4_5_periodicNoise

Code 4.8, Figure 4.9:

4_5_periodicNoise.frag

#version 300 es precision highp float; precision highp int; out vec4 fragColor; uniform float u_time; uniform vec2 u_resolution; //start xy<->pol const float PI = 3.1415926; float atan2(float y, float x){ return x == 0.0 ? sign(y) * PI / 2.0 : atan(y, x); } vec2 xy2pol(vec2 xy){ return vec2(atan2(xy.x, xy.y), length(xy)); } vec2 pol2xy(vec2 pol){ return pol.y * vec2(cos(pol.x), sin(pol.x)); } //end xy<->pol uint uhash11(uint n){ n ^= (n << 1u); n ^= (n >> 1u); n *= 0x456789abu; n ^= (n << 1u); return n * 0x456789abu; } float gtable2(vec2 lattice, vec2 p){ uvec2 n = floatBitsToUint(lattice); uint ind = (uhash11(uhash11(n.x) + n.y) >> 29); float u = 0.92387953 * (ind < 4u ? p.x : p.y); //0.92387953 = cos(pi/8) float v = 0.38268343 * (ind < 4u ? p.y : p.x); //0.38268343 = sin(pi/8) return ((ind & 1u) == 0u ? u : -u) + ((ind & 2u) == 0u? v : -v); } float periodicNoise21(vec2 p, float period){ vec2 n = floor(p); vec2 f = fract(p); float[4] v; for (int j = 0; j < 2; j ++){ for (int i = 0; i < 2; i++){ v[i+2*j] = gtable2(mod(n + vec2(i, j), period), f - vec2(i, j)); } } f = f * f * f * (10.0 - 15.0 * f + 6.0 * f * f); return 0.5 * mix(mix(v[0], v[1], f[0]), mix(v[2], v[3], f[0]), f[1]) + 0.5; } float gtable3(vec3 lattice, vec3 p){ uvec3 n = floatBitsToUint(lattice); uint ind = (uhash11(uhash11(uhash11(n.x) + n.y) + n.z) >> 28); float u = ind < 8u ? p.x : p.y; float v = ind < 4u ? p.y : ind == 12u || ind == 14u ? p.x : p.z; return ((ind & 1u) == 0u? u: -u) + ((ind & 2u) == 0u? v : -v); } float periodicNoise31(vec3 p, float period){ vec3 n = floor(p); vec3 f = fract(p); float[8] v; for (int k = 0; k < 2; k++ ){ for (int j = 0; j < 2; j++ ){ for (int i = 0; i < 2; i++){ v[i+2*j+4*k] = gtable3(mod(n + vec3(i, j, k), period), f - vec3(i, j, k)) * 0.70710678; } } } f = f * f * f * (10.0 - 15.0 * f + 6.0 * f * f); float[2] w; for (int i = 0; i < 2; i++){ w[i] = mix(mix(v[4*i], v[4*i+1], f[0]), mix(v[4*i+2], v[4*i+3], f[0]), f[1]); } return 0.5 * mix(w[0], w[1], f[2]) + 0.5; } void main(){ vec2 pos = gl_FragCoord.xy / u_resolution.xy; pos = 2.0 * pos.xy - vec2(1.0); pos = xy2pol(pos); pos = vec2(5.0 / PI, 5.0) * pos + u_time; fragColor = vec4(periodicNoise21(pos, 10.0)); fragColor.a = 1.0; }

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

//start xy<->pol
const float PI = 3.1415926;

float atan2(float y, float x){
  return x == 0.0 ? sign(y) * PI / 2.0 : atan(y, x);
}

vec2 xy2pol(vec2 xy){
  return vec2(atan2(xy.x, xy.y), length(xy));
}

vec2 pol2xy(vec2 pol){
  return pol.y * vec2(cos(pol.x), sin(pol.x));
}
//end xy<->pol

uint uhash11(uint n){
  n ^= (n << 1u);
  n ^= (n >> 1u);
  n *= 0x456789abu;
  n ^= (n << 1u);
  return n * 0x456789abu;
}

float gtable2(vec2 lattice, vec2 p){
  uvec2 n = floatBitsToUint(lattice);
  uint ind = (uhash11(uhash11(n.x) + n.y) >> 29);
  float u = 0.92387953 * (ind < 4u ? p.x : p.y);  //0.92387953 = cos(pi/8)
  float v = 0.38268343 * (ind < 4u ? p.y : p.x);  //0.38268343 = sin(pi/8)
  return ((ind & 1u) == 0u ? u : -u) + ((ind & 2u) == 0u? v : -v);
}

float periodicNoise21(vec2 p, float period){
  vec2 n = floor(p);
  vec2 f = fract(p);
  float[4] v;
  for (int j = 0; j < 2; j ++){
    for (int i = 0; i < 2; i++){
      v[i+2*j] = gtable2(mod(n + vec2(i, j), period), f - vec2(i, j));
    }
  }
  f = f * f * f * (10.0 - 15.0 * f + 6.0 * f * f);
  return 0.5 * mix(mix(v[0], v[1], f[0]), mix(v[2], v[3], f[0]), f[1]) + 0.5;
}

float gtable3(vec3 lattice, vec3 p){
  uvec3 n = floatBitsToUint(lattice);
  uint ind = (uhash11(uhash11(uhash11(n.x) + n.y) + n.z) >> 28);
  float u = ind < 8u ? p.x : p.y;
  float v = ind < 4u ? p.y : ind == 12u || ind == 14u ? p.x : p.z;
  return ((ind & 1u) == 0u? u: -u) + ((ind & 2u) == 0u? v : -v);
}

float periodicNoise31(vec3 p, float period){
  vec3 n = floor(p);
  vec3 f = fract(p);
  float[8] v;
  for (int k = 0; k < 2; k++ ){
    for (int j = 0; j < 2; j++ ){
      for (int i = 0; i < 2; i++){
        v[i+2*j+4*k] = gtable3(mod(n + vec3(i, j, k), period), f - vec3(i, j, k)) * 0.70710678;
      }
    }
  }
  f = f * f * f * (10.0 - 15.0 * f + 6.0 * f * f);
  float[2] w;
  for (int i = 0; i < 2; i++){
    w[i] = mix(mix(v[4*i], v[4*i+1], f[0]), mix(v[4*i+2], v[4*i+3], f[0]), f[1]);
  }
  return 0.5 * mix(w[0], w[1], f[2]) + 0.5;
}

void main(){
  vec2 pos = gl_FragCoord.xy / u_resolution.xy;
  pos = 2.0 * pos.xy - vec2(1.0);
  pos = xy2pol(pos);
  pos = vec2(5.0 / PI, 5.0) * pos + u_time;
  fragColor = vec4(periodicNoise21(pos, 10.0));
  fragColor.a = 1.0;
}