lygia/generative/snoise)Simplex Noise https://github.com/stegu/webgl-noise
Dependencies:
Use:
snoise(<vec2|vec3|vec4> pos)
#ifndef FNC_SNOISE
#define FNC_SNOISE
float snoise(in 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 snoise(in 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) ) );
}
float snoise(in 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(.309016994374947451)) ); // (sqrt(5) - 1)/4
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 ) ) ) ) ;
}
vec2 snoise2( vec2 x ){
float s = snoise(vec2( x ));
float s1 = snoise(vec2( x.y - 19.1, x.x + 47.2 ));
return vec2( s , s1 );
}
vec3 snoise3( vec3 x ){
float s = snoise(vec3( x ));
float s1 = snoise(vec3( x.y - 19.1 , x.z + 33.4 , x.x + 47.2 ));
float s2 = snoise(vec3( x.z + 74.2 , x.x - 124.5 , x.y + 99.4 ));
return vec3( s , s1 , s2 );
}
vec3 snoise3( vec4 x ){
float s = snoise(vec4( x ));
float s1 = snoise(vec4( x.y - 19.1 , x.z + 33.4 , x.x + 47.2, x.w ));
float s2 = snoise(vec4( x.z + 74.2 , x.x - 124.5 , x.y + 99.4, x.w ));
return vec3( s , s1 , s2 );
}
#endif
Dependencies:
Use:
snoise(<float2|float3|float4> pos)
#ifndef FNC_SNOISE
#define FNC_SNOISE
float snoise(float2 v) {
const float4 C = float4( 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
float2 i = floor(v + dot(v, C.yy));
float2 x0 = v - i + dot(i, C.xx);
// Other corners
float2 i1;
i1.x = step(x0.y, x0.x);
i1.y = 1.0 - i1.x;
// x1 = x0 - i1 + 1.0 * C.xx;
// x2 = x0 - 1.0 + 2.0 * C.xx;
float2 x1 = x0 + C.xx - i1;
float2 x2 = x0 + C.zz;
// Permutations
i = mod289(i); // Avoid truncation effects in permutation
float3 p =
permute(permute(i.y + float3(0.0, i1.y, 1.0))
+ i.x + float3(0.0, i1.x, 1.0));
float3 m = max(0.5 - float3(dot(x0, x0), dot(x1, x1), dot(x2, x2)), 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)
float3 x = 2.0 * frac(p * C.www) - 1.0;
float3 h = abs(x) - 0.5;
float3 ox = floor(x + 0.5);
float3 a0 = x - ox;
// Normalise gradients implicitly by scaling m
m *= taylorInvSqrt(a0 * a0 + h * h);
// Compute final noise value at P
float3 g;
g.x = a0.x * x0.x + h.x * x0.y;
g.y = a0.y * x1.x + h.y * x1.y;
g.z = a0.z * x2.x + h.z * x2.y;
return 130.0 * dot(m, g);
}
float snoise(float3 v) {
const float2 C = float2(1.0 / 6.0, 1.0 / 3.0);
// First corner
float3 i = floor(v + dot(v, C.yyy));
float3 x0 = v - i + dot(i, C.xxx);
// Other corners
float3 g = step(x0.yzx, x0.xyz);
float3 l = 1.0 - g;
float3 i1 = min(g.xyz, l.zxy);
float3 i2 = max(g.xyz, l.zxy);
// x1 = x0 - i1 + 1.0 * C.xxx;
// x2 = x0 - i2 + 2.0 * C.xxx;
// x3 = x0 - 1.0 + 3.0 * C.xxx;
float3 x1 = x0 - i1 + C.xxx;
float3 x2 = x0 - i2 + C.yyy;
float3 x3 = x0 - 0.5;
// Permutations
i = mod289(i); // Avoid truncation effects in permutation
float4 p =
permute(permute(permute(i.z + float4(0.0, i1.z, i2.z, 1.0))
+ i.y + float4(0.0, i1.y, i2.y, 1.0))
+ i.x + float4(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)
float4 j = p - 49.0 * floor(p / 49.0); // mod(p,7*7)
float4 x_ = floor(j / 7.0);
float4 y_ = floor(j - 7.0 * x_); // mod(j,N)
float4 x = (x_ * 2.0 + 0.5) / 7.0 - 1.0;
float4 y = (y_ * 2.0 + 0.5) / 7.0 - 1.0;
float4 h = 1.0 - abs(x) - abs(y);
float4 b0 = float4(x.xy, y.xy);
float4 b1 = float4(x.zw, y.zw);
//float4 s0 = float4(lessThan(b0, 0.0)) * 2.0 - 1.0;
//float4 s1 = float4(lessThan(b1, 0.0)) * 2.0 - 1.0;
float4 s0 = floor(b0) * 2.0 + 1.0;
float4 s1 = floor(b1) * 2.0 + 1.0;
float4 sh = -step(h, 0.0);
float4 a0 = b0.xzyw + s0.xzyw * sh.xxyy;
float4 a1 = b1.xzyw + s1.xzyw * sh.zzww;
float3 g0 = float3(a0.xy, h.x);
float3 g1 = float3(a0.zw, h.y);
float3 g2 = float3(a1.xy, h.z);
float3 g3 = float3(a1.zw, h.w);
// Normalise gradients
float4 norm = taylorInvSqrt(float4(dot(g0, g0), dot(g1, g1), dot(g2, g2), dot(g3, g3)));
g0 *= norm.x;
g1 *= norm.y;
g2 *= norm.z;
g3 *= norm.w;
// Mix final noise value
float4 m = max(0.6 - float4(dot(x0, x0), dot(x1, x1), dot(x2, x2), dot(x3, x3)), 0.0);
m = m * m;
m = m * m;
float4 px = float4(dot(x0, g0), dot(x1, g1), dot(x2, g2), dot(x3, g3));
return 42.0 * dot(m, px);
}
float snoise(in float4 v) {
const float4 C = float4( 0.138196601125011, // (5 - sqrt(5))/20 G4
0.276393202250021, // 2 * G4
0.414589803375032, // 3 * G4
-0.447213595499958); // -1 + 4 * G4
// First corner
float4 i = floor(v + dot(v, float4(.309016994374947451, .309016994374947451, .309016994374947451, .309016994374947451)) ); // (sqrt(5) - 1)/4
float4 x0 = v - i + dot(i, C.xxxx);
// Other corners
// Rank sorting originally contributed by Bill Licea-Kane, AMD (formerly ATI)
float4 i0;
float3 isX = step( x0.yzw, x0.xxx );
float3 isYZ = step( x0.zww, x0.yyz );
// i0.x = dot( isX, float3( 1.0 ) );
i0.x = isX.x + isX.y + isX.z;
i0.yzw = 1.0 - isX;
// i0.y += dot( isYZ.xy, float2( 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
float4 i3 = clamp( i0, 0.0, 1.0 );
float4 i2 = clamp( i0-1.0, 0.0, 1.0 );
float4 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
float4 x1 = x0 - i1 + C.xxxx;
float4 x2 = x0 - i2 + C.yyyy;
float4 x3 = x0 - i3 + C.zzzz;
float4 x4 = x0 + C.wwww;
// Permutations
i = mod289(i);
float j0 = permute( permute( permute( permute(i.w) + i.z) + i.y) + i.x);
float4 j1 = permute( permute( permute( permute (
i.w + float4(i1.w, i2.w, i3.w, 1.0 ))
+ i.z + float4(i1.z, i2.z, i3.z, 1.0 ))
+ i.y + float4(i1.y, i2.y, i3.y, 1.0 ))
+ i.x + float4(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.
float4 ip = float4(1.0/294.0, 1.0/49.0, 1.0/7.0, 0.0) ;
float4 p0 = grad4(j0, ip);
float4 p1 = grad4(j1.x, ip);
float4 p2 = grad4(j1.y, ip);
float4 p3 = grad4(j1.z, ip);
float4 p4 = grad4(j1.w, ip);
// Normalise gradients
float4 norm = taylorInvSqrt(float4(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
float3 m0 = max(0.6 - float3(dot(x0,x0), dot(x1,x1), dot(x2,x2)), 0.0);
float2 m1 = max(0.6 - float2(dot(x3,x3), dot(x4,x4) ), 0.0);
m0 = m0 * m0;
m1 = m1 * m1;
return 49.0 * ( dot(m0*m0, float3( dot( p0, x0 ), dot( p1, x1 ), dot( p2, x2 )))
+ dot(m1*m1, float2( dot( p3, x3 ), dot( p4, x4 ) ) ) ) ;
}
float2 snoise2( float2 x ){
float s = snoise( x );
float s1 = snoise(float2( x.y - 19.1, x.x + 47.2 ));
return float2( s , s1 );
}
float3 snoise3( float3 x ){
float s = snoise( x );
float s1 = snoise(float3( x.y - 19.1 , x.z + 33.4 , x.x + 47.2 ));
float s2 = snoise(float3( x.z + 74.2 , x.x - 124.5 , x.y + 99.4 ));
return float3( s , s1 , s2 );
}
float3 snoise3( float4 x ){
float s = snoise( x );
float s1 = snoise(float4( x.y - 19.1 , x.z + 33.4 , x.x + 47.2, x.w ));
float s2 = snoise(float4( x.z + 74.2 , x.x - 124.5 , x.y + 99.4, x.w ));
return float3( s , s1 , s2 );
}
#endif
Dependencies:
lygia/math/mod.glsllygia/math/mod289.glsllygia/math/permute.glsllygia/math/taylorInvSqrt.glsllygia/math/grad4.glslUse:
snoise(<float2|float3|float4> pos)
#ifndef FNC_SNOISE
#define FNC_SNOISE
float snoise(float2 v) {
const float4 C = float4(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
float2 i = floor(v + dot(v, C.yy) );
float2 x0 = v - i + dot(i, C.xx);
// Other corners
float2 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) ? float2(1.0, 0.0) : float2(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 ;
float4 x12 = x0.xyxy + C.xxzz;
x12.xy -= i1;
// Permutations
i = mod289(i); // Avoid truncation effects permutation
float3 p = permute( permute( i.y + float3(0.0, i1.y, 1.0 ))
+ i.x + float3(0.0, i1.x, 1.0 ));
float3 m = max(0.5 - float3(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)
float3 x = 2.0 * fract(p * C.www) - 1.0;
float3 h = abs(x) - 0.5;
float3 ox = floor(x + 0.5);
float3 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
float3 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 snoise(float3 v) {
const float2 C = float2(1.0/6.0, 1.0/3.0) ;
const float4 D = float4(0.0, 0.5, 1.0, 2.0);
// First corner
float3 i = floor(v + dot(v, C.yyy) );
float3 x0 = v - i + dot(i, C.xxx) ;
// Other corners
float3 g = step(x0.yzx, x0.xyz);
float3 l = 1.0 - g;
float3 i1 = min( g.xyz, l.zxy );
float3 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;
float3 x1 = x0 - i1 + C.xxx;
float3 x2 = x0 - i2 + C.yyy; // 2.0*C.x = 1/3 = C.y
float3 x3 = x0 - D.yyy; // -1.0+3.0*C.x = -0.5 = -D.y
// Permutations
i = mod289(i);
float4 p = permute( permute( permute(
i.z + float4(0.0, i1.z, i2.z, 1.0 ))
+ i.y + float4(0.0, i1.y, i2.y, 1.0 ))
+ i.x + float4(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
float3 ns = n_ * D.wyz - D.xzx;
float4 j = p - 49.0 * floor(p * ns.z * ns.z); // mod(p,7*7)
float4 x_ = floor(j * ns.z);
float4 y_ = floor(j - 7.0 * x_ ); // mod(j,N)
float4 x = x_ *ns.x + ns.yyyy;
float4 y = y_ *ns.x + ns.yyyy;
float4 h = 1.0 - abs(x) - abs(y);
float4 b0 = float4( x.xy, y.xy );
float4 b1 = float4( x.zw, y.zw );
//float4 s0 = float4(lessThan(b0,0.0))*2.0 - 1.0;
//float4 s1 = float4(lessThan(b1,0.0))*2.0 - 1.0;
float4 s0 = floor(b0)*2.0 + 1.0;
float4 s1 = floor(b1)*2.0 + 1.0;
float4 sh = -step(h, float4(0.0));
float4 a0 = b0.xzyw + s0.xzyw*sh.xxyy ;
float4 a1 = b1.xzyw + s1.xzyw*sh.zzww ;
float3 p0 = float3(a0.xy,h.x);
float3 p1 = float3(a0.zw,h.y);
float3 p2 = float3(a1.xy,h.z);
float3 p3 = float3(a1.zw,h.w);
//Normalise gradients
float4 norm = taylorInvSqrt(float4(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
float4 m = max(0.6 - float4(dot(x0,x0), dot(x1,x1), dot(x2,x2), dot(x3,x3)), 0.0);
m = m * m;
return 42.0 * dot( m*m, float4( dot(p0,x0), dot(p1,x1),
dot(p2,x2), dot(p3,x3) ) );
}
float snoise(float4 v) {
const float4 C = float4( 0.138196601125011, // (5 - sqrt(5))/20 G4
0.276393202250021, // 2 * G4
0.414589803375032, // 3 * G4
-0.447213595499958); // -1 + 4 * G4
// First corner
float4 i = floor(v + dot(v, float4(.309016994374947451)) ); // (sqrt(5) - 1)/4
float4 x0 = v - i + dot(i, C.xxxx);
// Other corners
// Rank sorting originally contributed by Bill Licea-Kane, AMD (formerly ATI)
float4 i0;
float3 isX = step( x0.yzw, x0.xxx );
float3 isYZ = step( x0.zww, x0.yyz );
// i0.x = dot( isX, float3( 1.0 ) );
i0.x = isX.x + isX.y + isX.z;
i0.yzw = 1.0 - isX;
// i0.y += dot( isYZ.xy, float2( 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 each channel
float4 i3 = clamp( i0, 0.0, 1.0 );
float4 i2 = clamp( i0-1.0, 0.0, 1.0 );
float4 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
float4 x1 = x0 - i1 + C.xxxx;
float4 x2 = x0 - i2 + C.yyyy;
float4 x3 = x0 - i3 + C.zzzz;
float4 x4 = x0 + C.wwww;
// Permutations
i = mod289(i);
float j0 = permute( permute( permute( permute(i.w) + i.z) + i.y) + i.x);
float4 j1 = permute( permute( permute( permute (
i.w + float4(i1.w, i2.w, i3.w, 1.0 ))
+ i.z + float4(i1.z, i2.z, i3.z, 1.0 ))
+ i.y + float4(i1.y, i2.y, i3.y, 1.0 ))
+ i.x + float4(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.
float4 ip = float4(1.0/294.0, 1.0/49.0, 1.0/7.0, 0.0) ;
float4 p0 = grad4(j0, ip);
float4 p1 = grad4(j1.x, ip);
float4 p2 = grad4(j1.y, ip);
float4 p3 = grad4(j1.z, ip);
float4 p4 = grad4(j1.w, ip);
// Normalise gradients
float4 norm = taylorInvSqrt(float4(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
float3 m0 = max(0.6 - float3(dot(x0,x0), dot(x1,x1), dot(x2,x2)), 0.0);
float2 m1 = max(0.6 - float2(dot(x3,x3), dot(x4,x4) ), 0.0);
m0 = m0 * m0;
m1 = m1 * m1;
return 49.0 * ( dot(m0*m0, float3( dot( p0, x0 ), dot( p1, x1 ), dot( p2, x2 )))
+ dot(m1*m1, float2( dot( p3, x3 ), dot( p4, x4 ) ) ) ) ;
}
float2 snoise2( float2 x ){
float s = snoise(float2( x ));
float s1 = snoise(float2( x.y - 19.1, x.x + 47.2 ));
return float2( s , s1 );
}
float3 snoise3( float3 x ){
float s = snoise(float3( x ));
float s1 = snoise(float3( x.y - 19.1 , x.z + 33.4 , x.x + 47.2 ));
float s2 = snoise(float3( x.z + 74.2 , x.x - 124.5 , x.y + 99.4 ));
return float3( s , s1 , s2 );
}
float3 snoise3( float4 x ){
float s = snoise(float4( x ));
float s1 = snoise(float4( x.y - 19.1 , x.z + 33.4 , x.x + 47.2, x.w ));
float s2 = snoise(float4( x.z + 74.2 , x.x - 124.5 , x.y + 99.4, x.w ));
return float3( s , s1 , s2 );
}
#endif
Dependencies:
Use:
snoise2/3/4(<vec2f|vec3f|vec4f> pos)
fn snoise2(v: vec2f) -> f32 {
let 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
var i = floor(v + dot(v, C.yy) );
let x0 = v - i + dot(i, C.xx);
// Other corners
//i1.x = step( x0.y, x0.x ); // x0.x > x0.y ? 1.0 : 0.0
//i1.y = 1.0 - i1.x;
let i1 = select(vec2(0.0, 1.0), vec2(1.0, 0.0), x0.x > x0.y);
// x0 = x0 - 0.0 + 0.0 * C.xx ;
// x1 = x0 - i1 + 1.0 * C.xx ;
// x2 = x0 - 1.0 + 2.0 * C.xx ;
let x12 = x0.xyxy + C.xxzz - vec4(i1, 0.0, 0.0);
// Permutations
i = mod289_2(i); // Avoid truncation effects in permutation
let p = permute3( permute3( i.y + vec3(0.0, i1.y, 1.0 )) + i.x + vec3(0.0, i1.x, 1.0 ));
var m = max(0.5 - vec3(dot(x0,x0), dot(x12.xy,x12.xy), dot(x12.zw,x12.zw)), vec3(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)
let x = 2.0 * fract(p * C.www) - 1.0;
let h = abs(x) - 0.5;
let ox = floor(x + 0.5);
let 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
let gx = a0.x * x0.x + h.x * x0.y;
let gyz = a0.yz * x12.xz + h.yz * x12.yw;
return 130.0 * dot(m, vec3(gx, gyz));
}
fn snoise3(v: vec3f) -> f32 {
let C = vec2(1.0/6.0, 1.0/3.0) ;
let D = vec4(0.0, 0.5, 1.0, 2.0);
// First corner
var i = floor(v + dot(v, C.yyy) );
let x0 = v - i + dot(i, C.xxx) ;
// Other corners
let g = step(x0.yzx, x0.xyz);
let l = 1.0 - g;
let i1 = min( g.xyz, l.zxy );
let 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;
let x1 = x0 - i1 + C.xxx;
let x2 = x0 - i2 + C.yyy; // 2.0*C.x = 1/3 = C.y
let x3 = x0 - D.yyy; // -1.0+3.0*C.x = -0.5 = -D.y
// Permutations
i = mod289_3(i);
let p = permute4( permute4( permute4(
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)
let n_ = 0.142857142857; // 1.0/7.0
let ns = n_ * D.wyz - D.xzx;
let j = p - 49.0 * floor(p * ns.z * ns.z); // mod(p,7*7)
let x_ = floor(j * ns.z);
let y_ = floor(j - 7.0 * x_ ); // mod(j,N)
let x = x_ *ns.x + ns.yyyy;
let y = y_ *ns.x + ns.yyyy;
let h = 1.0 - abs(x) - abs(y);
let b0 = vec4( x.xy, y.xy );
let b1 = vec4( x.zw, y.zw );
//let s0 = vec4(lessThan(b0,0.0))*2.0 - 1.0;
//let s1 = vec4(lessThan(b1,0.0))*2.0 - 1.0;
let s0 = floor(b0)*2.0 + 1.0;
let s1 = floor(b1)*2.0 + 1.0;
let sh = -step(h, vec4(0.0));
let a0 = b0.xzyw + s0.xzyw*sh.xxyy ;
let a1 = b1.xzyw + s1.xzyw*sh.zzww ;
var p0 = vec3(a0.xy,h.x);
var p1 = vec3(a0.zw,h.y);
var p2 = vec3(a1.xy,h.z);
var p3 = vec3(a1.zw,h.w);
//Normalise gradients
let norm = taylorInvSqrt4(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
var m = max(0.6 - vec4(dot(x0,x0), dot(x1,x1), dot(x2,x2), dot(x3,x3)), vec4(0.0));
m = m * m;
return 42.0 * dot( m*m, vec4( dot(p0,x0), dot(p1,x1),
dot(p2,x2), dot(p3,x3) ) );
}
fn snoise4(v: vec4f) -> f32 {
let C = vec4( 0.138196601125011, // (5 - sqrt(5))/20 G4
0.276393202250021, // 2 * G4
0.414589803375032, // 3 * G4
-0.447213595499958); // -1 + 4 * G4
// First corner
var i = floor(v + dot(v, vec4(.309016994374947451)) ); // (sqrt(5) - 1)/4
let x0 = v - i + dot(i, C.xxxx);
// Other corners
// Rank sorting originally contributed by Bill Licea-Kane, AMD (formerly ATI)
let isX = step( x0.yzw, x0.xxx );
let isYZ = step( x0.zww, x0.yyz );
// i0.x = dot( isX, vec3( 1.0 ) );
var i0 = vec4(isX.x + isX.y + isX.z, 1.0 - isX);
// i0.y += dot( isYZ.xy, vec2( 1.0 ) );
i0 += vec4(0.0, isYZ.x + isYZ.y, 1.0 - isYZ.xy);
i0 += vec4(0.0, 0.0, isYZ.z, 1.0 - isYZ.z);
// i0 now contains the unique values 0,1,2,3 in each channel
let i3 = clamp( i0, vec4(0.0), vec4(1.0) );
let i2 = clamp( i0 - 1.0, vec4(0.0), vec4(1.0) );
let i1 = clamp( i0 - 2.0, vec4(0.0), vec4(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
let x1 = x0 - i1 + C.xxxx;
let x2 = x0 - i2 + C.yyyy;
let x3 = x0 - i3 + C.zzzz;
let x4 = x0 + C.wwww;
// Permutations
i = mod289_4(i);
let j0 = permute( permute( permute( permute(i.w) + i.z) + i.y) + i.x);
let j1 = permute4( permute4( permute4( permute4 (
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.
let ip = vec4(1.0/294.0, 1.0/49.0, 1.0/7.0, 0.0) ;
var p0 = grad4(j0, ip);
var p1 = grad4(j1.x, ip);
var p2 = grad4(j1.y, ip);
var p3 = grad4(j1.z, ip);
var p4 = grad4(j1.w, ip);
// Normalise gradients
let norm = taylorInvSqrt4(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
var m0 = max(0.6 - vec3(dot(x0,x0), dot(x1,x1), dot(x2,x2)), vec3(0.0));
var m1 = max(0.6 - vec2(dot(x3,x3), dot(x4,x4) ), vec2(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 ) ) ) ) ;
}
fn snoise22(x: vec2f) -> vec2f {
let s = snoise2(vec2( x ));
let s1 = snoise2(vec2( x.y - 19.1, x.x + 47.2 ));
return vec2( s , s1 );
}
fn snoise33(x: vec3f) -> vec3f {
let s = snoise3(vec3( x ));
let s1 = snoise3(vec3( x.y - 19.1 , x.z + 33.4 , x.x + 47.2 ));
let s2 = snoise3(vec3( x.z + 74.2 , x.x - 124.5 , x.y + 99.4 ));
return vec3( s , s1 , s2 );
}
fn snoise34(x: vec4f) -> vec3f {
let s = snoise4(vec4( x ));
let s1 = snoise4(vec4( x.y - 19.1 , x.z + 33.4 , x.x + 47.2, x.w ));
let s2 = snoise4(vec4( x.z + 74.2 , x.x - 124.5 , x.y + 99.4, x.w ));
return vec3( s , s1 , s2 );
}
Copyright 2021-2023 by Stefan Gustavson and Ian McEwan. Published under the terms of the MIT license: https://opensource.org/license/mit/
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