))), cyclicperm(signperm(mvvec(vec(0, 2-PHI, 1)*(1/sqrt(PHI+2)))))));
printvvec(f, v);
fprintf(f, tstartmesh);
printvvectriangles(f, v, (2*PHI-2)*(1/sqrt(PHI+2)), (2*PHI-2)*(1/sqrt(PHI+2)), (2)*(1/sqrt(PHI+2)));
fprintf(f, tendmesh);
fprintf(f, tfooter);
fclose(f);
}
vector<vec> IcosaParse(const char *vs)
{
vector<vec> v, p;
v = cyclicperm(signperm(mvvec(vec(0, PHI, 1))));
vec av;
vector<vec>::iterator i, j, k;
int q;
static const vec2 rats[9] = {vec2(1, 0), vec2(PHI-1, 2-PHI), vec2(2-PHI, PHI-1), vec2(0, 1), vec2(0, PHI-1), vec2(0, 2-PHI), vec2(0, 0), vec2(2-PHI, 0), vec2(PHI-1, 0)};
for(i = v.begin(); i!=v.end(); ++i)
for(j = v.begin(); j!=v.end(); ++j)
for(k = v.begin(); k!=v.end(); ++k)
if(eqt((*i-*j).norm(), (*j-*k).norm(), (*k-*i).norm(), 2, 2, 2)&&(*i^*j)**k>0)
{
vec t3 = *i*PHI*PHI+*j*PHI*PHI-*k*PHI*PHI*PHI, t1 = *j*PHI*PHI+*k*PHI*PHI-*i*PHI*PHI*PHI, t2 = *k*PHI*PHI+*i*PHI*PHI-*j*PHI*PHI*PHI;
for(q = 0; vs[q]; )
{
if(vs[q]<48)
break;
if(vs[q+1]<48)
{
p = concat(p, mvvec(t3+(t1-t3)*rats[vs[q]-'0'].x+(t2-t3)*rats[vs[q]-'0'].y));
q += 2;
continue;
}
if(vs[q+4]<48)
{
vec2 a = rats[vs[q]-'0'], b = rats[vs[q+1]-'0'], c = rats[vs[q+2]-'0'], d = rats[vs[q+3]-'0'];
double idet = 1/((a-b).x*(d-c).y-(a-b).y*(d-c).x);
//fprintf(stderr, "%lf, %lf %lf, %lf %lf\n", (a-b).x, (d-c).x, (a-b).y, (d-c).y, idet);
vec2 e = vec2(vec2((d-c).y, (d-c).x*-1)*(d-b), vec2((a-b).y*-1, (a-b).x)*(d-b))*idet;
vec2 r = (a-b)*e.x+b;
//fprintf(stderr, "%lf, %lf %lf, %lf %lf\n", r.x, r.y, t1.x, t1.y, idet);
//fprintf(stderr, "(a-b)={%lf, %lf}, x=%lf, b={%lf, %lf}, e={%lf, %lf}\n(c-d)={%lf, %lf}, y=%lf, d={%lf, %lf}, e={%lf, %lf}\n",
//(a-b).x, (a-b).y, e.x, b.x, b.y, ((a-b)*e.x+b).x, ((a-b)*e.x+b).y,
//(c-d).x, (c-d).y, e.y, d.x, d.y, ((c-d)*e.y+d).x, ((c-d)*e.y+d).y
//);
//fprintf(stderr, "%lf %lf\n", r.x, r.y);
p = concat(p, mvvec(t3+(t1-t3)*r.x+(t2-t3)*r.y));
av = av+(t3+(t1-t3)*r.x+(t2-t3)*r.y);
//p = concat(p, mvvec(vec()));
q += 5;
continue;
}
break;
}
}
//printf("%lf %lf %lf\n", av.x, av.y, av.z);
double r = 0;
for(i = p.begin(); i!=p.end(); ++i)
//i = p.begin();
if(r<i->norm())
r = i->norm();
for(i = p.begin(); i!=p.end(); ++i)
*i = *i*(1/r);
return p;
}
void StellatedIcosahedron(const char *fn, int rs, const char *vs, const char *ls, const char *dls, const char *ts)
{
vector<vec> v;
FILE *f;
f = fopen(fn, "wb");
fprintf(f, theader, rs);
printvvec(f, IcosaParse(vs));
printvvecdottedlines(f, IcosaParse(dls));
printvveclines(f, IcosaParse(ls));
fprintf(f, tstartmesh);
printvvectriangles(f, IcosaParse(ts));
fprintf(f, tendmesh);
fprintf(f, tfooter);
fclose(f);
}
int main()
{
SmallStellatedDodecahedron();
GreatStellatedDodecahedron();
GreatDodecahedron();
StellatedIcosahedron("GreatIcosahedron.pov", 31234, "0 1 2 0417 1428 2538 ", "0 3 ", "0 0417 0417 1 1 1428 1428 2 2 2538 2538 3 ", "0 1 0417 1 2 1428 2 3 2538 ");
StellatedIcosahedron("CompoundOfFiveTetrahedra.pov", 22113, "2 2514 1427 2715 1528 ", "2 5 ", "2 2 2514 1427 1427 2715 2715 1528 ", "2 2514 1427 2 2715 1528 ");
return 0;
}
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