noise.org

Contents

• Noise & randomness
  • Pseudo RNGs
  • Fast Hash32
  • Fractal noise
  • Simplex noise
  • Complete namespace definition

Noise & randomness

Pseudo RNGs

• http://byteblacksmith.com/improvements-to-the-canonical-one-liner-glsl-rand-for-opengl-es-2-0/

highp float random(vec2 co) {
    highp float a = 12.9898;
    highp float b = 78.233;
    highp float c = 43758.5453;
    highp float dt = dot(co.xy, vec2(a, b));
    highp float sn = mod(dt, PI);
    return fract(sin(sn) * c);
}

float randomLowP(vec2 co) {
  return fract(sin(dot(co.xy, vec2(12.9898, 78.233))) * 43758.5453);
}

float hashN(float n) { return fract(sin(n) * 758.5453); }

float noise3(vec3 x) {
  vec3 p = floor(x);
  vec3 f = fract(x);
  float n = p.x + p.y * 57.0 + p.z * 800.0;
  return mix(mix(mix(hashN(n), hashN(n + 1.0), f.x),
                 mix(hashN(n + 57.0), hashN(n + 58.0), f.x), f.y),
             mix(mix(hashN(n + 800.0), hashN(n + 801.0), f.x),
                 mix(hashN(n + 857.0), hashN(n + 858.0), f.x), f.y), f.z);
}

Fast Hash32

• https://briansharpe.wordpress.com/2011/11/15/a-fast-and-simple-32bit-floating-point-hash-function/
• https://briansharpe.wordpress.com/2013/06/27/adding-a-4th-dimension/

vec4 fast_hash32(vec2 pos) {
  // pos is assumed to be an integer coordinate
  const vec2 OFFSET = vec2(403.839172, 377.242706);
  const float DOMAIN = 71.0;
  const float K = 32745.708984;
  const vec2 SCALE = vec2(2.009842, 1.372549);
  vec4 P = vec4(pos, pos + 1.0);
  P = P - floor(P * (1.0 / DOMAIN)) * DOMAIN;
  P = P * SCALE.xyxy + OFFSET.xyxy;
  P *= P;
  return fract(P.xzxz * P.yyww * (1.0 / K));
}

Fractal noise

float fbm3(vec3 p) {
  float f = 0.0;
  f += 0.50000 * noise3(p); p *= 2.02;
  f -= 0.25000 * noise3(p); p *= 2.03;
  f += 0.12500 * noise3(p); p *= 2.01;
  f += 0.06250 * noise3(p); p *= 2.04;
  f -= 0.03125 * noise3(p);
  return f / 0.984375;
}

Simplex noise

// Description : Array and textureless GLSL 2D simplex noise function.
//      Author : Ian McEwan, Ashima Arts.
//  Maintainer : ijm
//     Lastmod : 20110822 (ijm)
//     License : Copyright (C) 2011 Ashima Arts. All rights reserved.
//               Distributed under the MIT License. See LICENSE file.
//               https://github.com/ashima/webgl-noise
vec2 mod289(vec2 x) {
  return x - floor(x * (1.0 / 289.0)) * 289.0;
}

vec3 mod289(vec3 x) {
  return x - floor(x * (1.0 / 289.0)) * 289.0;
}

vec3 permute(vec3 x) {
  return mod289(((x*34.0)+1.0)*x);
}

float snoise(vec2 v) {
  const vec4 C = vec4(0.211324865405187,  // (3.0-sqrt(3.0))/6.0
                      0.366025403784439,  // 0.5*(sqrt(3.0)-1.0)
                      -0.577350269189626,  // -1.0 + 2.0 * C.x
                      0.024390243902439); // 1.0 / 41.0
  // First corner
  vec2 i  = floor(v + dot(v, C.yy) );
  vec2 x0 = v -   i + dot(i, C.xx);

  // Other corners
  vec2 i1;
  i1 = (x0.x > x0.y) ? vec2(1.0, 0.0) : vec2(0.0, 1.0);
  // x0 = x0 - 0.0 + 0.0 * C.xx ;
  // x1 = x0 - i1 + 1.0 * C.xx ;
  // x2 = x0 - 1.0 + 2.0 * C.xx ;
  vec4 x12 = x0.xyxy + C.xxzz;
  x12.xy -= i1;

  // Permutations
  i = mod289(i); // Avoid truncation effects in permutation
  vec3 p = permute( permute( i.y + vec3(0.0, i1.y, 1.0 ))
                    + i.x + vec3(0.0, i1.x, 1.0 ));

  vec3 m = max(0.5 - vec3(dot(x0, x0), dot(x12.xy, x12.xy), dot(x12.zw, x12.zw)), 0.0);
  m = m * m ;
  m = m * m ;

  // Gradients: 41 points uniformly over a line, mapped onto a diamond.
  // The ring size 17*17 = 289 is close to a multiple of 41 (41*7 = 287)

  vec3 x = 2.0 * fract(p * C.www) - 1.0;
  vec3 h = abs(x) - 0.5;
  vec3 ox = floor(x + 0.5);
  vec3 a0 = x - ox;

  // Normalise gradients implicitly by scaling m
  // Approximation of: m *= inversesqrt( a0*a0 + h*h );
  m *= 1.79284291400159 - 0.85373472095314 * ( a0 * a0 + h * h );

  // Compute final noise value at P
  vec3 g;
  g.x  = a0.x  * x0.x  + h.x  * x0.y;
  g.yz = a0.yz * x12.xz + h.yz * x12.yw;
  return 130.0 * dot(m, g);
}

Complete namespace definition

(ns thi.ng.glsl.noise
  (:require
   [thi.ng.glsl.core :as glsl :include-macros true]))

(glsl/defglsl random
  nil "
<<random>>")

(glsl/defglsl random-low-p
  nil "
<<random-lowp>>")

(glsl/defglsl hash-n
  nil "
<<hash-n>>")

(glsl/defglsl noise-3
  [hash-n] "
<<noise-3>>")

(glsl/defglsl fbm-3
  [noise-3] "
<<fbm-3>>")

(glsl/defglsl snoise
  nil "
<<snoise>>")