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Artistic License 2.0
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@ -0,0 +1,14 @@
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This work follows Stefan Gustavson's paper "Simplex noise demystified"
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http://staffwww.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf
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without using uniform arrays or texture engines.
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A single vec4 uniform 'pParam' is used to set the length and a and
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c constants respectively of the permutation polynomial to use. The
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last element of the vec4 is the number of gradients to select from
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on the vertices. An example vec4 is ( 19*19, 2*19, 1, 7 )
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Refer to http://en.wikipedia.org/wiki/Permutation_polynomial for
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||||
more information on permutation polynomials.
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@ -0,0 +1,265 @@
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//
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// Description : Array and textureless GLSL 2D/3D/4D simplex
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// noise functions.
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// Author : Ian McEwan, Ashima Arts.
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// Maintainer : ijm
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// Lastmod : 20110223
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// License : Copyright (C) 2011 Ashima Arts. All rights reserved.
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// Distributed under the Artistic License 2.0; See LICENCE file.
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//
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#undef NORMALIZE_GRADIENTS
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#undef USE_CIRCLE
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#define COLLAPSE_SORTNET
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vec2 permute(vec2 x,vec3 p) { return floor(mod( (p.y*x + p.z) * x , p.x )); }
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vec3 permute(vec3 x,vec3 p) { return floor(mod( (p.y*x + p.z) * x , p.x )); }
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vec4 permute(vec4 x,vec3 p) { return floor(mod( (p.y*x + p.z) * x , p.x )); }
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float permute(float x,vec3 p) { return floor(mod( (p.y*x + p.z) * x , p.x )); }
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uniform vec4 pParam;
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// Example
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// const vec4 pParam = vec4( 17.* 17., 34., 1., 7.);
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float taylorInvSqrt(float r)
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{
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return ( 0.83666002653408 + 0.7*0.85373472095314 - 0.85373472095314 * r );
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}
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float simplexNoise2(vec2 v)
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{
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const vec2 C = vec2(0.211324865405187134, // (3.0-sqrt(3.0))/6.;
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0.366025403784438597); // 0.5*(sqrt(3.0)-1.);
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const vec3 D = vec3( 0., 0.5, 2.0) * 3.14159265358979312;
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// First corner
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vec2 i = floor(v + dot(v, C.yy) );
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vec2 x0 = v - i + dot(i, C.xx);
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// Other corners
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vec2 i1 = (x0.x > x0.y) ? vec2(1.,0.) : vec2(0.,1.) ;
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// x0 = x0 - 0. + 0. * C
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vec2 x1 = x0 - i1 + 1. * C.xx ;
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vec2 x2 = x0 - 1. + 2. * C.xx ;
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// Permutations
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i = mod(i, pParam.x);
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vec3 p = permute( permute(
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i.y + vec3(0., i1.y, 1. ), pParam.xyz)
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+ i.x + vec3(0., i1.x, 1. ), pParam.xyz);
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#ifndef USE_CIRCLE
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// ( N points uniformly over a line, mapped onto a diamond.)
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vec3 x = fract(p / pParam.w) ;
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vec3 h = 0.5 - abs(x) ;
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vec3 sx = vec3(lessThan(x,D.xxx)) *2. -1.;
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vec3 sh = vec3(lessThan(h,D.xxx));
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vec3 a0 = x + sx*sh;
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vec2 p0 = vec2(a0.x,h.x);
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vec2 p1 = vec2(a0.y,h.y);
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vec2 p2 = vec2(a0.z,h.z);
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#ifdef NORMALISE_GRADIENTS
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p0 *= taylorInvSqrt(dot(p0,p0));
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p1 *= taylorInvSqrt(dot(p1,p1));
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p2 *= taylorInvSqrt(dot(p2,p2));
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#endif
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vec3 g = 2.0 * vec3( dot(p0, x0), dot(p1, x1), dot(p2, x2) );
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#else
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// N points around a unit circle.
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vec3 phi = D.z * mod(p,pParam.w) /pParam.w ;
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vec4 a0 = sin(phi.xxyy+D.xyxy);
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vec2 a1 = sin(phi.zz +D.xy);
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vec3 g = vec3( dot(a0.xy, x0), dot(a0.zw, x1), dot(a1.xy, x2) );
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#endif
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// mix
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vec3 m = max(0.5 - vec3(dot(x0,x0), dot(x1,x1), dot(x2,x2)), 0.);
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m = m*m ;
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return 1.66666* 70.*dot(m*m, g);
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}
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float simplexNoise3(vec3 v)
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{
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const vec2 C = vec2(1./6. , 1./3. ) ;
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const vec4 D = vec4(0., 0.5, 1.0, 2.0);
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// First corner
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vec3 i = floor(v + dot(v, C.yyy) );
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vec3 x0 = v - i + dot(i, C.xxx) ;
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// Other corners
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#ifdef COLLAPSE_SORTNET
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vec3 g = vec3( greaterThan( x0.xyz, x0.yzx) );
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vec3 l = vec3( lessThanEqual( x0.xyz, x0.yzx) );
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vec3 i1 = g.xyz * l.zxy;
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vec3 i2 = max( g.xyz, l.zxy);
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#else
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// Keeping this clean - let the compiler optimize.
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vec3 q1;
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q1.x = max(x0.x, x0.y);
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q1.y = min(x0.x, x0.y);
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q1.z = x0.z;
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vec3 q2;
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q2.x = max(q1.x,q1.z);
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q2.z = min(q1.x,q1.z);
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q2.y = q1.y;
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vec3 q3;
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q3.y = max(q2.y, q2.z);
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q3.z = min(q2.y, q2.z);
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q3.x = q2.x;
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vec3 i1 = vec3(equal(q3.xxx, x0));
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vec3 i2 = i1 + vec3(equal(q3.yyy, x0));
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#endif
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// x0 = x0 - 0. + 0. * C
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vec3 x1 = x0 - i1 + 1. * C.xxx;
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vec3 x2 = x0 - i2 + 2. * C.xxx;
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vec3 x3 = x0 - 1. + 3. * C.xxx;
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// Permutations
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i = mod(i, pParam.x );
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vec4 p = permute( permute( permute(
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i.z + vec4(0., i1.z, i2.z, 1. ), pParam.xyz)
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+ i.y + vec4(0., i1.y, i2.y, 1. ), pParam.xyz)
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+ i.x + vec4(0., i1.x, i2.x, 1. ), pParam.xyz);
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// Gradients
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// ( N*N points uniformly over a square, mapped onto a octohedron.)
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float n_ = 1.0/pParam.w ;
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vec3 ns = n_ * D.wyz - D.xzx ;
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vec4 j = p - pParam.w*pParam.w*floor(p * ns.z *ns.z); // mod(p,N*N)
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vec4 x_ = floor(j * ns.z) ;
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vec4 y_ = floor(j - pParam.w * x_ ) ; // mod(j,N)
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vec4 x = x_ *ns.x + ns.yyyy;
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vec4 y = y_ *ns.x + ns.yyyy;
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vec4 h = 1. - abs(x) - abs(y);
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vec4 b0 = vec4( x.xy, y.xy );
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vec4 b1 = vec4( x.zw, y.zw );
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vec4 s0 = vec4(lessThan(b0,D.xxxx)) *2. -1.;
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vec4 s1 = vec4(lessThan(b1,D.xxxx)) *2. -1.;
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vec4 sh = vec4(lessThan(h, D.xxxx));
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vec4 a0 = b0.xzyw + s0.xzyw*sh.xxyy ;
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vec4 a1 = b1.xzyw + s1.xzyw*sh.zzww ;
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vec3 p0 = vec3(a0.xy,h.x);
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vec3 p1 = vec3(a0.zw,h.y);
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vec3 p2 = vec3(a1.xy,h.z);
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vec3 p3 = vec3(a1.zw,h.w);
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#ifdef NORMALISE_GRADIENTS
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p0 *= taylorInvSqrt(dot(p0,p0));
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p1 *= taylorInvSqrt(dot(p1,p1));
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p2 *= taylorInvSqrt(dot(p2,p2));
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p3 *= taylorInvSqrt(dot(p3,p3));
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#endif
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// Mix
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vec4 m = max(0.6 - vec4(dot(x0,x0), dot(x1,x1), dot(x2,x2), dot(x3,x3)), 0.);
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m = m * m;
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||||
//used to be 64.
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||||
return 48.0 * dot( m*m, vec4( dot(p0,x0), dot(p1,x1),
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||||
dot(p2,x2), dot(p3,x3) ) );
|
||||
}
|
||||
|
||||
vec4 grad4(float j, vec4 ip, float iw)
|
||||
{
|
||||
const vec4 ones = vec4(1.,1.,1.,-1.);
|
||||
vec4 p,s;
|
||||
|
||||
//p = floor( fract (vec4(j) * ip) *pParam.w) * iw - ones;
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||||
p.xyz = floor( fract (vec3(j) * ip.xyz) *pParam.w) * iw -1.0;
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||||
p.w = 1.5 - dot(abs(p.xyz), ones.xyz);
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||||
//p.w = dot( -abs(p), ones);
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||||
s = vec4(lessThan(p,vec4(0.)));
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||||
p.xyz = p.xyz + (s.xyz*2.-1.) * s.www;
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||||
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||||
return p;
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||||
}
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||||
|
||||
float simplexNoise4(vec4 v)
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||||
{
|
||||
const vec2 C = vec2( 0.138196601125010504, // (5 - sqrt(5))/20 G4
|
||||
0.309016994374947451); // (sqrt(5) - 1)/4 F4
|
||||
// First corner
|
||||
vec4 i = floor(v + dot(v, C.yyyy) );
|
||||
vec4 x0 = v - i + dot(i, C.xxxx);
|
||||
|
||||
// Other corners
|
||||
vec4 q1;
|
||||
q1.xy = max(x0.xy,x0.zw); // x:z y:w
|
||||
q1.zw = min(x0.xy,x0.zw);
|
||||
|
||||
vec4 q2;
|
||||
q2.xz = max(q1.xz,q1.yw); // x:y z:w
|
||||
q2.yw = min(q1.xz,q1.yw);
|
||||
|
||||
vec4 q3;
|
||||
q3.y = max(q2.y,q2.z); // y:z
|
||||
q3.z = min(q2.y,q2.z);
|
||||
q3.xw = q2.xw;
|
||||
|
||||
vec4 i1 = vec4(equal(q3.xxxx, x0));
|
||||
vec4 i2 = i1 + vec4(equal(q3.yyyy, x0));
|
||||
vec4 i3 = i2 + vec4(equal(q3.zzzz, x0));
|
||||
|
||||
// x0 = x0 - 0. + 0. * C
|
||||
vec4 x1 = x0 - i1 + 1. * C.xxxx;
|
||||
vec4 x2 = x0 - i2 + 2. * C.xxxx;
|
||||
vec4 x3 = x0 - i3 + 3. * C.xxxx;
|
||||
vec4 x4 = x0 - 1. + 4. * C.xxxx;
|
||||
|
||||
// Permutations
|
||||
i = mod(i, pParam.x );
|
||||
float j0 = permute( permute( permute( permute (
|
||||
i.w, pParam.xyz) + i.z, pParam.xyz)
|
||||
+ i.y, pParam.xyz) + i.x, pParam.xyz);
|
||||
vec4 j1 = permute( permute( permute( permute (
|
||||
i.w + vec4(i1.w, i2.w, i3.w, 1. ), pParam.xyz)
|
||||
+ i.z + vec4(i1.z, i2.z, i3.z, 1. ), pParam.xyz)
|
||||
+ i.y + vec4(i1.y, i2.y, i3.y, 1. ), pParam.xyz)
|
||||
+ i.x + vec4(i1.x, i2.x, i3.x, 1. ), pParam.xyz);
|
||||
// Gradients
|
||||
// ( N*N*N points uniformly over a cube, mapped onto a 4-octohedron.)
|
||||
vec4 ip = 1.0 / vec4(pParam.w*pParam.w*pParam.w,
|
||||
pParam.w*pParam.w,
|
||||
pParam.w,0.);
|
||||
float iw = 2.0 * ip.z ;
|
||||
|
||||
vec4 p0 = grad4(j0, ip, iw);
|
||||
vec4 p1 = grad4(j1.x, ip, iw);
|
||||
vec4 p2 = grad4(j1.y, ip, iw);
|
||||
vec4 p3 = grad4(j1.z, ip, iw);
|
||||
vec4 p4 = grad4(j1.w, ip, iw);
|
||||
|
||||
#ifdef NORMALISE_GRADIENTS
|
||||
p0 *= taylorInvSqrt(dot(p0,p0));
|
||||
p1 *= taylorInvSqrt(dot(p1,p1));
|
||||
p2 *= taylorInvSqrt(dot(p2,p2));
|
||||
p3 *= taylorInvSqrt(dot(p3,p3));
|
||||
p4 *= taylorInvSqrt(dot(p4,p4));
|
||||
#endif
|
||||
|
||||
// Mix
|
||||
vec3 m0 = max(0.6 - vec3(dot(x0,x0), dot(x1,x1), dot(x2,x2)), 0.);
|
||||
vec2 m1 = max(0.6 - vec2(dot(x3,x3), dot(x4,x4) ), 0.);
|
||||
m0 = m0 * m0;
|
||||
m1 = m1 * m1;
|
||||
return 32. * ( dot(m0*m0, vec3( dot( p0, x0 ), dot( p1, x1 ), dot( p2, x2 )))
|
||||
+ dot(m1*m1, vec2( dot( p3, x3 ), dot( p4, x4 ) ) ) ) ;
|
||||
|
||||
}
|
||||
|
||||
|
Loading…
Reference in New Issue