Demo 87 - ClassicNoise3D.cginc

//
// Noise Shader Library for Unity - https://github.com/keijiro/NoiseShader
//
// Original work (webgl-noise) Copyright (C) 2011 Stefan Gustavson
// Translation and modification was made by Keijiro Takahashi.
//
// This shader is based on the webgl-noise GLSL shader. For further details
// of the original shader, please see the following description from the
// original source code.
//

//
// GLSL textureless classic 3D noise "cnoise",
// with an RSL-style periodic variant "pnoise".
// Author:  Stefan Gustavson (stefan.gustavson@liu.se)
// Version: 2011-10-11
//
// Many thanks to Ian McEwan of Ashima Arts for the
// ideas for permutation and gradient selection.
//
// Copyright (c) 2011 Stefan Gustavson. All rights reserved.
// Distributed under the MIT license. See LICENSE file.
// https://github.com/ashima/webgl-noise
//

float3 mod(float3 x, float3 y)
{
  return x - y * floor(x / y);
}

float3 mod289(float3 x)
{
  return x - floor(x / 289.0) * 289.0;
}

float4 mod289(float4 x)
{
  return x - floor(x / 289.0) * 289.0;
}

float4 permute(float4 x)
{
  return mod289(((x*34.0)+1.0)*x);
}

float4 taylorInvSqrt(float4 r)
{
  return (float4)1.79284291400159 - r * 0.85373472095314;
}

float3 fade(float3 t) {
  return t*t*t*(t*(t*6.0-15.0)+10.0);
}

// Classic Perlin noise
float cnoise(float3 P)
{
  float3 Pi0 = floor(P); // Integer part for indexing
  float3 Pi1 = Pi0 + (float3)1.0; // Integer part + 1
  Pi0 = mod289(Pi0);
  Pi1 = mod289(Pi1);
  float3 Pf0 = frac(P); // Fractional part for interpolation
  float3 Pf1 = Pf0 - (float3)1.0; // Fractional part - 1.0
  float4 ix = float4(Pi0.x, Pi1.x, Pi0.x, Pi1.x);
  float4 iy = float4(Pi0.y, Pi0.y, Pi1.y, Pi1.y);
  float4 iz0 = (float4)Pi0.z;
  float4 iz1 = (float4)Pi1.z;

  float4 ixy = permute(permute(ix) + iy);
  float4 ixy0 = permute(ixy + iz0);
  float4 ixy1 = permute(ixy + iz1);

  float4 gx0 = ixy0 / 7.0;
  float4 gy0 = frac(floor(gx0) / 7.0) - 0.5;
  gx0 = frac(gx0);
  float4 gz0 = (float4)0.5 - abs(gx0) - abs(gy0);
  float4 sz0 = step(gz0, (float4)0.0);
  gx0 -= sz0 * (step((float4)0.0, gx0) - 0.5);
  gy0 -= sz0 * (step((float4)0.0, gy0) - 0.5);

  float4 gx1 = ixy1 / 7.0;
  float4 gy1 = frac(floor(gx1) / 7.0) - 0.5;
  gx1 = frac(gx1);
  float4 gz1 = (float4)0.5 - abs(gx1) - abs(gy1);
  float4 sz1 = step(gz1, (float4)0.0);
  gx1 -= sz1 * (step((float4)0.0, gx1) - 0.5);
  gy1 -= sz1 * (step((float4)0.0, gy1) - 0.5);

  float3 g000 = float3(gx0.x,gy0.x,gz0.x);
  float3 g100 = float3(gx0.y,gy0.y,gz0.y);
  float3 g010 = float3(gx0.z,gy0.z,gz0.z);
  float3 g110 = float3(gx0.w,gy0.w,gz0.w);
  float3 g001 = float3(gx1.x,gy1.x,gz1.x);
  float3 g101 = float3(gx1.y,gy1.y,gz1.y);
  float3 g011 = float3(gx1.z,gy1.z,gz1.z);
  float3 g111 = float3(gx1.w,gy1.w,gz1.w);

  float4 norm0 = taylorInvSqrt(float4(dot(g000, g000), dot(g010, g010), dot(g100, g100), dot(g110, g110)));
  g000 *= norm0.x;
  g010 *= norm0.y;
  g100 *= norm0.z;
  g110 *= norm0.w;

  float4 norm1 = taylorInvSqrt(float4(dot(g001, g001), dot(g011, g011), dot(g101, g101), dot(g111, g111)));
  g001 *= norm1.x;
  g011 *= norm1.y;
  g101 *= norm1.z;
  g111 *= norm1.w;

  float n000 = dot(g000, Pf0);
  float n100 = dot(g100, float3(Pf1.x, Pf0.y, Pf0.z));
  float n010 = dot(g010, float3(Pf0.x, Pf1.y, Pf0.z));
  float n110 = dot(g110, float3(Pf1.x, Pf1.y, Pf0.z));
  float n001 = dot(g001, float3(Pf0.x, Pf0.y, Pf1.z));
  float n101 = dot(g101, float3(Pf1.x, Pf0.y, Pf1.z));
  float n011 = dot(g011, float3(Pf0.x, Pf1.y, Pf1.z));
  float n111 = dot(g111, Pf1);

  float3 fade_xyz = fade(Pf0);
  float4 n_z = lerp(float4(n000, n100, n010, n110), float4(n001, n101, n011, n111), fade_xyz.z);
  float2 n_yz = lerp(n_z.xy, n_z.zw, fade_xyz.y);
  float n_xyz = lerp(n_yz.x, n_yz.y, fade_xyz.x);
  return 2.2 * n_xyz;
}

// Classic Perlin noise, periodic variant
float pnoise(float3 P, float3 rep)
{
  float3 Pi0 = mod(floor(P), rep); // Integer part, modulo period
  float3 Pi1 = mod(Pi0 + (float3)1.0, rep); // Integer part + 1, mod period
  Pi0 = mod289(Pi0);
  Pi1 = mod289(Pi1);
  float3 Pf0 = frac(P); // Fractional part for interpolation
  float3 Pf1 = Pf0 - (float3)1.0; // Fractional part - 1.0
  float4 ix = float4(Pi0.x, Pi1.x, Pi0.x, Pi1.x);
  float4 iy = float4(Pi0.y, Pi0.y, Pi1.y, Pi1.y);
  float4 iz0 = (float4)Pi0.z;
  float4 iz1 = (float4)Pi1.z;

  float4 ixy = permute(permute(ix) + iy);
  float4 ixy0 = permute(ixy + iz0);
  float4 ixy1 = permute(ixy + iz1);

  float4 gx0 = ixy0 / 7.0;
  float4 gy0 = frac(floor(gx0) / 7.0) - 0.5;
  gx0 = frac(gx0);
  float4 gz0 = (float4)0.5 - abs(gx0) - abs(gy0);
  float4 sz0 = step(gz0, (float4)0.0);
  gx0 -= sz0 * (step((float4)0.0, gx0) - 0.5);
  gy0 -= sz0 * (step((float4)0.0, gy0) - 0.5);

  float4 gx1 = ixy1 / 7.0;
  float4 gy1 = frac(floor(gx1) / 7.0) - 0.5;
  gx1 = frac(gx1);
  float4 gz1 = (float4)0.5 - abs(gx1) - abs(gy1);
  float4 sz1 = step(gz1, (float4)0.0);
  gx1 -= sz1 * (step((float4)0.0, gx1) - 0.5);
  gy1 -= sz1 * (step((float4)0.0, gy1) - 0.5);

  float3 g000 = float3(gx0.x,gy0.x,gz0.x);
  float3 g100 = float3(gx0.y,gy0.y,gz0.y);
  float3 g010 = float3(gx0.z,gy0.z,gz0.z);
  float3 g110 = float3(gx0.w,gy0.w,gz0.w);
  float3 g001 = float3(gx1.x,gy1.x,gz1.x);
  float3 g101 = float3(gx1.y,gy1.y,gz1.y);
  float3 g011 = float3(gx1.z,gy1.z,gz1.z);
  float3 g111 = float3(gx1.w,gy1.w,gz1.w);

  float4 norm0 = taylorInvSqrt(float4(dot(g000, g000), dot(g010, g010), dot(g100, g100), dot(g110, g110)));
  g000 *= norm0.x;
  g010 *= norm0.y;
  g100 *= norm0.z;
  g110 *= norm0.w;
  float4 norm1 = taylorInvSqrt(float4(dot(g001, g001), dot(g011, g011), dot(g101, g101), dot(g111, g111)));
  g001 *= norm1.x;
  g011 *= norm1.y;
  g101 *= norm1.z;
  g111 *= norm1.w;

  float n000 = dot(g000, Pf0);
  float n100 = dot(g100, float3(Pf1.x, Pf0.y, Pf0.z));
  float n010 = dot(g010, float3(Pf0.x, Pf1.y, Pf0.z));
  float n110 = dot(g110, float3(Pf1.x, Pf1.y, Pf0.z));
  float n001 = dot(g001, float3(Pf0.x, Pf0.y, Pf1.z));
  float n101 = dot(g101, float3(Pf1.x, Pf0.y, Pf1.z));
  float n011 = dot(g011, float3(Pf0.x, Pf1.y, Pf1.z));
  float n111 = dot(g111, Pf1);

  float3 fade_xyz = fade(Pf0);
  float4 n_z = lerp(float4(n000, n100, n010, n110), float4(n001, n101, n011, n111), fade_xyz.z);
  float2 n_yz = lerp(n_z.xy, n_z.zw, fade_xyz.y);
  float n_xyz = lerp(n_yz.x, n_yz.y, fade_xyz.x);
  return 2.2 * n_xyz;
}