float snoise(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);
vec3 i = floor(v + dot(v, C.yyy));
vec3 x0 = v - i + dot(i, C.xxx);
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);
vec3 x1 = x0 - i1 + C.xxx;
vec3 x2 = x0 - i2 + C.yyy;
vec3 x3 = x0 - D.yyy;
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));
float n_ = 0.142857142857;
vec3 ns = n_ * D.wyz - D.xzx;
vec4 j = p - 49.0 * floor(p * ns.z * ns.z);
vec4 x_ = floor(j * ns.z);
vec4 y_ = floor(j - 7.0 * x_);
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 = 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);
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;
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(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);
}
GLM_FUNC_QUALIFIER tvec4<T, P> permute(tvec4<T, P> const & x)
{
return mod289(((x * static_cast<T>(34)) + static_cast<T>(1)) * x);
}
GLM_FUNC_QUALIFIER T permute(T const & x)
{
return mod289(((x * static_cast<T>(34)) + static_cast<T>(1)) * x);
}
GLM_FUNC_QUALIFIER tvec4<T, P> permute(tvec4<T, P> const & x)
{
return mod289(((x * T(34)) + T(1)) * x);
}
GLM_FUNC_QUALIFIER T permute(T const & x)
{
return mod289(((x * T(34)) + T(1)) * x);
}
float permute(float x) {
return mod289(((x*34.0)+1.0)*x);
}
vec4 permute(vec4 x) {
return mod289(((x*34.0)+1.0)*x);
}
float snoise(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(F4)) );
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 ) ) ) ) ;
}
float snoise(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) ) );
}
// Vectorized 2d simplex noise.
float noise2d(float v1, float v2) {
const float C[] = {
0.211324865405187f,
0.366025403784439f,
-0.577350269189626f,
0.024390243902439f };
// First corner
float i[2];
i[0] = floorf(v1 + v1*C[1] + v2*C[1]);
i[1] = floorf(v2 + v1*C[1] + v2*C[1]);
float x0[2];
x0[0] = v1 - i[0] + i[0]*C[0] + i[1]*C[0];
x0[1] = v2 - i[1] + i[0]*C[0] + i[1]*C[0];
// Other corners
float i1[2];
if (x0[0] > x0[1]) {
i1[0] = 1;
i1[1] = 0;
} else {
i1[0] = 0;
i1[1] = 1;
}
float x12[4];
x12[0] = x0[0] + C[0] - i1[0];
x12[1] = x0[1] + C[0] - i1[1];
x12[2] = x0[0] + C[2];
x12[3] = x0[1] + C[2];
// Permutations
i[0] = mod289(i[0]);
i[1] = mod289(i[1]);
float p[3];
p[0] = permute(permute(i[1]) + i[0]);
p[1] = permute(permute(i[1] + i1[1]) + i[0] + i1[0]);
p[2] = permute(permute(i[1] + 1) + i[0] + 1);
float m[3];
m[0] = std::max<float>(0.5f - x0[0]*x0[0] - x0[1]*x0[1], 0);
m[1] = std::max<float>(0.5f - x12[0]*x12[0] - x12[1]*x12[1], 0);
m[2] = std::max<float>(0.5f - x12[2]*x12[2] - x12[3]*x12[3], 0);
m[0] = m[0] * m[0] * m[0] * m[0];
m[1] = m[1] * m[1] * m[1] * m[1];
m[2] = m[2] * m[2] * m[2] * m[2];
// Gradients
float tmp;
float x[3];
x[0] = 2 * modff(p[0] * C[3], &tmp) - 1;
x[1] = 2 * modff(p[1] * C[3], &tmp) - 1;
x[2] = 2 * modff(p[2] * C[3], &tmp) - 1;
float h[3];
h[0] = fabsf(x[0]) - 0.5f;
h[1] = fabsf(x[1]) - 0.5f;
h[2] = fabsf(x[2]) - 0.5f;
float ox[3];
ox[0] = floorf(x[0] + 0.5f);
ox[1] = floorf(x[1] + 0.5f);
ox[2] = floorf(x[2] + 0.5f);
float a0[3];
a0[0] = x[0] - ox[0];
a0[1] = x[1] - ox[1];
a0[2] = x[2] - ox[2];
// Normalize
m[0] *= 1.79284291400159f - 0.85373472095314f * (a0[0]*a0[0] + h[0]*h[0]);
m[1] *= 1.79284291400159f - 0.85373472095314f * (a0[1]*a0[1] + h[1]*h[1]);
m[2] *= 1.79284291400159f - 0.85373472095314f * (a0[2]*a0[2] + h[2]*h[2]);
// Compute final value
float g[3];
g[0] = a0[0] * x0[0] + h[0] * x0[1];
g[1] = a0[1] * x12[0] + h[1] * x12[1];
g[2] = a0[2] * x12[2] + h[2] * x12[3];
return 130 * (m[0] * g[0] + m[1] * g[1] + m[2] * g[2]);
}
static inline float permute(float x) {
return mod289(((x*34.0f)+1.0f)*x);
}