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//
// Description : Array and textureless GLSL 2D/3D/4D simplex
// noise functions.
// 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
//
vec4 mod289(vec4 x) {
return x - floor (x * (1.0 / 289.0 )) * 289.0 ;
}
float mod289(float x) {
return x - floor (x * (1.0 / 289.0 )) * 289.0 ;
}
vec4 permute(vec4 x) {
return mod289(((x* 34.0 )+ 1.0 )* x);
}
float permute(float x) {
return mod289(((x* 34.0 )+ 1.0 )* x);
}
vec4 taylorInvSqrt(vec4 r)
{
return 1.79284291400159 - 0.85373472095314 * r;
}
float taylorInvSqrt(float r)
{
return 1.79284291400159 - 0.85373472095314 * r;
}
vec4 grad4(float j, vec4 ip)
{
const vec4 ones = vec4 (1.0 , 1.0 , 1.0 , - 1.0 );
vec4 p,s;
p.xyz = floor ( fract (vec3 (j) * ip.xyz) * 7.0 ) * ip.z - 1.0 ;
p.w = 1.5 - dot (abs (p.xyz), ones.xyz);
s = vec4 (lessThan (p, vec4 (0.0 )));
p.xyz = p.xyz + (s.xyz* 2.0 - 1.0 ) * s.www;
return p;
}
// (sqrt(5) - 1)/4 = F4, used once below
#define F4 0.309016994374947451
float snoise(vec4 v)
{
const vec4 C = vec4 ( 0.138196601125011 , // (5 - sqrt(5))/20 G4
0.276393202250021 , // 2 * G4
0.414589803375032 , // 3 * G4
- 0.447213595499958 ); // -1 + 4 * G4
// First corner
vec4 i = floor (v + dot (v, vec4 (F4)) );
vec4 x0 = v - i + dot (i, C.xxxx);
// Other corners
// Rank sorting originally contributed by Bill Licea-Kane, AMD (formerly ATI)
vec4 i0;
vec3 isX = step ( x0.yzw, x0.xxx );
vec3 isYZ = step ( x0.zww, x0.yyz );
// i0.x = dot( isX, vec3( 1.0 ) );
i0.x = isX.x + isX.y + isX.z;
i0.yzw = 1.0 - isX;
// i0.y += dot( isYZ.xy, vec2( 1.0 ) );
i0.y += isYZ.x + isYZ.y;
i0.zw += 1.0 - isYZ.xy;
i0.z += isYZ.z;
i0.w += 1.0 - isYZ.z;
// i0 now contains the unique values 0,1,2,3 in each channel
vec4 i3 = clamp ( i0, 0.0 , 1.0 );
vec4 i2 = clamp ( i0- 1.0 , 0.0 , 1.0 );
vec4 i1 = clamp ( i0- 2.0 , 0.0 , 1.0 );
// x0 = x0 - 0.0 + 0.0 * C.xxxx
// x1 = x0 - i1 + 1.0 * C.xxxx
// x2 = x0 - i2 + 2.0 * C.xxxx
// x3 = x0 - i3 + 3.0 * C.xxxx
// x4 = x0 - 1.0 + 4.0 * C.xxxx
vec4 x1 = x0 - i1 + C.xxxx;
vec4 x2 = x0 - i2 + C.yyyy;
vec4 x3 = x0 - i3 + C.zzzz;
vec4 x4 = x0 + C.wwww;
// Permutations
i = mod289(i);
float j0 = permute( permute( permute( permute(i.w) + i.z) + i.y) + i.x);
vec4 j1 = permute( permute( permute( permute (
i.w + vec4 (i1.w, i2.w, i3.w, 1.0 ))
+ i.z + vec4 (i1.z, i2.z, i3.z, 1.0 ))
+ i.y + vec4 (i1.y, i2.y, i3.y, 1.0 ))
+ i.x + vec4 (i1.x, i2.x, i3.x, 1.0 ));
// Gradients: 7x7x6 points over a cube, mapped onto a 4-cross polytope
// 7*7*6 = 294, which is close to the ring size 17*17 = 289.
vec4 ip = vec4 (1.0 / 294.0 , 1.0 / 49.0 , 1.0 / 7.0 , 0.0 ) ;
vec4 p0 = grad4(j0, ip);
vec4 p1 = grad4(j1.x, ip);
vec4 p2 = grad4(j1.y, ip);
vec4 p3 = grad4(j1.z, ip);
vec4 p4 = grad4(j1.w, ip);
// Normalise gradients
vec4 norm = taylorInvSqrt(vec4 (dot (p0,p0), dot (p1,p1), dot (p2, p2), dot (p3,p3)));
p0 *= norm.x;
p1 *= norm.y;
p2 *= norm.z;
p3 *= norm.w;
p4 *= taylorInvSqrt(dot (p4,p4));
// Mix contributions from the five corners
vec3 m0 = max (0.6 - vec3 (dot (x0,x0), dot (x1,x1), dot (x2,x2)), 0.0 );
vec2 m1 = max (0.6 - vec2 (dot (x3,x3), dot (x4,x4) ), 0.0 );
m0 = m0 * m0;
m1 = m1 * m1;
return 49.0 * ( dot (m0* m0, vec3 ( dot ( p0, x0 ), dot ( p1, x1 ), dot ( p2, x2 )))
+ dot (m1* m1, vec2 ( dot ( p3, x3 ), dot ( p4, x4 ) ) ) ) ;
}
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