glsl.fragment.noise.perlinNoise4d.glsl Maven / Gradle / Ivy
//
// GLSL textureless classic 4D noise "cnoise",
// with an RSL-style periodic variant "pnoise".
// Author: Stefan Gustavson ([email protected])
// Version: 2011-04-03
//
// Many thanks to Ian McEwan of Ashima Arts for the
// ideas for permutation and gradient selection.
//
// This code is licensed under the terms of the MIT license:
//
// Copyright (c) 2011 Stefan Gustavson ([email protected])
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
// THE SOFTWARE.
//
// Classic Perlin noise
float perlinNoise4d(vec4 P)
{
vec4 Pi0 = floor(P);// Integer part for indexing
vec4 Pi1 = Pi0 + 1.0;// Integer part + 1
Pi0 = mod(Pi0, 289.0);
Pi1 = mod(Pi1, 289.0);
vec4 Pf0 = fract(P);// Fractional part for interpolation
vec4 Pf1 = Pf0 - 1.0;// Fractional part - 1.0
vec4 ix = vec4(Pi0.x, Pi1.x, Pi0.x, Pi1.x);
vec4 iy = vec4(Pi0.yy, Pi1.yy);
vec4 iz0 = vec4(Pi0.zzzz);
vec4 iz1 = vec4(Pi1.zzzz);
vec4 iw0 = vec4(Pi0.wwww);
vec4 iw1 = vec4(Pi1.wwww);
vec4 ixy = permute(permute(ix) + iy);
vec4 ixy0 = permute(ixy + iz0);
vec4 ixy1 = permute(ixy + iz1);
vec4 ixy00 = permute(ixy0 + iw0);
vec4 ixy01 = permute(ixy0 + iw1);
vec4 ixy10 = permute(ixy1 + iw0);
vec4 ixy11 = permute(ixy1 + iw1);
vec4 gx00 = ixy00 / 7.0;
vec4 gy00 = floor(gx00) / 7.0;
vec4 gz00 = floor(gy00) / 6.0;
gx00 = fract(gx00) - 0.5;
gy00 = fract(gy00) - 0.5;
gz00 = fract(gz00) - 0.5;
vec4 gw00 = vec4(0.75) - abs(gx00) - abs(gy00) - abs(gz00);
vec4 sw00 = step(gw00, vec4(0.0));
gx00 -= sw00 * (step(0.0, gx00) - 0.5);
gy00 -= sw00 * (step(0.0, gy00) - 0.5);
vec4 gx01 = ixy01 / 7.0;
vec4 gy01 = floor(gx01) / 7.0;
vec4 gz01 = floor(gy01) / 6.0;
gx01 = fract(gx01) - 0.5;
gy01 = fract(gy01) - 0.5;
gz01 = fract(gz01) - 0.5;
vec4 gw01 = vec4(0.75) - abs(gx01) - abs(gy01) - abs(gz01);
vec4 sw01 = step(gw01, vec4(0.0));
gx01 -= sw01 * (step(0.0, gx01) - 0.5);
gy01 -= sw01 * (step(0.0, gy01) - 0.5);
vec4 gx10 = ixy10 / 7.0;
vec4 gy10 = floor(gx10) / 7.0;
vec4 gz10 = floor(gy10) / 6.0;
gx10 = fract(gx10) - 0.5;
gy10 = fract(gy10) - 0.5;
gz10 = fract(gz10) - 0.5;
vec4 gw10 = vec4(0.75) - abs(gx10) - abs(gy10) - abs(gz10);
vec4 sw10 = step(gw10, vec4(0.0));
gx10 -= sw10 * (step(0.0, gx10) - 0.5);
gy10 -= sw10 * (step(0.0, gy10) - 0.5);
vec4 gx11 = ixy11 / 7.0;
vec4 gy11 = floor(gx11) / 7.0;
vec4 gz11 = floor(gy11) / 6.0;
gx11 = fract(gx11) - 0.5;
gy11 = fract(gy11) - 0.5;
gz11 = fract(gz11) - 0.5;
vec4 gw11 = vec4(0.75) - abs(gx11) - abs(gy11) - abs(gz11);
vec4 sw11 = step(gw11, vec4(0.0));
gx11 -= sw11 * (step(0.0, gx11) - 0.5);
gy11 -= sw11 * (step(0.0, gy11) - 0.5);
vec4 g0000 = vec4(gx00.x, gy00.x, gz00.x, gw00.x);
vec4 g1000 = vec4(gx00.y, gy00.y, gz00.y, gw00.y);
vec4 g0100 = vec4(gx00.z, gy00.z, gz00.z, gw00.z);
vec4 g1100 = vec4(gx00.w, gy00.w, gz00.w, gw00.w);
vec4 g0010 = vec4(gx10.x, gy10.x, gz10.x, gw10.x);
vec4 g1010 = vec4(gx10.y, gy10.y, gz10.y, gw10.y);
vec4 g0110 = vec4(gx10.z, gy10.z, gz10.z, gw10.z);
vec4 g1110 = vec4(gx10.w, gy10.w, gz10.w, gw10.w);
vec4 g0001 = vec4(gx01.x, gy01.x, gz01.x, gw01.x);
vec4 g1001 = vec4(gx01.y, gy01.y, gz01.y, gw01.y);
vec4 g0101 = vec4(gx01.z, gy01.z, gz01.z, gw01.z);
vec4 g1101 = vec4(gx01.w, gy01.w, gz01.w, gw01.w);
vec4 g0011 = vec4(gx11.x, gy11.x, gz11.x, gw11.x);
vec4 g1011 = vec4(gx11.y, gy11.y, gz11.y, gw11.y);
vec4 g0111 = vec4(gx11.z, gy11.z, gz11.z, gw11.z);
vec4 g1111 = vec4(gx11.w, gy11.w, gz11.w, gw11.w);
vec4 norm00 = taylorInvSqrt(vec4(dot(g0000, g0000), dot(g0100, g0100), dot(g1000, g1000), dot(g1100, g1100)));
g0000 *= norm00.x;
g0100 *= norm00.y;
g1000 *= norm00.z;
g1100 *= norm00.w;
vec4 norm01 = taylorInvSqrt(vec4(dot(g0001, g0001), dot(g0101, g0101), dot(g1001, g1001), dot(g1101, g1101)));
g0001 *= norm01.x;
g0101 *= norm01.y;
g1001 *= norm01.z;
g1101 *= norm01.w;
vec4 norm10 = taylorInvSqrt(vec4(dot(g0010, g0010), dot(g0110, g0110), dot(g1010, g1010), dot(g1110, g1110)));
g0010 *= norm10.x;
g0110 *= norm10.y;
g1010 *= norm10.z;
g1110 *= norm10.w;
vec4 norm11 = taylorInvSqrt(vec4(dot(g0011, g0011), dot(g0111, g0111), dot(g1011, g1011), dot(g1111, g1111)));
g0011 *= norm11.x;
g0111 *= norm11.y;
g1011 *= norm11.z;
g1111 *= norm11.w;
float n0000 = dot(g0000, Pf0);
float n1000 = dot(g1000, vec4(Pf1.x, Pf0.yzw));
float n0100 = dot(g0100, vec4(Pf0.x, Pf1.y, Pf0.zw));
float n1100 = dot(g1100, vec4(Pf1.xy, Pf0.zw));
float n0010 = dot(g0010, vec4(Pf0.xy, Pf1.z, Pf0.w));
float n1010 = dot(g1010, vec4(Pf1.x, Pf0.y, Pf1.z, Pf0.w));
float n0110 = dot(g0110, vec4(Pf0.x, Pf1.yz, Pf0.w));
float n1110 = dot(g1110, vec4(Pf1.xyz, Pf0.w));
float n0001 = dot(g0001, vec4(Pf0.xyz, Pf1.w));
float n1001 = dot(g1001, vec4(Pf1.x, Pf0.yz, Pf1.w));
float n0101 = dot(g0101, vec4(Pf0.x, Pf1.y, Pf0.z, Pf1.w));
float n1101 = dot(g1101, vec4(Pf1.xy, Pf0.z, Pf1.w));
float n0011 = dot(g0011, vec4(Pf0.xy, Pf1.zw));
float n1011 = dot(g1011, vec4(Pf1.x, Pf0.y, Pf1.zw));
float n0111 = dot(g0111, vec4(Pf0.x, Pf1.yzw));
float n1111 = dot(g1111, Pf1);
vec4 fade_xyzw = fade(Pf0);
vec4 n_0w = mix(vec4(n0000, n1000, n0100, n1100), vec4(n0001, n1001, n0101, n1101), fade_xyzw.w);
vec4 n_1w = mix(vec4(n0010, n1010, n0110, n1110), vec4(n0011, n1011, n0111, n1111), fade_xyzw.w);
vec4 n_zw = mix(n_0w, n_1w, fade_xyzw.z);
vec2 n_yzw = mix(n_zw.xy, n_zw.zw, fade_xyzw.y);
float n_xyzw = mix(n_yzw.x, n_yzw.y, fade_xyzw.x);
return 2.2 * n_xyzw;
}
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