Завантаження...

-2f
 

 

 

This photo was viewed 1 times and was downloaded in full size 0 times.

This photo was liked 0 times

Please login in order to see the source link

Summary

Great stellated dodecahedron, rendered with POVRay

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:
GNU head 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.

w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 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 attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).
  • share alike – If you alter, transform, or build upon this work, you may distribute the resulting work only under the same or similar license to this one.
This licensing tag was added to this file as part of the GFDL licensing update.

w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 2.5 Generic, 2.0 Generic and 1.0 Generic 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 attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).
  • share alike – If you alter, transform, or build upon this work, you may distribute the resulting work only under the same or similar license to this one.

You may select the license of your choice.

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;
}


Licensing:
GNU Free Documentation License

Comments

Only registered users can post comments. Please login



EXIF data:
File name -2f.jpg
Size, bytes 8038
Mime type image/jpeg
The images at Free-Photos.biz come mainly from Wikimedia Commons or from our own production. The photos are either in the public domain, or licensed under free linceses: Free-Photos.biz license, GPL, Creative Commons or Free-Art license. Some very few other photos where uploaded to Free-Photos.biz by our users and released into the public domain or into free usage under another free license (like GPL etc.)

All photos in average size can be saved by everyone without registration (by right-clicking) - and all photos can be downloaded in full-size and without the big watermark by members (by left-clicking) (registration and free membership required).

While the copyright and licensing information supplied for each photo is believed to be accurate, Free-Photos.biz does not provide any warranty regarding the copyright status or correctness of licensing terms. If you decide to reuse the images from Free-Photos.biz, you should verify the copyright status of each image just as you would when obtaining images from other sources.


The use of depictions of living or deceased persons may be restricted in some jurisdictions by laws regarding personality rights. Such images are exhibited at Free-Photos.biz as works of art that serve higher artistic interests.

christianity portal