Simon Schneegans
207 lines
6.3 KiB
GLSL
207 lines
6.3 KiB
GLSL
// These noise algorithms are based on implementations by various authors from
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// shadertoy.com, which are all available under the MIT License. See the respective links
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// in the comments below.
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////////////////////////////////////////////////////////////////////////////////////////
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// Hash without Sine //
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// MIT License, https://www.shadertoy.com/view/4djSRW //
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// Copyright (c) 2014 David Hoskins. //
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////////////////////////////////////////////////////////////////////////////////////////
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// 1 out, 1 in...
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float hash11(float p) {
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p = fract(p * .1031);
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p *= p + 33.33;
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p *= p + p;
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return fract(p);
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}
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// 1 out, 2 in...
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float hash12(vec2 p) {
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vec3 p3 = fract(vec3(p.xyx) * .1031);
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p3 += dot(p3, p3.yzx + 33.33);
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return fract((p3.x + p3.y) * p3.z);
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}
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// 1 out, 3 in...
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float hash13(vec3 p3) {
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p3 = fract(p3 * .1031);
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p3 += dot(p3, p3.zyx + 31.32);
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return fract((p3.x + p3.y) * p3.z);
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}
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// 2 out, 1 in...
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vec2 hash21(float p) {
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vec3 p3 = fract(vec3(p) * vec3(.1031, .1030, .0973));
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p3 += dot(p3, p3.yzx + 33.33);
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return fract((p3.xx + p3.yz) * p3.zy);
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}
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// 2 out, 2 in...
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vec2 hash22(vec2 p) {
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vec3 p3 = fract(vec3(p.xyx) * vec3(.1031, .1030, .0973));
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p3 += dot(p3, p3.yzx + 33.33);
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return fract((p3.xx + p3.yz) * p3.zy);
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}
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// 2 out, 3 in...
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vec2 hash23(vec3 p3) {
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p3 = fract(p3 * vec3(.1031, .1030, .0973));
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p3 += dot(p3, p3.yzx + 33.33);
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return fract((p3.xx + p3.yz) * p3.zy);
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}
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// 3 out, 1 in...
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vec3 hash31(float p) {
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vec3 p3 = fract(vec3(p) * vec3(.1031, .1030, .0973));
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p3 += dot(p3, p3.yzx + 33.33);
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return fract((p3.xxy + p3.yzz) * p3.zyx);
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}
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// 3 out, 2 in...
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vec3 hash32(vec2 p) {
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vec3 p3 = fract(vec3(p.xyx) * vec3(.1031, .1030, .0973));
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p3 += dot(p3, p3.yxz + 33.33);
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return fract((p3.xxy + p3.yzz) * p3.zyx);
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}
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// 3 out, 3 in...
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vec3 hash33(vec3 p3) {
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p3 = fract(p3 * vec3(.1031, .1030, .0973));
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p3 += dot(p3, p3.yxz + 33.33);
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return fract((p3.xxy + p3.yxx) * p3.zyx);
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}
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// 4 out, 1 in...
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vec4 hash41(float p) {
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vec4 p4 = fract(vec4(p) * vec4(.1031, .1030, .0973, .1099));
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p4 += dot(p4, p4.wzxy + 33.33);
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return fract((p4.xxyz + p4.yzzw) * p4.zywx);
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}
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// 4 out, 2 in...
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vec4 hash42(vec2 p) {
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vec4 p4 = fract(vec4(p.xyxy) * vec4(.1031, .1030, .0973, .1099));
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p4 += dot(p4, p4.wzxy + 33.33);
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return fract((p4.xxyz + p4.yzzw) * p4.zywx);
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}
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// 4 out, 3 in...
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vec4 hash43(vec3 p) {
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vec4 p4 = fract(vec4(p.xyzx) * vec4(.1031, .1030, .0973, .1099));
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p4 += dot(p4, p4.wzxy + 33.33);
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return fract((p4.xxyz + p4.yzzw) * p4.zywx);
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}
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// 4 out, 4 in...
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vec4 hash44(vec4 p4) {
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p4 = fract(p4 * vec4(.1031, .1030, .0973, .1099));
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p4 += dot(p4, p4.wzxy + 33.33);
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return fract((p4.xxyz + p4.yzzw) * p4.zywx);
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}
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////////////////////////////////////////////////////////////////////////////////////////
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// 2D Simplex Noise //
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// MIT License, https://www.shadertoy.com/view/Msf3WH //
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// Copyright © 2013 Inigo Quilez //
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////////////////////////////////////////////////////////////////////////////////////////
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float simplex2D(vec2 p) {
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const float K1 = 0.366025404; // (sqrt(3)-1)/2;
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const float K2 = 0.211324865; // (3-sqrt(3))/6;
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vec2 i = floor(p + (p.x + p.y) * K1);
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vec2 a = p - i + (i.x + i.y) * K2;
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float m = step(a.y, a.x);
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vec2 o = vec2(m, 1.0 - m);
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vec2 b = a - o + K2;
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vec2 c = a - 1.0 + 2.0 * K2;
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vec3 h = max(0.5 - vec3(dot(a, a), dot(b, b), dot(c, c)), 0.0);
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vec3 n = h * h * h * h *
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vec3(dot(a, -1.0 + 2.0 * hash22(i + 0.0)), dot(b, -1.0 + 2.0 * hash22(i + o)),
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dot(c, -1.0 + 2.0 * hash22(i + 1.0)));
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return 0.5 + 0.5 * dot(n, vec3(70.0));
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}
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float simplex2DFractal(vec2 p) {
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mat2 m = mat2(1.6, 1.2, -1.2, 1.6);
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float f = 0.5000 * simplex2D(p);
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p = m * p;
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f += 0.2500 * simplex2D(p);
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p = m * p;
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f += 0.1250 * simplex2D(p);
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p = m * p;
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f += 0.0625 * simplex2D(p);
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p = m * p;
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return f;
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}
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////////////////////////////////////////////////////////////////////////////////////////
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// 3D Simplex Noise //
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// MIT License, https://www.shadertoy.com/view/XsX3zB //
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// Copyright © 2013 Nikita Miropolskiy //
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////////////////////////////////////////////////////////////////////////////////////////
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float simplex3D(vec3 p) {
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// skew constants for 3D simplex functions
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const float F3 = 0.3333333;
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const float G3 = 0.1666667;
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// 1. find current tetrahedron T and it's four vertices
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// s, s+i1, s+i2, s+1.0 - absolute skewed (integer) coordinates of T vertices
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// x, x1, x2, x3 - unskewed coordinates of p relative to each of T vertice
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// calculate s and x
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vec3 s = floor(p + dot(p, vec3(F3)));
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vec3 x = p - s + dot(s, vec3(G3));
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// calculate i1 and i2
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vec3 e = step(vec3(0.0), x - x.yzx);
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vec3 i1 = e * (1.0 - e.zxy);
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vec3 i2 = 1.0 - e.zxy * (1.0 - e);
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// x1, x2, x3
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vec3 x1 = x - i1 + G3;
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vec3 x2 = x - i2 + 2.0 * G3;
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vec3 x3 = x - 1.0 + 3.0 * G3;
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// 2. find four surflets and store them in d
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vec4 w, d;
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// calculate surflet weights
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w.x = dot(x, x);
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w.y = dot(x1, x1);
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w.z = dot(x2, x2);
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w.w = dot(x3, x3);
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// w fades from 0.6 at the center of the surflet to 0.0 at the margin
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w = max(0.6 - w, 0.0);
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// calculate surflet components
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d.x = dot(-0.5 + hash33(s), x);
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d.y = dot(-0.5 + hash33(s + i1), x1);
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d.z = dot(-0.5 + hash33(s + i2), x2);
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d.w = dot(-0.5 + hash33(s + 1.0), x3);
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// multiply d by w^4
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w *= w;
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w *= w;
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d *= w;
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// 3. return the sum of the four surflets
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return dot(d, vec4(52.0)) * 0.5 + 0.5;
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}
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// directional artifacts can be reduced by rotating each octave
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float simplex3DFractal(vec3 m) {
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// const matrices for 3D rotation
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const mat3 rot1 = mat3(-0.37, 0.36, 0.85, -0.14, -0.93, 0.34, 0.92, 0.01, 0.4);
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const mat3 rot2 = mat3(-0.55, -0.39, 0.74, 0.33, -0.91, -0.24, 0.77, 0.12, 0.63);
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const mat3 rot3 = mat3(-0.71, 0.52, -0.47, -0.08, -0.72, -0.68, -0.7, -0.45, 0.56);
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return 0.5333333 * simplex3D(m * rot1) + 0.2666667 * simplex3D(2.0 * m * rot2) +
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0.1333333 * simplex3D(4.0 * m * rot3) + 0.0666667 * simplex3D(8.0 * m);
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} |