Exercise 9.3-2

13 Semi-Regular Polyhedrons:

11 polyhedrons except for snubs

Truncated tetrahedron -> Truncated cube -> Truncated octahedron -> Truncated dodecahedron -> Truncated icosahedron -> Cuboctahedron -> Icosidodecahedron -> Rhombicuboctahedron -> Rhombicosidodecahedron -> Truncated cuboctahedron -> Truncated icosidodecahedron

exercise_9_3-2-1.frag

#version 300 es precision highp float; precision highp int; out vec4 fragColor; uniform float u_time; uniform vec2 u_resolution; //begin rot vec2 rot2(vec2 p, float t){ return vec2(cos(t) * p.x -sin(t) * p.y, sin(t) * p.x + cos(t) * p.y); } vec3 rotX(vec3 p, float t){ return vec3(p.x, rot2(p.yz, t)); } vec3 rotY(vec3 p, float t){ return vec3(p.y, rot2(p.zx, t)).zxy; } vec3 rotZ(vec3 p, float t){ return vec3(rot2(p.xy, t), p.z); } vec3 euler(vec3 p, vec3 t){ return rotZ(rotY(rotX(p, t.x), t.y), t.z); } //end rot float smin(float d1, float d2, float r){ float c = clamp(0.5 + (d2 - d1) * (0.5 / r), 0.0, 1.0); return mix(d2, d1, c) - r * c * (1.0 - c); } // Reference: MIT License Copyright (c) 2018 Mikael Hvidtfeldt Christensen // https://github.com/Syntopia/Polytopia/blob/master/polyhedron.glsl // https://syntopia.github.io/Polytopia/polytopes.html // Reference: Polyhedron again // https://www.shadertoy.com/view/XlX3zB by knighty #define PI 3.141592 vec3 nc,initVertex,pab,pbc,pca; float Degree = 5.0; float V=0., W=1., U = 0.; // degree, v, w, u vec4[11] paramArray = vec4[]( vec4(3.0, 1.0, 0.0, 1.0), // 切頂四面体, Truncated tetrahedron vec4(4.0, 1.0, 0.0, 1.0), // 切頂六面体, Truncated cube vec4(4.0, 1.0, 1.0, 0.0), // 切頂八面体, Truncated octahedron vec4(5.0, 1.0, 0.0, 1.0), // 切頂十二面体, Truncated dodecahedron vec4(5.0, 1.0, 1.0, 0.0), // 切頂二十面体, Truncated icosahedron vec4(4.0, 1.0, 0.0, 0.0), // 立方八面体, Cuboctahedron vec4(5.0, 1.0, 0.0, 0.0), // 二十・十二面体, Icosidodecahedron vec4(4.0, 0.0, 1.0, 1.0), // 斜方立方八面体, Rhombicuboctahedron vec4(5.0, 0.0, 1.0, 1.0), // 斜方二十・十二面体, Rhombicosidodecahedron vec4(4.0, 1.0, 1.0, 1.0), // 斜方切頂立方八面体, Truncated cuboctahedron vec4(5.0, 1.0, 1.0, 1.0) // 斜方切頂二十・十二面体, Truncated icosidodecahedron // 変形立方体、変形十二面体はこの形では作れない。 ); void init( int idx ) { vec4 param = paramArray[idx]; Degree = param.x; V = param.y; W = param.z; U = param.w; float cospin=cos(PI/Degree), scospin=sqrt(0.75-cospin*cospin); nc=vec3(-0.5,-cospin,scospin);// 3rd folding plane. The two others are xz and yz planes pab=vec3(0.,0.,1.); pbc=vec3(scospin,0.,0.5); pca=vec3(0.,scospin,cospin); initVertex=normalize((V*pab+W*pbc+U*pca)); pbc=normalize(pbc); pca=normalize(pca); } vec3 fold(vec3 pos) { int max = 5; //int(Degree); for(int i=0;i<7;i++){ pos.xy=abs(pos.xy); float t=-2.*min(0.,dot(pos,nc)); pos+=t*nc; if (i>=max) break; } return pos; } float D2Planes(vec3 pos) { float d0=dot(pos,pab)-dot(pab,initVertex); float d1=dot(pos,pbc)-dot(pbc,initVertex); float d2=dot(pos,pca)-dot(pca,initVertex); return abs(max(max(d0,d1),d2)); } float regularPolyhedronSDF(vec3 pos, float s){ vec3 oPos = pos; pos=fold(pos); float d=10000.; d=min(d,D2Planes(pos)); return d; } float sceneSDF(vec3 p){ return regularPolyhedronSDF(p, 0.5); } vec3 gradSDF(vec3 p){ float eps = 0.003; return normalize(vec3( sceneSDF(p + vec3(eps, 0.0, 0.0)) - sceneSDF(p - vec3(eps, 0.0, 0.0)), sceneSDF(p + vec3(0.0, eps, 0.0)) - sceneSDF(p - vec3(0.0, eps, 0.0)), sceneSDF(p + vec3(0.0, 0.0, eps)) - sceneSDF(p - vec3(0.0, 0.0, eps)) )); } void main(){ vec2 p = (gl_FragCoord.xy * 2.0 - u_resolution) / min(u_resolution.x, u_resolution.y); vec3 t = 2.0 + vec3(u_time * 0.5); vec3 cPos = euler(vec3(0.0, 0.0, 2.0), t); vec3 cDir = euler(vec3(0.0, 0.0, -1.0), t); vec3 cUp = euler(vec3(0.0, 1.0, 0.0), t); vec3 cSide = cross(cDir, cUp); float targetDepth = 1.0; vec3 lDir = euler(vec3(0.0, 0.0, 1.0), t); float sec = 6.0; int polyidx = int(floor(mod(float(u_time),11.0*sec)/sec)); init(polyidx); vec3 ray = cSide * p.x + cUp * p.y + cDir * targetDepth; vec3 rPos = ray + cPos; ray = normalize(ray); fragColor.rgb = vec3(0.078, 0.129, 0.239); for(int i = 0; i < 50; i ++ ){ if (sceneSDF(rPos) > 0.001){ rPos += sceneSDF(rPos) * ray; } else { float amb = 0.1; float diff = 0.9 * max(dot(normalize(lDir), gradSDF(rPos)), 0.0); vec3 col = vec3(0.988, 0.639, 0.067); fragColor.rgb = col * (diff + amb); break; } } fragColor.a = 1.0; }

#version 300 es
precision highp float;
precision highp int;
out vec4 fragColor;
uniform float u_time;
uniform vec2 u_resolution;

//begin rot
vec2 rot2(vec2 p, float t){
  return vec2(cos(t) * p.x -sin(t) * p.y, sin(t) * p.x + cos(t) * p.y);
}

vec3 rotX(vec3 p, float t){
  return vec3(p.x, rot2(p.yz, t));
}

vec3 rotY(vec3 p, float t){
  return vec3(p.y, rot2(p.zx, t)).zxy;
}

vec3 rotZ(vec3 p, float t){
  return vec3(rot2(p.xy, t), p.z);
}

vec3 euler(vec3 p, vec3 t){
  return rotZ(rotY(rotX(p, t.x), t.y), t.z);
}
//end rot

float smin(float d1, float d2, float r){
  float c = clamp(0.5 + (d2 - d1) * (0.5 / r), 0.0, 1.0);
  return mix(d2, d1, c) - r * c * (1.0 - c);
}

// Reference: MIT License Copyright (c) 2018 Mikael Hvidtfeldt Christensen
// https://github.com/Syntopia/Polytopia/blob/master/polyhedron.glsl
// https://syntopia.github.io/Polytopia/polytopes.html

// Reference: Polyhedron again
// https://www.shadertoy.com/view/XlX3zB by knighty 

#define PI 3.141592

vec3 nc,initVertex,pab,pbc,pca;
float Degree = 5.0;
float V=0., W=1., U = 0.;

// degree, v, w, u
vec4[11] paramArray = vec4[](
  vec4(3.0, 1.0, 0.0, 1.0), // 切頂四面体, Truncated tetrahedron
  vec4(4.0, 1.0, 0.0, 1.0), // 切頂六面体, Truncated cube
  vec4(4.0, 1.0, 1.0, 0.0), // 切頂八面体, Truncated octahedron
  vec4(5.0, 1.0, 0.0, 1.0), // 切頂十二面体, Truncated dodecahedron
  vec4(5.0, 1.0, 1.0, 0.0), // 切頂二十面体, Truncated icosahedron
  vec4(4.0, 1.0, 0.0, 0.0), // 立方八面体, Cuboctahedron
  vec4(5.0, 1.0, 0.0, 0.0), // 二十・十二面体, Icosidodecahedron
  vec4(4.0, 0.0, 1.0, 1.0), // 斜方立方八面体, Rhombicuboctahedron
  vec4(5.0, 0.0, 1.0, 1.0), // 斜方二十・十二面体, Rhombicosidodecahedron
  vec4(4.0, 1.0, 1.0, 1.0), // 斜方切頂立方八面体, Truncated cuboctahedron
  vec4(5.0, 1.0, 1.0, 1.0) // 斜方切頂二十・十二面体, Truncated icosidodecahedron
  // 変形立方体、変形十二面体はこの形では作れない。
);

void init( int idx ) {
  vec4 param = paramArray[idx];
  Degree = param.x;
  V = param.y;
  W = param.z;
  U = param.w;

  float cospin=cos(PI/Degree), scospin=sqrt(0.75-cospin*cospin);
  nc=vec3(-0.5,-cospin,scospin);// 3rd folding plane. The two others are xz and yz planes
  pab=vec3(0.,0.,1.);
  pbc=vec3(scospin,0.,0.5);
  pca=vec3(0.,scospin,cospin);

  initVertex=normalize((V*pab+W*pbc+U*pca));
  pbc=normalize(pbc);
  pca=normalize(pca);
}

vec3 fold(vec3 pos) {
  int max = 5; //int(Degree);
  for(int i=0;i<7;i++){
    pos.xy=abs(pos.xy);
    float t=-2.*min(0.,dot(pos,nc));
    pos+=t*nc;
    if (i>=max) break;
  }
  return pos;
}

float D2Planes(vec3 pos) {
  float d0=dot(pos,pab)-dot(pab,initVertex);
  float d1=dot(pos,pbc)-dot(pbc,initVertex);
  float d2=dot(pos,pca)-dot(pca,initVertex);
  
  return abs(max(max(d0,d1),d2));
}

float regularPolyhedronSDF(vec3 pos, float s){
  vec3 oPos = pos;
  pos=fold(pos);
  float d=10000.;
  d=min(d,D2Planes(pos));
  return d;
}

float sceneSDF(vec3 p){
  return regularPolyhedronSDF(p, 0.5);
}

vec3 gradSDF(vec3 p){
  float eps = 0.003;
  return normalize(vec3(
    sceneSDF(p + vec3(eps, 0.0, 0.0)) - sceneSDF(p - vec3(eps, 0.0, 0.0)),
    sceneSDF(p + vec3(0.0, eps, 0.0)) - sceneSDF(p - vec3(0.0, eps, 0.0)),
    sceneSDF(p + vec3(0.0, 0.0, eps)) - sceneSDF(p - vec3(0.0, 0.0, eps))
  ));
}

void main(){
  vec2 p = (gl_FragCoord.xy * 2.0 - u_resolution) / min(u_resolution.x, u_resolution.y);
  
  vec3 t = 2.0 + vec3(u_time * 0.5);
  vec3 cPos = euler(vec3(0.0, 0.0, 2.0), t);
  vec3 cDir = euler(vec3(0.0, 0.0, -1.0), t);
  vec3 cUp = euler(vec3(0.0, 1.0, 0.0), t);
  vec3 cSide = cross(cDir, cUp);
  
  float targetDepth = 1.0;
  
  vec3 lDir = euler(vec3(0.0, 0.0, 1.0), t);

  float sec = 6.0;
  int polyidx = int(floor(mod(float(u_time),11.0*sec)/sec));
  init(polyidx);

  vec3 ray = cSide * p.x + cUp * p.y + cDir * targetDepth;
  vec3 rPos = ray + cPos;
  ray = normalize(ray);
  fragColor.rgb = vec3(0.078, 0.129, 0.239);
  for(int i = 0; i < 50; i ++ ){
    if (sceneSDF(rPos) > 0.001){
      rPos += sceneSDF(rPos) * ray;
    } else {
      float amb = 0.1;
      float diff = 0.9 * max(dot(normalize(lDir), gradSDF(rPos)), 0.0);
      vec3 col = vec3(0.988, 0.639, 0.067);
      fragColor.rgb = col * (diff + amb);
      break;
    }
  }
  fragColor.a = 1.0;
}

2 snub polyhedrons

(Not Yet...) Snub cube -> Snub dodecahedron

exercise_9_3-2-2.frag

#version 300 es precision highp float; out vec4 fragColor; void main(){ fragColor = vec4(0.0, 0.0, 0.0, 1.0); }

#version 300 es
precision highp float;
out vec4 fragColor;
void main(){
  fragColor = vec4(0.0, 0.0, 0.0, 1.0);
}