//
// Description : Array and textureless GLSL 2D simplex noise function.
//      Author : Ian McEwan, Ashima Arts.
//  Maintainer : stegu
//     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
//               https://github.com/stegu/webgl-noise
//

// (sqrt(5) - 1)/4 = F4, used once below
#define F4 0.309016994374947451
float mod289(float x){return x - floor(x * (1.0 / 289.0)) * 289.0;}
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;}
vec4  mod289(vec4 x) {return x - floor(x * (1.0 / 289.0)) * 289.0;}
float permute(float x){return mod289(((x*34.0)+1.0)*x);}
vec3  permute(vec3 x) {return mod289(((x*34.0)+1.0)*x);}
vec4  permute(vec4 x) {return mod289(((x*34.0)+1.0)*x);}
float taylorInvSqrt(float r){return 1.79284291400159 - 0.85373472095314 * r;}
vec4  taylorInvSqrt(vec4 r) {return 1.79284291400159 - 0.85373472095314 * r;}
float snoise2D(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.x = step( x0.y, x0.x ); // x0.x > x0.y ? 1.0 : 0.0
  //i1.y = 1.0 - i1.x;
  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);
}
float snoise3D(vec3 v){
  const vec2 C = vec2(1.0 / 6.0, 1.0 / 3.0);
  const vec4 D = vec4(0.0, 0.5, 1.0, 2.0);

  // First corner
  vec3 i  = floor(v + dot(v, C.yyy) );
  vec3 x0 =   v - i + dot(i, C.xxx) ;

  // Other corners
  vec3 g = step(x0.yzx, x0.xyz);
  vec3 l = 1.0 - g;
  vec3 i1 = min( g.xyz, l.zxy );
  vec3 i2 = max( g.xyz, l.zxy );

  //   x0 = x0 - 0.0 + 0.0 * C.xxx;
  //   x1 = x0 - i1  + 1.0 * C.xxx;
  //   x2 = x0 - i2  + 2.0 * C.xxx;
  //   x3 = x0 - 1.0 + 3.0 * C.xxx;
  vec3 x1 = x0 - i1 + C.xxx;
  vec3 x2 = x0 - i2 + C.yyy; // 2.0*C.x = 1/3 = C.y
  vec3 x3 = x0 - D.yyy;      // -1.0+3.0*C.x = -0.5 = -D.y

  // Permutations
  i = mod289(i);
  vec4 p = permute( permute( permute(
             i.z + vec4(0.0, i1.z, i2.z, 1.0 ))
           + i.y + vec4(0.0, i1.y, i2.y, 1.0 ))
           + i.x + vec4(0.0, i1.x, i2.x, 1.0 ));

  // Gradients: 7x7 points over a square, mapped onto an octahedron.
  // The ring size 17*17 = 289 is close to a multiple of 49 (49*6 = 294)
  float n_ = 0.142857142857; // 1.0/7.0
  vec3  ns = n_ * D.wyz - D.xzx;

  vec4 j = p - 49.0 * floor(p * ns.z * ns.z);  //  mod(p,7*7)

  vec4 x_ = floor(j * ns.z);
  vec4 y_ = floor(j - 7.0 * x_ );    // mod(j,N)

  vec4 x = x_ *ns.x + ns.yyyy;
  vec4 y = y_ *ns.x + ns.yyyy;
  vec4 h = 1.0 - abs(x) - abs(y);

  vec4 b0 = vec4( x.xy, y.xy );
  vec4 b1 = vec4( x.zw, y.zw );

  //vec4 s0 = vec4(lessThan(b0,0.0))*2.0 - 1.0;
  //vec4 s1 = vec4(lessThan(b1,0.0))*2.0 - 1.0;
  vec4 s0 = floor(b0)*2.0 + 1.0;
  vec4 s1 = floor(b1)*2.0 + 1.0;
  vec4 sh = -step(h, vec4(0.0));

  vec4 a0 = b0.xzyw + s0.xzyw*sh.xxyy ;
  vec4 a1 = b1.xzyw + s1.xzyw*sh.zzww ;

  vec3 p0 = vec3(a0.xy,h.x);
  vec3 p1 = vec3(a0.zw,h.y);
  vec3 p2 = vec3(a1.xy,h.z);
  vec3 p3 = vec3(a1.zw,h.w);

  //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;

  // Mix final noise value
  vec4 m = max(0.6 - vec4(dot(x0,x0), dot(x1,x1), dot(x2,x2), dot(x3,x3)), 0.0);
  m = m * m;
  return 42.0 * dot( m*m, vec4( dot(p0,x0), dot(p1,x1), dot(p2,x2), dot(p3,x3) ) );
}
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;
}
float snoise4D(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 ) ) ) ) ;
}
float fsnoise      (vec2 c){return fract(sin(dot(c, vec2(12.9898, 78.233))) * 43758.5453);}
float fsnoiseDigits(vec2 c){return fract(sin(dot(c, vec2(0.129898, 0.78233))) * 437.585453);}
vec3 hsv(float h, float s, float v){
    vec4 t = vec4(1.0, 2.0 / 3.0, 1.0 / 3.0, 3.0);
    vec3 p = abs(fract(vec3(h) + t.xyz) * 6.0 - vec3(t.w));
    return v * mix(vec3(t.x), clamp(p - vec3(t.x), 0.0, 1.0), s);
}
mat2 rotate2D(float r){
    return mat2(cos(r), sin(r), -sin(r), cos(r));
}
mat3 rotate3D(float angle, vec3 axis){
    vec3 a = normalize(axis);
    float s = sin(angle);
    float c = cos(angle);
    float r = 1.0 - c;
    return mat3(
        a.x * a.x * r + c,
        a.y * a.x * r + a.z * s,
        a.z * a.x * r - a.y * s,
        a.x * a.y * r - a.z * s,
        a.y * a.y * r + c,
        a.z * a.y * r + a.x * s,
        a.x * a.z * r + a.y * s,
        a.y * a.z * r - a.x * s,
        a.z * a.z * r + c
    );
}
const float PI = 3.141592653589793;
const float PI2 = PI * 2.0;

