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+// Virtually all of these were taken from: https://www.shadertoy.com/view/ttc3zr
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+
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+uvec4 murmurHash42(uvec2 src) {
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+ const uint M = 0x5bd1e995u;
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+ uvec4 h = uvec4(1190494759u, 2147483647u, 3559788179u, 179424673u);
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+ src *= M; src ^= src>>24u; src *= M;
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+ h *= M; h ^= src.x; h *= M; h ^= src.y;
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+ h ^= h>>13u; h *= M; h ^= h>>15u;
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+ return h;
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+}
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+
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+uint murmurHash11(uint src) {
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+ const uint M = 0x5bd1e995u;
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+ uint h = 1190494759u;
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+ src *= M; src ^= src>>24u; src *= M;
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+ h *= M; h ^= src;
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+ h ^= h>>13u; h *= M; h ^= h>>15u;
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+ return h;
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+}
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+
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+uint murmurHash12(uvec2 src) {
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+ const uint M = 0x5bd1e995u;
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+ uint h = 1190494759u;
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+ src *= M; src ^= src>>24u; src *= M;
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+ h *= M; h ^= src.x; h *= M; h ^= src.y;
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+ h ^= h>>13u; h *= M; h ^= h>>15u;
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+ return h;
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+}
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+
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+uint murmurHash13(uvec3 src) {
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+ const uint M = 0x5bd1e995u;
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+ uint h = 1190494759u;
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+ src *= M; src ^= src>>24u; src *= M;
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+ h *= M; h ^= src.x; h *= M; h ^= src.y; h *= M; h ^= src.z;
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+ h ^= h>>13u; h *= M; h ^= h>>15u;
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+ return h;
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+}
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+
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+uvec2 murmurHash22(uvec2 src) {
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+ const uint M = 0x5bd1e995u;
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+ uvec2 h = uvec2(1190494759u, 2147483647u);
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+ src *= M; src ^= src>>24u; src *= M;
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+ h *= M; h ^= src.x; h *= M; h ^= src.y;
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+ h ^= h>>13u; h *= M; h ^= h>>15u;
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+ return h;
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+}
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+
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+uvec2 murmurHash21(uint src) {
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+ const uint M = 0x5bd1e995u;
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+ uvec2 h = uvec2(1190494759u, 2147483647u);
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+ src *= M; src ^= src>>24u; src *= M;
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+ h *= M; h ^= src;
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+ h ^= h>>13u; h *= M; h ^= h>>15u;
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+ return h;
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+}
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+
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+uvec2 murmurHash23(uvec3 src) {
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+ const uint M = 0x5bd1e995u;
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+ uvec2 h = uvec2(1190494759u, 2147483647u);
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+ src *= M; src ^= src>>24u; src *= M;
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+ h *= M; h ^= src.x; h *= M; h ^= src.y; h *= M; h ^= src.z;
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+ h ^= h>>13u; h *= M; h ^= h>>15u;
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+ return h;
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+}
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+
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+uvec3 murmurHash31(uint src) {
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+ const uint M = 0x5bd1e995u;
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+ uvec3 h = uvec3(1190494759u, 2147483647u, 3559788179u);
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+ src *= M; src ^= src>>24u; src *= M;
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+ h *= M; h ^= src;
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+ h ^= h>>13u; h *= M; h ^= h>>15u;
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+ return h;
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+}
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+
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+uvec3 murmurHash33(uvec3 src) {
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+ const uint M = 0x5bd1e995u;
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+ uvec3 h = uvec3(1190494759u, 2147483647u, 3559788179u);
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+ src *= M; src ^= src>>24u; src *= M;
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+ h *= M; h ^= src.x; h *= M; h ^= src.y; h *= M; h ^= src.z;
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+ h ^= h>>13u; h *= M; h ^= h>>15u;
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+ return h;
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+}
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+
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+// 3 outputs, 3 inputs
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+vec3 hash33(vec3 src) {
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+ uvec3 h = murmurHash33(floatBitsToUint(src));
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+ return uintBitsToFloat(h & 0x007fffffu | 0x3f800000u) - 1.0;
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+}
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+
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+// 1 output, 1 input
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+float hash11(float src) {
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+ uint h = murmurHash11(floatBitsToUint(src));
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+ return uintBitsToFloat(h & 0x007fffffu | 0x3f800000u) - 1.0;
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+}
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+
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+// 1 output, 2 inputs
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+float hash12(vec2 src) {
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+ uint h = murmurHash12(floatBitsToUint(src));
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+ return uintBitsToFloat(h & 0x007fffffu | 0x3f800000u) - 1.0;
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+}
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+
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+// 1 output, 3 inputs
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+float hash13(vec3 src) {
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+ uint h = murmurHash13(floatBitsToUint(src));
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+ return uintBitsToFloat(h & 0x007fffffu | 0x3f800000u) - 1.0;
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+}
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+
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+// 2 outputs, 1 input
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+vec2 hash21(float src) {
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+ uvec2 h = murmurHash21(floatBitsToUint(src));
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+ return uintBitsToFloat(h & 0x007fffffu | 0x3f800000u) - 1.0;
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+}
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+
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+// 3 outputs, 1 input
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+vec3 hash31(float src) {
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+ uvec3 h = murmurHash31(floatBitsToUint(src));
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+ return uintBitsToFloat(h & 0x007fffffu | 0x3f800000u) - 1.0;
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+}
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+
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+// 2 outputs, 2 inputs
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+vec2 hash22(vec2 src) {
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+ uvec2 h = murmurHash22(floatBitsToUint(src));
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+ return uintBitsToFloat(h & 0x007fffffu | 0x3f800000u) - 1.0;
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+}
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+
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+// 4 outputs, 2 inputs
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+vec4 hash42(vec2 src) {
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+ uvec4 h = murmurHash42(floatBitsToUint(src));
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+ return uintBitsToFloat(h & 0x007fffffu | 0x3f800000u) - 1.0;
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+}
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+
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+
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+// 2 outputs, 3 inputs
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+vec2 hash23(vec3 src) {
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+ uvec2 h = murmurHash23(floatBitsToUint(src));
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+ return uintBitsToFloat(h & 0x007fffffu | 0x3f800000u) - 1.0;
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+}
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+
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+float noise11(float p) {
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+ float i = floor(p);
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+
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+ float f = fract(p);
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+ float u = smoothstep(0.0, 1.0, f);
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+
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+ float val = mix( hash11(i + 0.0),
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+ hash11(i + 1.0), u);
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+ return val * 2.0 - 1.0;
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+}
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+
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+float noise12(vec2 p) {
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+ vec2 i = floor(p);
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+
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+ vec2 f = fract(p);
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+ vec2 u = smoothstep(vec2(0.0), vec2(1.0), f);
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+
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+ float val = mix( mix( hash12( i + vec2(0.0, 0.0) ),
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+ hash12( i + vec2(1.0, 0.0) ), u.x),
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+ mix( hash12( i + vec2(0.0, 1.0) ),
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+ hash12( i + vec2(1.0, 1.0) ), u.x), u.y);
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+ return val * 2.0 - 1.0;
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+}
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+
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+float noise13(vec3 x) {
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+ vec3 i = floor(x);
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+ vec3 f = fract(x);
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+ f = f*f*(3.0-2.0*f);
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+
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+ return mix(mix(mix( hash13(i+vec3(0.0, 0.0, 0.0)),
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+ hash13(i+vec3(1.0, 0.0, 0.0)),f.x),
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+ mix( hash13(i+vec3(0.0, 1.0, 0.0)),
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+ hash13(i+vec3(1.0, 1.0, 0.0)),f.x),f.y),
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+ mix(mix( hash13(i+vec3(0.0, 0.0, 1.0)),
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+ hash13(i+vec3(1.0, 0.0, 1.0)),f.x),
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+ mix( hash13(i+vec3(0.0, 1.0, 1.0)),
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+ hash13(i+vec3(1.0, 1.0, 1.0)),f.x),f.y),f.z);
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+}
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+
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+vec2 noise23(vec3 x) {
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+ vec3 i = floor(x);
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+ vec3 f = fract(x);
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+ f = f*f*(3.0-2.0*f);
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+
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+ return mix(mix(mix( hash23(i+vec3(0.0, 0.0, 0.0)),
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+ hash23(i+vec3(1.0, 0.0, 0.0)),f.x),
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+ mix( hash23(i+vec3(0.0, 1.0, 0.0)),
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+ hash23(i+vec3(1.0, 1.0, 0.0)),f.x),f.y),
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+ mix(mix( hash23(i+vec3(0.0, 0.0, 1.0)),
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+ hash23(i+vec3(1.0, 0.0, 1.0)),f.x),
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+ mix( hash23(i+vec3(0.0, 1.0, 1.0)),
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+ hash23(i+vec3(1.0, 1.0, 1.0)),f.x),f.y),f.z);
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+}
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+
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+vec2 noise22(vec2 p) {
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+ vec2 i = floor(p);
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+
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+ vec2 f = fract(p);
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+ vec2 u = smoothstep(vec2(0.0), vec2(1.0), f);
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+
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+ vec2 val = mix( mix( hash22( i + vec2(0.0, 0.0) ),
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+ hash22( i + vec2(1.0, 0.0) ), u.x),
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+ mix( hash22( i + vec2(0.0, 1.0) ),
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+ hash22( i + vec2(1.0, 1.0) ), u.x), u.y);
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+ return val * 2.0 - 1.0;
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+}
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+
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+// The MIT License
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+// Copyright © 2017 Inigo Quilez
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+// 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.
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+// https://www.youtube.com/c/InigoQuilez
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+// https://iquilezles.org/
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+vec4 noised_1_3(vec3 x) {
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+ vec3 i = floor(x);
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+ vec3 f = fract(x);
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+
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+ // quintic interpolant
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+ vec3 u = f*f*f*(f*(f*6.0-15.0)+10.0);
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+ vec3 du = 30.0*f*f*(f*(f-2.0)+1.0);
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+
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+ // gradients
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+ vec3 ga = hash33( i+vec3(0.0,0.0,0.0) ) * 2.0 - 1.0;
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+ vec3 gb = hash33( i+vec3(1.0,0.0,0.0) ) * 2.0 - 1.0;
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+ vec3 gc = hash33( i+vec3(0.0,1.0,0.0) ) * 2.0 - 1.0;
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+ vec3 gd = hash33( i+vec3(1.0,1.0,0.0) ) * 2.0 - 1.0;
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+ vec3 ge = hash33( i+vec3(0.0,0.0,1.0) ) * 2.0 - 1.0;
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+ vec3 gf = hash33( i+vec3(1.0,0.0,1.0) ) * 2.0 - 1.0;
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+ vec3 gg = hash33( i+vec3(0.0,1.0,1.0) ) * 2.0 - 1.0;
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+ vec3 gh = hash33( i+vec3(1.0,1.0,1.0) ) * 2.0 - 1.0;
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+
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+ // projections
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+ float va = dot( ga, f-vec3(0.0,0.0,0.0) );
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+ float vb = dot( gb, f-vec3(1.0,0.0,0.0) );
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+ float vc = dot( gc, f-vec3(0.0,1.0,0.0) );
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+ float vd = dot( gd, f-vec3(1.0,1.0,0.0) );
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+ float ve = dot( ge, f-vec3(0.0,0.0,1.0) );
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+ float vf = dot( gf, f-vec3(1.0,0.0,1.0) );
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+ float vg = dot( gg, f-vec3(0.0,1.0,1.0) );
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+ float vh = dot( gh, f-vec3(1.0,1.0,1.0) );
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+
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+ // interpolations
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+ return vec4( va + u.x*(vb-va) + u.y*(vc-va) + u.z*(ve-va) + u.x*u.y*(va-vb-vc+vd) + u.y*u.z*(va-vc-ve+vg) + u.z*u.x*(va-vb-ve+vf) + (-va+vb+vc-vd+ve-vf-vg+vh)*u.x*u.y*u.z, // value
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+ ga + u.x*(gb-ga) + u.y*(gc-ga) + u.z*(ge-ga) + u.x*u.y*(ga-gb-gc+gd) + u.y*u.z*(ga-gc-ge+gg) + u.z*u.x*(ga-gb-ge+gf) + (-ga+gb+gc-gd+ge-gf-gg+gh)*u.x*u.y*u.z + // derivatives
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+ du * (vec3(vb,vc,ve) - va + u.yzx*vec3(va-vb-vc+vd,va-vc-ve+vg,va-vb-ve+vf) + u.zxy*vec3(va-vb-ve+vf,va-vb-vc+vd,va-vc-ve+vg) + u.yzx*u.zxy*(-va+vb+vc-vd+ve-vf-vg+vh) ));
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+}
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+
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+float FBM_1_2(vec2 p, int octaves, float persistence, float lacunarity) {
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+ float amplitude = 1.0;
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+ float frequency = 1.0;
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+ float total = 0.0;
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+ float normalization = 0.0;
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+
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+ for (int i = 0; i < octaves; ++i) {
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+ float noiseValue = noise12(p * frequency);
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+ total += noiseValue * amplitude;
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+ normalization += amplitude;
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+ amplitude *= persistence;
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+ frequency *= lacunarity;
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+ }
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+
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+ total /= normalization;
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+ total = total * 0.5 + 0.5;
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+
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+ return total;
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+}
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+
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+float FBM_1_3(vec3 p, int octaves, float persistence, float lacunarity) {
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+ float amplitude = 1.0;
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+ float frequency = 1.0;
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+ float total = 0.0;
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+ float normalization = 0.0;
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+
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+ for (int i = 0; i < octaves; ++i) {
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+ float noiseValue = noise13(p * frequency);
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+ total += noiseValue * amplitude;
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+ normalization += amplitude;
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+ amplitude *= persistence;
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+ frequency *= lacunarity;
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+ }
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+
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+ total /= normalization;
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+ total = total * 0.5 + 0.5;
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+
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+ return total;
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+}
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+
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+const mat3 m3 = mat3( 0.00, 0.80, 0.60,
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+ -0.80, 0.36, -0.48,
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+ -0.60, -0.48, 0.64 );
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+const mat3 m3i = mat3( 0.00, -0.80, -0.60,
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+ 0.80, 0.36, -0.48,
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+ 0.60, -0.48, 0.64 );
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+
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+vec4 FBM_D_1_4(in vec3 x, int octaves) {
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+ float f = 1.98; // could be 2.0
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+ float s = 0.49; // could be 0.5
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+ float a = 0.0;
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+ float b = 0.5;
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+ vec3 d = vec3(0.0);
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+ mat3 m = mat3(
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+ 1.0,0.0,0.0,
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+ 0.0,1.0,0.0,
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+ 0.0,0.0,1.0);
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+ for( int i=0; i < octaves; i++ )
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+ {
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+ vec4 n = noised_1_3(x);
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+ a += b*n.x; // accumulate values
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+ d += b*m*n.yzw; // accumulate derivatives
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+ b *= s;
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+ x = f*m3*x;
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+ m = f*m3i*m;
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+ }
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+ return vec4( a, d );
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+}
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