// 3D simplex noise
float noise(float x, float y, float z) {
// Simple skewing factors for the 3D case
#define F3 0.333333333
#define G3 0.166666667
float n0, n1, n2, n3; // Noise contributions from the four corners
// Skew the input space to determine which simplex cell we're in
float s = (x+y+z)*F3; // Very nice and simple skew factor for 3D
float xs = x+s;
float ys = y+s;
float zs = z+s;
int i = FASTFLOOR(xs);
int j = FASTFLOOR(ys);
int k = FASTFLOOR(zs);
float t = (float)(i+j+k)*G3;
float X0 = i-t; // Unskew the cell origin back to (x,y,z) space
float Y0 = j-t;
float Z0 = k-t;
float x0 = x-X0; // The x,y,z distances from the cell origin
float y0 = y-Y0;
float z0 = z-Z0;
// For the 3D case, the simplex shape is a slightly irregular tetrahedron.
// Determine which simplex we are in.
int i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords
int i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords
/* This code would benefit from a backport from the GLSL version! */
if(x0>=y0) {
if(y0>=z0)
{ i1=1; j1=0; k1=0; i2=1; j2=1; k2=0; } // X Y Z order
else if(x0>=z0) { i1=1; j1=0; k1=0; i2=1; j2=0; k2=1; } // X Z Y order
else { i1=0; j1=0; k1=1; i2=1; j2=0; k2=1; } // Z X Y order
}
else { // x0<y0
if(y0<z0) { i1=0; j1=0; k1=1; i2=0; j2=1; k2=1; } // Z Y X order
else if(x0<z0) { i1=0; j1=1; k1=0; i2=0; j2=1; k2=1; } // Y Z X order
else { i1=0; j1=1; k1=0; i2=1; j2=1; k2=0; } // Y X Z order
}
// A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z),
// a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and
// a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where
// c = 1/6.
float x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
float y1 = y0 - j1 + G3;
float z1 = z0 - k1 + G3;
float x2 = x0 - i2 + 2.0f*G3; // Offsets for third corner in (x,y,z) coords
float y2 = y0 - j2 + 2.0f*G3;
float z2 = z0 - k2 + 2.0f*G3;
float x3 = x0 - 1.0f + 3.0f*G3; // Offsets for last corner in (x,y,z) coords
float y3 = y0 - 1.0f + 3.0f*G3;
float z3 = z0 - 1.0f + 3.0f*G3;
// Wrap the integer indices at 256, to avoid indexing perm[] out of bounds
int ii = i % 256;
int jj = j % 256;
int kk = k % 256;
// Calculate the contribution from the four corners
float t0 = 0.6f - x0*x0 - y0*y0 - z0*z0;
if(t0 < 0.0f) n0 = 0.0f;
else {
t0 *= t0;
n0 = t0 * t0 * grad(perm[ii+perm[jj+perm[kk]]], x0, y0, z0);
}
float t1 = 0.6f - x1*x1 - y1*y1 - z1*z1;
if(t1 < 0.0f) n1 = 0.0f;
else {
t1 *= t1;
n1 = t1 * t1 * grad(perm[ii+i1+perm[jj+j1+perm[kk+k1]]], x1, y1, z1);
}
float t2 = 0.6f - x2*x2 - y2*y2 - z2*z2;
if(t2 < 0.0f) n2 = 0.0f;
else {
t2 *= t2;
n2 = t2 * t2 * grad(perm[ii+i2+perm[jj+j2+perm[kk+k2]]], x2, y2, z2);
}
float t3 = 0.6f - x3*x3 - y3*y3 - z3*z3;
if(t3<0.0f) n3 = 0.0f;
else {
t3 *= t3;
n3 = t3 * t3 * grad(perm[ii+1+perm[jj+1+perm[kk+1]]], x3, y3, z3);
}
// Add contributions from each corner to get the final noise value.
// The result is scaled to stay just inside [-1,1]
return 32.0f * (n0 + n1 + n2 + n3); // TODO: The scale factor is preliminary!
}
// 4D simplex noise
float SimplexNoise1234::noise(float x, float y, float z, float w) {
// The skewing and unskewing factors are hairy again for the 4D case
#define F4 0.309016994f // F4 = (Math.sqrt(5.0)-1.0)/4.0
#define G4 0.138196601f // G4 = (5.0-Math.sqrt(5.0))/20.0
float n0, n1, n2, n3, n4; // Noise contributions from the five corners
// Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in
float s = (x + y + z + w) * F4; // Factor for 4D skewing
float xs = x + s;
float ys = y + s;
float zs = z + s;
float ws = w + s;
int i = FASTFLOOR(xs);
int j = FASTFLOOR(ys);
int k = FASTFLOOR(zs);
int l = FASTFLOOR(ws);
float t = (i + j + k + l) * G4; // Factor for 4D unskewing
float X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
float Y0 = j - t;
float Z0 = k - t;
float W0 = l - t;
float x0 = x - X0; // The x,y,z,w distances from the cell origin
float y0 = y - Y0;
float z0 = z - Z0;
float w0 = w - W0;
// For the 4D case, the simplex is a 4D shape I won't even try to describe.
// To find out which of the 24 possible simplices we're in, we need to
// determine the magnitude ordering of x0, y0, z0 and w0.
// The method below is a good way of finding the ordering of x,y,z,w and
// then find the correct traversal order for the simplex we’re in.
// First, six pair-wise comparisons are performed between each possible pair
// of the four coordinates, and the results are used to add up binary bits
// for an integer index.
int c1 = (x0 > y0) ? 32 : 0;
int c2 = (x0 > z0) ? 16 : 0;
int c3 = (y0 > z0) ? 8 : 0;
int c4 = (x0 > w0) ? 4 : 0;
int c5 = (y0 > w0) ? 2 : 0;
int c6 = (z0 > w0) ? 1 : 0;
int c = c1 + c2 + c3 + c4 + c5 + c6;
int i1, j1, k1, l1; // The integer offsets for the second simplex corner
int i2, j2, k2, l2; // The integer offsets for the third simplex corner
int i3, j3, k3, l3; // The integer offsets for the fourth simplex corner
// simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order.
// Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w and x<w
// impossible. Only the 24 indices which have non-zero entries make any sense.
// We use a thresholding to set the coordinates in turn from the largest magnitude.
// The number 3 in the "simplex" array is at the position of the largest coordinate.
i1 = simplex[c][0]>=3 ? 1 : 0;
j1 = simplex[c][1]>=3 ? 1 : 0;
k1 = simplex[c][2]>=3 ? 1 : 0;
l1 = simplex[c][3]>=3 ? 1 : 0;
// The number 2 in the "simplex" array is at the second largest coordinate.
i2 = simplex[c][0]>=2 ? 1 : 0;
j2 = simplex[c][1]>=2 ? 1 : 0;
k2 = simplex[c][2]>=2 ? 1 : 0;
l2 = simplex[c][3]>=2 ? 1 : 0;
// The number 1 in the "simplex" array is at the second smallest coordinate.
i3 = simplex[c][0]>=1 ? 1 : 0;
j3 = simplex[c][1]>=1 ? 1 : 0;
k3 = simplex[c][2]>=1 ? 1 : 0;
l3 = simplex[c][3]>=1 ? 1 : 0;
// The fifth corner has all coordinate offsets = 1, so no need to look that up.
float x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
float y1 = y0 - j1 + G4;
float z1 = z0 - k1 + G4;
float w1 = w0 - l1 + G4;
float x2 = x0 - i2 + 2.0f*G4; // Offsets for third corner in (x,y,z,w) coords
float y2 = y0 - j2 + 2.0f*G4;
float z2 = z0 - k2 + 2.0f*G4;
float w2 = w0 - l2 + 2.0f*G4;
float x3 = x0 - i3 + 3.0f*G4; // Offsets for fourth corner in (x,y,z,w) coords
float y3 = y0 - j3 + 3.0f*G4;
float z3 = z0 - k3 + 3.0f*G4;
float w3 = w0 - l3 + 3.0f*G4;
float x4 = x0 - 1.0f + 4.0f*G4; // Offsets for last corner in (x,y,z,w) coords
float y4 = y0 - 1.0f + 4.0f*G4;
float z4 = z0 - 1.0f + 4.0f*G4;
float w4 = w0 - 1.0f + 4.0f*G4;
// Wrap the integer indices at 256, to avoid indexing perm[] out of bounds
int ii = i & 0xff;
int jj = j & 0xff;
int kk = k & 0xff;
int ll = l & 0xff;
// Calculate the contribution from the five corners
float t0 = 0.6f - x0*x0 - y0*y0 - z0*z0 - w0*w0;
if(t0 < 0.0f) n0 = 0.0f;
else {
t0 *= t0;
n0 = t0 * t0 * grad(perm[ii+perm[jj+perm[kk+perm[ll]]]], x0, y0, z0, w0);
}
float t1 = 0.6f - x1*x1 - y1*y1 - z1*z1 - w1*w1;
if(t1 < 0.0f) n1 = 0.0f;
else {
t1 *= t1;
n1 = t1 * t1 * grad(perm[ii+i1+perm[jj+j1+perm[kk+k1+perm[ll+l1]]]], x1, y1, z1, w1);
}
float t2 = 0.6f - x2*x2 - y2*y2 - z2*z2 - w2*w2;
if(t2 < 0.0f) n2 = 0.0f;
else {
t2 *= t2;
n2 = t2 * t2 * grad(perm[ii+i2+perm[jj+j2+perm[kk+k2+perm[ll+l2]]]], x2, y2, z2, w2);
}
float t3 = 0.6f - x3*x3 - y3*y3 - z3*z3 - w3*w3;
if(t3 < 0.0f) n3 = 0.0f;
else {
t3 *= t3;
n3 = t3 * t3 * grad(perm[ii+i3+perm[jj+j3+perm[kk+k3+perm[ll+l3]]]], x3, y3, z3, w3);
}
float t4 = 0.6f - x4*x4 - y4*y4 - z4*z4 - w4*w4;
if(t4 < 0.0f) n4 = 0.0f;
else {
t4 *= t4;
n4 = t4 * t4 * grad(perm[ii+1+perm[jj+1+perm[kk+1+perm[ll+1]]]], x4, y4, z4, w4);
}
// Sum up and scale the result to cover the range [-1,1]
return 27.0f * (n0 + n1 + n2 + n3 + n4); // TODO: The scale factor is preliminary!
}
// 2D simplex noise
float noise(float x, float y) {
#define F2 0.366025403 // F2 = 0.5*(sqrt(3.0)-1.0)
#define G2 0.211324865 // G2 = (3.0-Math.sqrt(3.0))/6.0
float n0, n1, n2; // Noise contributions from the three corners
// Skew the input space to determine which simplex cell we're in
float s = (x+y)*F2; // Hairy factor for 2D
float xs = x + s;
float ys = y + s;
int i = FASTFLOOR(xs);
int j = FASTFLOOR(ys);
float t = (float)(i+j)*G2;
float X0 = i-t; // Unskew the cell origin back to (x,y) space
float Y0 = j-t;
float x0 = x-X0; // The x,y distances from the cell origin
float y0 = y-Y0;
// For the 2D case, the simplex shape is an equilateral triangle.
// Determine which simplex we are in.
int i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords
if(x0>y0) {i1=1; j1=0;} // lower triangle, XY order: (0,0)->(1,0)->(1,1)
else {i1=0; j1=1;} // upper triangle, YX order: (0,0)->(0,1)->(1,1)
// A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and
// a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
// c = (3-sqrt(3))/6
float x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
float y1 = y0 - j1 + G2;
float x2 = x0 - 1.0f + 2.0f * G2; // Offsets for last corner in (x,y) unskewed coords
float y2 = y0 - 1.0f + 2.0f * G2;
// Wrap the integer indices at 256, to avoid indexing perm[] out of bounds
int ii = i % 256;
int jj = j % 256;
// Calculate the contribution from the three corners
float t0 = 0.5f - x0*x0-y0*y0;
if(t0 < 0.0f) n0 = 0.0f;
else {
t0 *= t0;
n0 = t0 * t0 * grad(perm[ii+perm[jj]], x0, y0);
}
float t1 = 0.5f - x1*x1-y1*y1;
if(t1 < 0.0f) n1 = 0.0f;
else {
t1 *= t1;
n1 = t1 * t1 * grad(perm[ii+i1+perm[jj+j1]], x1, y1);
}
float t2 = 0.5f - x2*x2-y2*y2;
if(t2 < 0.0f) n2 = 0.0f;
else {
t2 *= t2;
n2 = t2 * t2 * grad(perm[ii+1+perm[jj+1]], x2, y2);
}
// Add contributions from each corner to get the final noise value.
// The result is scaled to return values in the interval [-1,1].
return 40.0f * (n0 + n1 + n2); // TODO: The scale factor is preliminary!
}
static double _simplex_noise(double xin, double yin, double zin)
{
double n0, n1, n2, n3; // Noise contributions from the four corners
// Skew the input space to determine which simplex cell we're in
double F3 = 1.0/3.0;
double s = (xin+yin+zin)*F3; // Very nice and simple skew factor for 3D
int i = FASTFLOOR(xin+s);
int j = FASTFLOOR(yin+s);
int k = FASTFLOOR(zin+s);
double G3 = 1.0/6.0; // Very nice and simple unskew factor, too
double t = (i+j+k)*G3;
double X0 = i-t; // Unskew the cell origin back to (x,y,z) space
double Y0 = j-t;
double Z0 = k-t;
double x0 = xin-X0; // The x,y,z distances from the cell origin
double y0 = yin-Y0;
double z0 = zin-Z0;
// For the 3D case, the simplex shape is a slightly irregular tetrahedron.
// Determine which simplex we are in.
int i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords
int i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords
if(x0>=y0)
{
if(y0>=z0)
{
i1=1; // X Y Z order
j1=0;
k1=0;
i2=1;
j2=1;
k2=0;
}
else if(x0>=z0)
{
i1=1; // X Z Y order
j1=0;
k1=0;
i2=1;
j2=0;
k2=1;
}
else
{
i1=0; // Z X Y order
j1=0;
k1=1;
i2=1;
j2=0;
k2=1;
}
}
else // x0<y0
{
if(y0<z0)
{
i1=0; // Z Y X order
j1=0;
k1=1;
i2=0;
j2=1;
k2=1;
}
else if(x0<z0)
{
i1=0; // Y Z X order
j1=1;
k1=0;
i2=0;
j2=1;
k2=1;
}
else
{
i1=0; // Y X Z order
j1=1;
k1=0;
i2=1;
j2=1;
k2=0;
}
}
// A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z),
// a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and
// a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where
// c = 1/6.
double x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
double y1 = y0 - j1 + G3;
double z1 = z0 - k1 + G3;
double x2 = x0 - i2 + 2.0*G3; // Offsets for third corner in (x,y,z) coords
double y2 = y0 - j2 + 2.0*G3;
double z2 = z0 - k2 + 2.0*G3;
double x3 = x0 - 1.0 + 3.0*G3; // Offsets for last corner in (x,y,z) coords
double y3 = y0 - 1.0 + 3.0*G3;
double z3 = z0 - 1.0 + 3.0*G3;
// Work out the hashed gradient indices of the four simplex corners
int ii = i & 255;
int jj = j & 255;
int kk = k & 255;
int gi0 = perm[ii+perm[jj+perm[kk]]] % 12;
int gi1 = perm[ii+i1+perm[jj+j1+perm[kk+k1]]] % 12;
int gi2 = perm[ii+i2+perm[jj+j2+perm[kk+k2]]] % 12;
int gi3 = perm[ii+1+perm[jj+1+perm[kk+1]]] % 12;
// Calculate the contribution from the four corners
double t0 = 0.6 - x0*x0 - y0*y0 - z0*z0;
if(t0<0) n0 = 0.0;
else
{
t0 *= t0;
n0 = t0 * t0 * dot(grad3[gi0], x0, y0, z0);
}
double t1 = 0.6 - x1*x1 - y1*y1 - z1*z1;
if(t1<0) n1 = 0.0;
else
{
t1 *= t1;
n1 = t1 * t1 * dot(grad3[gi1], x1, y1, z1);
}
double t2 = 0.6 - x2*x2 - y2*y2 - z2*z2;
if(t2<0) n2 = 0.0;
else
{
t2 *= t2;
n2 = t2 * t2 * dot(grad3[gi2], x2, y2, z2);
}
double t3 = 0.6 - x3*x3 - y3*y3 - z3*z3;
if(t3<0) n3 = 0.0;
else
{
t3 *= t3;
n3 = t3 * t3 * dot(grad3[gi3], x3, y3, z3);
}
// Add contributions from each corner to get the final noise value.
// The result is scaled to stay just inside [-1,1]
return 32.0*(n0 + n1 + n2 + n3);
}
float Noise1234::pnoise( float x, float y, float z, float w,
int px, int py, int pz, int pw )
{
int ix0, iy0, iz0, iw0, ix1, iy1, iz1, iw1;
float fx0, fy0, fz0, fw0, fx1, fy1, fz1, fw1;
float s, t, r, q;
float nxyz0, nxyz1, nxy0, nxy1, nx0, nx1, n0, n1;
ix0 = FASTFLOOR( x ); // Integer part of x
iy0 = FASTFLOOR( y ); // Integer part of y
iz0 = FASTFLOOR( z ); // Integer part of y
iw0 = FASTFLOOR( w ); // Integer part of w
fx0 = x - ix0; // Fractional part of x
fy0 = y - iy0; // Fractional part of y
fz0 = z - iz0; // Fractional part of z
fw0 = w - iw0; // Fractional part of w
fx1 = fx0 - 1.0f;
fy1 = fy0 - 1.0f;
fz1 = fz0 - 1.0f;
fw1 = fw0 - 1.0f;
ix1 = (( ix0 + 1 ) % px ) & 0xff; // Wrap to 0..px-1 and wrap to 0..255
iy1 = (( iy0 + 1 ) % py ) & 0xff; // Wrap to 0..py-1 and wrap to 0..255
iz1 = (( iz0 + 1 ) % pz ) & 0xff; // Wrap to 0..pz-1 and wrap to 0..255
iw1 = (( iw0 + 1 ) % pw ) & 0xff; // Wrap to 0..pw-1 and wrap to 0..255
ix0 = ( ix0 % px ) & 0xff;
iy0 = ( iy0 % py ) & 0xff;
iz0 = ( iz0 % pz ) & 0xff;
iw0 = ( iw0 % pw ) & 0xff;
q = FADE( fw0 );
r = FADE( fz0 );
t = FADE( fy0 );
s = FADE( fx0 );
nxyz0 = grad(perm[ix0 + perm[iy0 + perm[iz0 + perm[iw0]]]], fx0, fy0, fz0, fw0);
nxyz1 = grad(perm[ix0 + perm[iy0 + perm[iz0 + perm[iw1]]]], fx0, fy0, fz0, fw1);
nxy0 = LERP( q, nxyz0, nxyz1 );
nxyz0 = grad(perm[ix0 + perm[iy0 + perm[iz1 + perm[iw0]]]], fx0, fy0, fz1, fw0);
nxyz1 = grad(perm[ix0 + perm[iy0 + perm[iz1 + perm[iw1]]]], fx0, fy0, fz1, fw1);
nxy1 = LERP( q, nxyz0, nxyz1 );
nx0 = LERP ( r, nxy0, nxy1 );
nxyz0 = grad(perm[ix0 + perm[iy1 + perm[iz0 + perm[iw0]]]], fx0, fy1, fz0, fw0);
nxyz1 = grad(perm[ix0 + perm[iy1 + perm[iz0 + perm[iw1]]]], fx0, fy1, fz0, fw1);
nxy0 = LERP( q, nxyz0, nxyz1 );
nxyz0 = grad(perm[ix0 + perm[iy1 + perm[iz1 + perm[iw0]]]], fx0, fy1, fz1, fw0);
nxyz1 = grad(perm[ix0 + perm[iy1 + perm[iz1 + perm[iw1]]]], fx0, fy1, fz1, fw1);
nxy1 = LERP( q, nxyz0, nxyz1 );
nx1 = LERP ( r, nxy0, nxy1 );
n0 = LERP( t, nx0, nx1 );
nxyz0 = grad(perm[ix1 + perm[iy0 + perm[iz0 + perm[iw0]]]], fx1, fy0, fz0, fw0);
nxyz1 = grad(perm[ix1 + perm[iy0 + perm[iz0 + perm[iw1]]]], fx1, fy0, fz0, fw1);
nxy0 = LERP( q, nxyz0, nxyz1 );
nxyz0 = grad(perm[ix1 + perm[iy0 + perm[iz1 + perm[iw0]]]], fx1, fy0, fz1, fw0);
nxyz1 = grad(perm[ix1 + perm[iy0 + perm[iz1 + perm[iw1]]]], fx1, fy0, fz1, fw1);
nxy1 = LERP( q, nxyz0, nxyz1 );
nx0 = LERP ( r, nxy0, nxy1 );
nxyz0 = grad(perm[ix1 + perm[iy1 + perm[iz0 + perm[iw0]]]], fx1, fy1, fz0, fw0);
nxyz1 = grad(perm[ix1 + perm[iy1 + perm[iz0 + perm[iw1]]]], fx1, fy1, fz0, fw1);
nxy0 = LERP( q, nxyz0, nxyz1 );
nxyz0 = grad(perm[ix1 + perm[iy1 + perm[iz1 + perm[iw0]]]], fx1, fy1, fz1, fw0);
nxyz1 = grad(perm[ix1 + perm[iy1 + perm[iz1 + perm[iw1]]]], fx1, fy1, fz1, fw1);
nxy1 = LERP( q, nxyz0, nxyz1 );
nx1 = LERP ( r, nxy0, nxy1 );
n1 = LERP( t, nx0, nx1 );
return 0.87f * ( LERP( s, n0, n1 ) );
}
/** 2D simplex noise */
GLfloat
_mesa_noise2(GLfloat x, GLfloat y)
{
#define F2 0.366025403f /* F2 = 0.5*(sqrt(3.0)-1.0) */
#define G2 0.211324865f /* G2 = (3.0-Math.sqrt(3.0))/6.0 */
float n0, n1, n2; /* Noise contributions from the three corners */
/* Skew the input space to determine which simplex cell we're in */
float s = (x + y) * F2; /* Hairy factor for 2D */
float xs = x + s;
float ys = y + s;
int i = FASTFLOOR(xs);
int j = FASTFLOOR(ys);
float t = (float) (i + j) * G2;
float X0 = i - t; /* Unskew the cell origin back to (x,y) space */
float Y0 = j - t;
float x0 = x - X0; /* The x,y distances from the cell origin */
float y0 = y - Y0;
float x1, y1, x2, y2;
int ii, jj;
float t0, t1, t2;
/* For the 2D case, the simplex shape is an equilateral triangle. */
/* Determine which simplex we are in. */
int i1, j1; /* Offsets for second (middle) corner of simplex in (i,j) coords */
if (x0 > y0) {
i1 = 1;
j1 = 0;
} /* lower triangle, XY order: (0,0)->(1,0)->(1,1) */
else {
i1 = 0;
j1 = 1;
} /* upper triangle, YX order: (0,0)->(0,1)->(1,1) */
/* A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and */
/* a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where */
/* c = (3-sqrt(3))/6 */
x1 = x0 - i1 + G2; /* Offsets for middle corner in (x,y) unskewed coords */
y1 = y0 - j1 + G2;
x2 = x0 - 1.0f + 2.0f * G2; /* Offsets for last corner in (x,y) unskewed coords */
y2 = y0 - 1.0f + 2.0f * G2;
/* Wrap the integer indices at 256, to avoid indexing perm[] out of bounds */
ii = i % 256;
jj = j % 256;
/* Calculate the contribution from the three corners */
t0 = 0.5f - x0 * x0 - y0 * y0;
if (t0 < 0.0f)
n0 = 0.0f;
else {
t0 *= t0;
n0 = t0 * t0 * grad2(perm[ii + perm[jj]], x0, y0);
}
t1 = 0.5f - x1 * x1 - y1 * y1;
if (t1 < 0.0f)
n1 = 0.0f;
else {
t1 *= t1;
n1 = t1 * t1 * grad2(perm[ii + i1 + perm[jj + j1]], x1, y1);
}
t2 = 0.5f - x2 * x2 - y2 * y2;
if (t2 < 0.0f)
n2 = 0.0f;
else {
t2 *= t2;
n2 = t2 * t2 * grad2(perm[ii + 1 + perm[jj + 1]], x2, y2);
}
/* Add contributions from each corner to get the final noise value. */
/* The result is scaled to return values in the interval [-1,1]. */
return 40.0f * (n0 + n1 + n2); /* TODO: The scale factor is preliminary! */
}
float noise4( float x, float y, float z, float w )
{
int ix0, iy0, iz0, iw0, ix1, iy1, iz1, iw1;
float fx0, fy0, fz0, fw0, fx1, fy1, fz1, fw1;
float s, t, r, q;
float nxyz0, nxyz1, nxy0, nxy1, nx0, nx1, n0, n1;
ix0 = FASTFLOOR( x ); // Integer part of x
iy0 = FASTFLOOR( y ); // Integer part of y
iz0 = FASTFLOOR( z ); // Integer part of y
iw0 = FASTFLOOR( w ); // Integer part of w
fx0 = x - ix0; // Fractional part of x
fy0 = y - iy0; // Fractional part of y
fz0 = z - iz0; // Fractional part of z
fw0 = w - iw0; // Fractional part of w
fx1 = fx0 - 1.0f;
fy1 = fy0 - 1.0f;
fz1 = fz0 - 1.0f;
fw1 = fw0 - 1.0f;
ix1 = ( ix0 + 1 ) & 0xff; // Wrap to 0..255
iy1 = ( iy0 + 1 ) & 0xff;
iz1 = ( iz0 + 1 ) & 0xff;
iw1 = ( iw0 + 1 ) & 0xff;
ix0 = ix0 & 0xff;
iy0 = iy0 & 0xff;
iz0 = iz0 & 0xff;
iw0 = iw0 & 0xff;
q = FADE( fw0 );
r = FADE( fz0 );
t = FADE( fy0 );
s = FADE( fx0 );
nxyz0 = grad4(perm[ix0 + perm[iy0 + perm[iz0 + perm[iw0]]]], fx0, fy0, fz0, fw0);
nxyz1 = grad4(perm[ix0 + perm[iy0 + perm[iz0 + perm[iw1]]]], fx0, fy0, fz0, fw1);
nxy0 = LERP( q, nxyz0, nxyz1 );
nxyz0 = grad4(perm[ix0 + perm[iy0 + perm[iz1 + perm[iw0]]]], fx0, fy0, fz1, fw0);
nxyz1 = grad4(perm[ix0 + perm[iy0 + perm[iz1 + perm[iw1]]]], fx0, fy0, fz1, fw1);
nxy1 = LERP( q, nxyz0, nxyz1 );
nx0 = LERP ( r, nxy0, nxy1 );
nxyz0 = grad4(perm[ix0 + perm[iy1 + perm[iz0 + perm[iw0]]]], fx0, fy1, fz0, fw0);
nxyz1 = grad4(perm[ix0 + perm[iy1 + perm[iz0 + perm[iw1]]]], fx0, fy1, fz0, fw1);
nxy0 = LERP( q, nxyz0, nxyz1 );
nxyz0 = grad4(perm[ix0 + perm[iy1 + perm[iz1 + perm[iw0]]]], fx0, fy1, fz1, fw0);
nxyz1 = grad4(perm[ix0 + perm[iy1 + perm[iz1 + perm[iw1]]]], fx0, fy1, fz1, fw1);
nxy1 = LERP( q, nxyz0, nxyz1 );
nx1 = LERP ( r, nxy0, nxy1 );
n0 = LERP( t, nx0, nx1 );
nxyz0 = grad4(perm[ix1 + perm[iy0 + perm[iz0 + perm[iw0]]]], fx1, fy0, fz0, fw0);
nxyz1 = grad4(perm[ix1 + perm[iy0 + perm[iz0 + perm[iw1]]]], fx1, fy0, fz0, fw1);
nxy0 = LERP( q, nxyz0, nxyz1 );
nxyz0 = grad4(perm[ix1 + perm[iy0 + perm[iz1 + perm[iw0]]]], fx1, fy0, fz1, fw0);
nxyz1 = grad4(perm[ix1 + perm[iy0 + perm[iz1 + perm[iw1]]]], fx1, fy0, fz1, fw1);
nxy1 = LERP( q, nxyz0, nxyz1 );
nx0 = LERP ( r, nxy0, nxy1 );
nxyz0 = grad4(perm[ix1 + perm[iy1 + perm[iz0 + perm[iw0]]]], fx1, fy1, fz0, fw0);
nxyz1 = grad4(perm[ix1 + perm[iy1 + perm[iz0 + perm[iw1]]]], fx1, fy1, fz0, fw1);
nxy0 = LERP( q, nxyz0, nxyz1 );
nxyz0 = grad4(perm[ix1 + perm[iy1 + perm[iz1 + perm[iw0]]]], fx1, fy1, fz1, fw0);
nxyz1 = grad4(perm[ix1 + perm[iy1 + perm[iz1 + perm[iw1]]]], fx1, fy1, fz1, fw1);
nxy1 = LERP( q, nxyz0, nxyz1 );
nx1 = LERP ( r, nxy0, nxy1 );
n1 = LERP( t, nx0, nx1 );
return 0.87f * ( LERP( s, n0, n1 ) );
}
/** 4D simplex noise with derivatives.
* If the last four arguments are not null, the analytic derivative
* (the 4D gradient of the scalar noise field) is also calculated.
*/
float sdnoise4( float x, float y, float z, float w,
float *dnoise_dx, float *dnoise_dy,
float *dnoise_dz, float *dnoise_dw)
{
float n0, n1, n2, n3, n4; // Noise contributions from the five corners
float noise; // Return value
float gx0, gy0, gz0, gw0, gx1, gy1, gz1, gw1; /* Gradients at simplex corners */
float gx2, gy2, gz2, gw2, gx3, gy3, gz3, gw3, gx4, gy4, gz4, gw4;
float t20, t21, t22, t23, t24;
float t40, t41, t42, t43, t44;
// Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in
float s = (x + y + z + w) * F4; // Factor for 4D skewing
float xs = x + s;
float ys = y + s;
float zs = z + s;
float ws = w + s;
int i = FASTFLOOR(xs);
int j = FASTFLOOR(ys);
int k = FASTFLOOR(zs);
int l = FASTFLOOR(ws);
float t = (i + j + k + l) * G4; // Factor for 4D unskewing
float X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
float Y0 = j - t;
float Z0 = k - t;
float W0 = l - t;
float x0 = x - X0; // The x,y,z,w distances from the cell origin
float y0 = y - Y0;
float z0 = z - Z0;
float w0 = w - W0;
// For the 4D case, the simplex is a 4D shape I won't even try to describe.
// To find out which of the 24 possible simplices we're in, we need to
// determine the magnitude ordering of x0, y0, z0 and w0.
// The method below is a reasonable way of finding the ordering of x,y,z,w
// and then find the correct traversal order for the simplex we’re in.
// First, six pair-wise comparisons are performed between each possible pair
// of the four coordinates, and then the results are used to add up binary
// bits for an integer index into a precomputed lookup table, simplex[].
int c1 = (x0 > y0) ? 32 : 0;
int c2 = (x0 > z0) ? 16 : 0;
int c3 = (y0 > z0) ? 8 : 0;
int c4 = (x0 > w0) ? 4 : 0;
int c5 = (y0 > w0) ? 2 : 0;
int c6 = (z0 > w0) ? 1 : 0;
int c = c1 & c2 & c3 & c4 & c5 & c6; // '&' is mostly faster than '+'
int i1, j1, k1, l1; // The integer offsets for the second simplex corner
int i2, j2, k2, l2; // The integer offsets for the third simplex corner
int i3, j3, k3, l3; // The integer offsets for the fourth simplex corner
// simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order.
// Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w and x<w
// impossible. Only the 24 indices which have non-zero entries make any sense.
// We use a thresholding to set the coordinates in turn from the largest magnitude.
// The number 3 in the "simplex" array is at the position of the largest coordinate.
i1 = simplex[c][0]>=3 ? 1 : 0;
j1 = simplex[c][1]>=3 ? 1 : 0;
k1 = simplex[c][2]>=3 ? 1 : 0;
l1 = simplex[c][3]>=3 ? 1 : 0;
// The number 2 in the "simplex" array is at the second largest coordinate.
i2 = simplex[c][0]>=2 ? 1 : 0;
j2 = simplex[c][1]>=2 ? 1 : 0;
k2 = simplex[c][2]>=2 ? 1 : 0;
l2 = simplex[c][3]>=2 ? 1 : 0;
// The number 1 in the "simplex" array is at the second smallest coordinate.
i3 = simplex[c][0]>=1 ? 1 : 0;
j3 = simplex[c][1]>=1 ? 1 : 0;
k3 = simplex[c][2]>=1 ? 1 : 0;
l3 = simplex[c][3]>=1 ? 1 : 0;
// The fifth corner has all coordinate offsets = 1, so no need to look that up.
float x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
float y1 = y0 - j1 + G4;
float z1 = z0 - k1 + G4;
float w1 = w0 - l1 + G4;
float x2 = x0 - i2 + 2.0f * G4; // Offsets for third corner in (x,y,z,w) coords
float y2 = y0 - j2 + 2.0f * G4;
float z2 = z0 - k2 + 2.0f * G4;
float w2 = w0 - l2 + 2.0f * G4;
float x3 = x0 - i3 + 3.0f * G4; // Offsets for fourth corner in (x,y,z,w) coords
float y3 = y0 - j3 + 3.0f * G4;
float z3 = z0 - k3 + 3.0f * G4;
float w3 = w0 - l3 + 3.0f * G4;
float x4 = x0 - 1.0f + 4.0f * G4; // Offsets for last corner in (x,y,z,w) coords
float y4 = y0 - 1.0f + 4.0f * G4;
float z4 = z0 - 1.0f + 4.0f * G4;
float w4 = w0 - 1.0f + 4.0f * G4;
// Wrap the integer indices at 256, to avoid indexing perm[] out of bounds
int ii = i & 0xff;
int jj = j & 0xff;
int kk = k & 0xff;
int ll = l & 0xff;
// Calculate the contribution from the five corners
float t0 = 0.6f - x0*x0 - y0*y0 - z0*z0 - w0*w0;
if(t0 < 0.0f) n0 = t0 = t20 = t40 = gx0 = gy0 = gz0 = gw0 = 0.0f;
else {
t20 = t0 * t0;
t40 = t20 * t20;
grad4(perm[ii+perm[jj+perm[kk+perm[ll]]]], &gx0, &gy0, &gz0, &gw0);
n0 = t40 * ( gx0 * x0 + gy0 * y0 + gz0 * z0 + gw0 * w0 );
}
float t1 = 0.6f - x1*x1 - y1*y1 - z1*z1 - w1*w1;
if(t1 < 0.0f) n1 = t1 = t21 = t41 = gx1 = gy1 = gz1 = gw1 = 0.0f;
else {
t21 = t1 * t1;
t41 = t21 * t21;
grad4(perm[ii+i1+perm[jj+j1+perm[kk+k1+perm[ll+l1]]]], &gx1, &gy1, &gz1, &gw1);
n1 = t41 * ( gx1 * x1 + gy1 * y1 + gz1 * z1 + gw1 * w1 );
}
float t2 = 0.6f - x2*x2 - y2*y2 - z2*z2 - w2*w2;
if(t2 < 0.0f) n2 = t2 = t22 = t42 = gx2 = gy2 = gz2 = gw2 = 0.0f;
else {
t22 = t2 * t2;
t42 = t22 * t22;
grad4(perm[ii+i2+perm[jj+j2+perm[kk+k2+perm[ll+l2]]]], &gx2, &gy2, &gz2, &gw2);
n2 = t42 * ( gx2 * x2 + gy2 * y2 + gz2 * z2 + gw2 * w2 );
}
float t3 = 0.6f - x3*x3 - y3*y3 - z3*z3 - w3*w3;
if(t3 < 0.0f) n3 = t3 = t23 = t43 = gx3 = gy3 = gz3 = gw3 = 0.0f;
else {
t23 = t3 * t3;
t43 = t23 * t23;
grad4(perm[ii+i3+perm[jj+j3+perm[kk+k3+perm[ll+l3]]]], &gx3, &gy3, &gz3, &gw3);
n3 = t43 * ( gx3 * x3 + gy3 * y3 + gz3 * z3 + gw3 * w3 );
}
float t4 = 0.6f - x4*x4 - y4*y4 - z4*z4 - w4*w4;
if(t4 < 0.0f) n4 = t4 = t24 = t44 = gx4 = gy4 = gz4 = gw4 = 0.0f;
else {
t24 = t4 * t4;
t44 = t24 * t24;
grad4(perm[ii+1+perm[jj+1+perm[kk+1+perm[ll+1]]]], &gx4, &gy4, &gz4, &gw4);
n4 = t44 * ( gx4 * x4 + gy4 * y4 + gz4 * z4 + gw4 * w4 );
}
// Sum up and scale the result to cover the range [-1,1]
noise = 27.0f * (n0 + n1 + n2 + n3 + n4); // TODO: The scale factor is preliminary!
/* Compute derivative, if requested by supplying non-null pointers
* for the last four arguments */
if( ( dnoise_dx != 0 ) && ( dnoise_dy != 0 ) && ( dnoise_dz != 0 ) && ( dnoise_dw != 0 ) )
{
/* A straight, unoptimised calculation would be like:
* *dnoise_dx = -8.0f * t20 * t0 * x0 * dot(gx0, gy0, gz0, gw0, x0, y0, z0, w0) + t40 * gx0;
* *dnoise_dy = -8.0f * t20 * t0 * y0 * dot(gx0, gy0, gz0, gw0, x0, y0, z0, w0) + t40 * gy0;
* *dnoise_dz = -8.0f * t20 * t0 * z0 * dot(gx0, gy0, gz0, gw0, x0, y0, z0, w0) + t40 * gz0;
* *dnoise_dw = -8.0f * t20 * t0 * w0 * dot(gx0, gy0, gz0, gw0, x0, y0, z0, w0) + t40 * gw0;
* *dnoise_dx += -8.0f * t21 * t1 * x1 * dot(gx1, gy1, gz1, gw1, x1, y1, z1, w1) + t41 * gx1;
* *dnoise_dy += -8.0f * t21 * t1 * y1 * dot(gx1, gy1, gz1, gw1, x1, y1, z1, w1) + t41 * gy1;
* *dnoise_dz += -8.0f * t21 * t1 * z1 * dot(gx1, gy1, gz1, gw1, x1, y1, z1, w1) + t41 * gz1;
* *dnoise_dw = -8.0f * t21 * t1 * w1 * dot(gx1, gy1, gz1, gw1, x1, y1, z1, w1) + t41 * gw1;
* *dnoise_dx += -8.0f * t22 * t2 * x2 * dot(gx2, gy2, gz2, gw2, x2, y2, z2, w2) + t42 * gx2;
* *dnoise_dy += -8.0f * t22 * t2 * y2 * dot(gx2, gy2, gz2, gw2, x2, y2, z2, w2) + t42 * gy2;
* *dnoise_dz += -8.0f * t22 * t2 * z2 * dot(gx2, gy2, gz2, gw2, x2, y2, z2, w2) + t42 * gz2;
* *dnoise_dw += -8.0f * t22 * t2 * w2 * dot(gx2, gy2, gz2, gw2, x2, y2, z2, w2) + t42 * gw2;
* *dnoise_dx += -8.0f * t23 * t3 * x3 * dot(gx3, gy3, gz3, gw3, x3, y3, z3, w3) + t43 * gx3;
* *dnoise_dy += -8.0f * t23 * t3 * y3 * dot(gx3, gy3, gz3, gw3, x3, y3, z3, w3) + t43 * gy3;
* *dnoise_dz += -8.0f * t23 * t3 * z3 * dot(gx3, gy3, gz3, gw3, x3, y3, z3, w3) + t43 * gz3;
* *dnoise_dw += -8.0f * t23 * t3 * w3 * dot(gx3, gy3, gz3, gw3, x3, y3, z3, w3) + t43 * gw3;
* *dnoise_dx += -8.0f * t24 * t4 * x4 * dot(gx4, gy4, gz4, gw4, x4, y4, z4, w4) + t44 * gx4;
* *dnoise_dy += -8.0f * t24 * t4 * y4 * dot(gx4, gy4, gz4, gw4, x4, y4, z4, w4) + t44 * gy4;
* *dnoise_dz += -8.0f * t24 * t4 * z4 * dot(gx4, gy4, gz4, gw4, x4, y4, z4, w4) + t44 * gz4;
* *dnoise_dw += -8.0f * t24 * t4 * w4 * dot(gx4, gy4, gz4, gw4, x4, y4, z4, w4) + t44 * gw4;
*/
float temp0 = t20 * t0 * ( gx0 * x0 + gy0 * y0 + gz0 * z0 + gw0 * w0 );
*dnoise_dx = temp0 * x0;
*dnoise_dy = temp0 * y0;
*dnoise_dz = temp0 * z0;
*dnoise_dw = temp0 * w0;
float temp1 = t21 * t1 * ( gx1 * x1 + gy1 * y1 + gz1 * z1 + gw1 * w1 );
*dnoise_dx += temp1 * x1;
*dnoise_dy += temp1 * y1;
*dnoise_dz += temp1 * z1;
*dnoise_dw += temp1 * w1;
float temp2 = t22 * t2 * ( gx2 * x2 + gy2 * y2 + gz2 * z2 + gw2 * w2 );
*dnoise_dx += temp2 * x2;
*dnoise_dy += temp2 * y2;
*dnoise_dz += temp2 * z2;
*dnoise_dw += temp2 * w2;
float temp3 = t23 * t3 * ( gx3 * x3 + gy3 * y3 + gz3 * z3 + gw3 * w3 );
*dnoise_dx += temp3 * x3;
*dnoise_dy += temp3 * y3;
*dnoise_dz += temp3 * z3;
*dnoise_dw += temp3 * w3;
float temp4 = t24 * t4 * ( gx4 * x4 + gy4 * y4 + gz4 * z4 + gw4 * w4 );
*dnoise_dx += temp4 * x4;
*dnoise_dy += temp4 * y4;
*dnoise_dz += temp4 * z4;
*dnoise_dw += temp4 * w4;
*dnoise_dx *= -8.0f;
*dnoise_dy *= -8.0f;
*dnoise_dz *= -8.0f;
*dnoise_dw *= -8.0f;
*dnoise_dx += t40 * gx0 + t41 * gx1 + t42 * gx2 + t43 * gx3 + t44 * gx4;
*dnoise_dy += t40 * gy0 + t41 * gy1 + t42 * gy2 + t43 * gy3 + t44 * gy4;
*dnoise_dz += t40 * gz0 + t41 * gz1 + t42 * gz2 + t43 * gz3 + t44 * gz4;
*dnoise_dw += t40 * gw0 + t41 * gw1 + t42 * gw2 + t43 * gw3 + t44 * gw4;
*dnoise_dx *= 27.0f; /* Scale derivative to match the noise scaling */
*dnoise_dy *= 27.0f;
*dnoise_dz *= 27.0f;
*dnoise_dw *= 27.0f;
}
return noise;
}
/** 3D simplex noise with derivatives.
* If the last tthree arguments are not null, the analytic derivative
* (the 3D gradient of the scalar noise field) is also calculated.
*/
float sdnoise3( float x, float y, float z,
float *dnoise_dx, float *dnoise_dy, float *dnoise_dz )
{
float n0, n1, n2, n3; /* Noise contributions from the four simplex corners */
float noise; /* Return value */
float gx0, gy0, gz0, gx1, gy1, gz1; /* Gradients at simplex corners */
float gx2, gy2, gz2, gx3, gy3, gz3;
/* Skew the input space to determine which simplex cell we're in */
float s = (x+y+z)*F3; /* Very nice and simple skew factor for 3D */
float xs = x+s;
float ys = y+s;
float zs = z+s;
int i = FASTFLOOR(xs);
int j = FASTFLOOR(ys);
int k = FASTFLOOR(zs);
float t = (float)(i+j+k)*G3;
float X0 = i-t; /* Unskew the cell origin back to (x,y,z) space */
float Y0 = j-t;
float Z0 = k-t;
float x0 = x-X0; /* The x,y,z distances from the cell origin */
float y0 = y-Y0;
float z0 = z-Z0;
/* For the 3D case, the simplex shape is a slightly irregular tetrahedron.
* Determine which simplex we are in. */
int i1, j1, k1; /* Offsets for second corner of simplex in (i,j,k) coords */
int i2, j2, k2; /* Offsets for third corner of simplex in (i,j,k) coords */
/* TODO: This code would benefit from a backport from the GLSL version! */
if(x0>=y0) {
if(y0>=z0)
{ i1=1; j1=0; k1=0; i2=1; j2=1; k2=0; } /* X Y Z order */
else if(x0>=z0) { i1=1; j1=0; k1=0; i2=1; j2=0; k2=1; } /* X Z Y order */
else { i1=0; j1=0; k1=1; i2=1; j2=0; k2=1; } /* Z X Y order */
}
else { // x0<y0
if(y0<z0) { i1=0; j1=0; k1=1; i2=0; j2=1; k2=1; } /* Z Y X order */
else if(x0<z0) { i1=0; j1=1; k1=0; i2=0; j2=1; k2=1; } /* Y Z X order */
else { i1=0; j1=1; k1=0; i2=1; j2=1; k2=0; } /* Y X Z order */
}
/* A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z),
* a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and
* a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where
* c = 1/6. */
float x1 = x0 - i1 + G3; /* Offsets for second corner in (x,y,z) coords */
float y1 = y0 - j1 + G3;
float z1 = z0 - k1 + G3;
float x2 = x0 - i2 + 2.0f * G3; /* Offsets for third corner in (x,y,z) coords */
float y2 = y0 - j2 + 2.0f * G3;
float z2 = z0 - k2 + 2.0f * G3;
float x3 = x0 - 1.0f + 3.0f * G3; /* Offsets for last corner in (x,y,z) coords */
float y3 = y0 - 1.0f + 3.0f * G3;
float z3 = z0 - 1.0f + 3.0f * G3;
/* Wrap the integer indices at 256, to avoid indexing perm[] out of bounds */
int ii = i % 256;
int jj = j % 256;
int kk = k % 256;
/* Calculate the contribution from the four corners */
float t0 = 0.6f - x0*x0 - y0*y0 - z0*z0;
float t20, t40;
if(t0 < 0.0f) n0 = t0 = t20 = t40 = gx0 = gy0 = gz0 = 0.0f;
else {
grad3( perm[ii + perm[jj + perm[kk]]], &gx0, &gy0, &gz0 );
t20 = t0 * t0;
t40 = t20 * t20;
n0 = t40 * ( gx0 * x0 + gy0 * y0 + gz0 * z0 );
}
float t1 = 0.6f - x1*x1 - y1*y1 - z1*z1;
float t21, t41;
if(t1 < 0.0f) n1 = t1 = t21 = t41 = gx1 = gy1 = gz1 = 0.0f;
else {
grad3( perm[ii + i1 + perm[jj + j1 + perm[kk + k1]]], &gx1, &gy1, &gz1 );
t21 = t1 * t1;
t41 = t21 * t21;
n1 = t41 * ( gx1 * x1 + gy1 * y1 + gz1 * z1 );
}
float t2 = 0.6f - x2*x2 - y2*y2 - z2*z2;
float t22, t42;
if(t2 < 0.0f) n2 = t2 = t22 = t42 = gx2 = gy2 = gz2 = 0.0f;
else {
grad3( perm[ii + i2 + perm[jj + j2 + perm[kk + k2]]], &gx2, &gy2, &gz2 );
t22 = t2 * t2;
t42 = t22 * t22;
n2 = t42 * ( gx2 * x2 + gy2 * y2 + gz2 * z2 );
}
float t3 = 0.6f - x3*x3 - y3*y3 - z3*z3;
float t23, t43;
if(t3 < 0.0f) n3 = t3 = t23 = t43 = gx3 = gy3 = gz3 = 0.0f;
else {
grad3( perm[ii + 1 + perm[jj + 1 + perm[kk + 1]]], &gx3, &gy3, &gz3 );
t23 = t3 * t3;
t43 = t23 * t23;
n3 = t43 * ( gx3 * x3 + gy3 * y3 + gz3 * z3 );
}
/* Add contributions from each corner to get the final noise value.
* The result is scaled to return values in the range [-1,1] */
noise = 28.0f * (n0 + n1 + n2 + n3);
/* Compute derivative, if requested by supplying non-null pointers
* for the last three arguments */
if( ( dnoise_dx != 0 ) && ( dnoise_dy != 0 ) && ( dnoise_dz != 0 ))
{
/* A straight, unoptimised calculation would be like:
* *dnoise_dx = -8.0f * t20 * t0 * x0 * dot(gx0, gy0, gz0, x0, y0, z0) + t40 * gx0;
* *dnoise_dy = -8.0f * t20 * t0 * y0 * dot(gx0, gy0, gz0, x0, y0, z0) + t40 * gy0;
* *dnoise_dz = -8.0f * t20 * t0 * z0 * dot(gx0, gy0, gz0, x0, y0, z0) + t40 * gz0;
* *dnoise_dx += -8.0f * t21 * t1 * x1 * dot(gx1, gy1, gz1, x1, y1, z1) + t41 * gx1;
* *dnoise_dy += -8.0f * t21 * t1 * y1 * dot(gx1, gy1, gz1, x1, y1, z1) + t41 * gy1;
* *dnoise_dz += -8.0f * t21 * t1 * z1 * dot(gx1, gy1, gz1, x1, y1, z1) + t41 * gz1;
* *dnoise_dx += -8.0f * t22 * t2 * x2 * dot(gx2, gy2, gz2, x2, y2, z2) + t42 * gx2;
* *dnoise_dy += -8.0f * t22 * t2 * y2 * dot(gx2, gy2, gz2, x2, y2, z2) + t42 * gy2;
* *dnoise_dz += -8.0f * t22 * t2 * z2 * dot(gx2, gy2, gz2, x2, y2, z2) + t42 * gz2;
* *dnoise_dx += -8.0f * t23 * t3 * x3 * dot(gx3, gy3, gz3, x3, y3, z3) + t43 * gx3;
* *dnoise_dy += -8.0f * t23 * t3 * y3 * dot(gx3, gy3, gz3, x3, y3, z3) + t43 * gy3;
* *dnoise_dz += -8.0f * t23 * t3 * z3 * dot(gx3, gy3, gz3, x3, y3, z3) + t43 * gz3;
*/
float temp0 = t20 * t0 * ( gx0 * x0 + gy0 * y0 + gz0 * z0 );
*dnoise_dx = temp0 * x0;
*dnoise_dy = temp0 * y0;
*dnoise_dz = temp0 * z0;
float temp1 = t21 * t1 * ( gx1 * x1 + gy1 * y1 + gz1 * z1 );
*dnoise_dx += temp1 * x1;
*dnoise_dy += temp1 * y1;
*dnoise_dz += temp1 * z1;
float temp2 = t22 * t2 * ( gx2 * x2 + gy2 * y2 + gz2 * z2 );
*dnoise_dx += temp2 * x2;
*dnoise_dy += temp2 * y2;
*dnoise_dz += temp2 * z2;
float temp3 = t23 * t3 * ( gx3 * x3 + gy3 * y3 + gz3 * z3 );
*dnoise_dx += temp3 * x3;
*dnoise_dy += temp3 * y3;
*dnoise_dz += temp3 * z3;
*dnoise_dx *= -8.0f;
*dnoise_dy *= -8.0f;
*dnoise_dz *= -8.0f;
*dnoise_dx += t40 * gx0 + t41 * gx1 + t42 * gx2 + t43 * gx3;
*dnoise_dy += t40 * gy0 + t41 * gy1 + t42 * gy2 + t43 * gy3;
*dnoise_dz += t40 * gz0 + t41 * gz1 + t42 * gz2 + t43 * gz3;
*dnoise_dx *= 28.0f; /* Scale derivative to match the noise scaling */
*dnoise_dy *= 28.0f;
*dnoise_dz *= 28.0f;
}
return noise;
}
/** 2D simplex noise with derivatives.
* If the last two arguments are not null, the analytic derivative
* (the 2D gradient of the scalar noise field) is also calculated.
*/
float sdnoise2( float x, float y, float *dnoise_dx, float *dnoise_dy )
{
float n0, n1, n2; /* Noise contributions from the three simplex corners */
float gx0, gy0, gx1, gy1, gx2, gy2; /* Gradients at simplex corners */
/* Skew the input space to determine which simplex cell we're in */
float s = ( x + y ) * F2; /* Hairy factor for 2D */
float xs = x + s;
float ys = y + s;
int i = FASTFLOOR( xs );
int j = FASTFLOOR( ys );
float t = ( float ) ( i + j ) * G2;
float X0 = i - t; /* Unskew the cell origin back to (x,y) space */
float Y0 = j - t;
float x0 = x - X0; /* The x,y distances from the cell origin */
float y0 = y - Y0;
/* For the 2D case, the simplex shape is an equilateral triangle.
* Determine which simplex we are in. */
int i1, j1; /* Offsets for second (middle) corner of simplex in (i,j) coords */
if( x0 > y0 ) { i1 = 1; j1 = 0; } /* lower triangle, XY order: (0,0)->(1,0)->(1,1) */
else { i1 = 0; j1 = 1; } /* upper triangle, YX order: (0,0)->(0,1)->(1,1) */
/* A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and
* a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
* c = (3-sqrt(3))/6 */
float x1 = x0 - i1 + G2; /* Offsets for middle corner in (x,y) unskewed coords */
float y1 = y0 - j1 + G2;
float x2 = x0 - 1.0f + 2.0f * G2; /* Offsets for last corner in (x,y) unskewed coords */
float y2 = y0 - 1.0f + 2.0f * G2;
/* Wrap the integer indices at 256, to avoid indexing perm[] out of bounds */
int ii = i % 256;
int jj = j % 256;
/* Calculate the contribution from the three corners */
float t0 = 0.5f - x0 * x0 - y0 * y0;
float t20, t40;
if( t0 < 0.0f ) t40 = t20 = t0 = n0 = gx0 = gy0 = 0.0f; /* No influence */
else {
grad2( perm[ii + perm[jj]], &gx0, &gy0 );
t20 = t0 * t0;
t40 = t20 * t20;
n0 = t40 * ( gx0 * x0 + gy0 * y0 );
}
float t1 = 0.5f - x1 * x1 - y1 * y1;
float t21, t41;
if( t1 < 0.0f ) t21 = t41 = t1 = n1 = gx1 = gy1 = 0.0f; /* No influence */
else {
grad2( perm[ii + i1 + perm[jj + j1]], &gx1, &gy1 );
t21 = t1 * t1;
t41 = t21 * t21;
n1 = t41 * ( gx1 * x1 + gy1 * y1 );
}
float t2 = 0.5f - x2 * x2 - y2 * y2;
float t22, t42;
if( t2 < 0.0f ) t42 = t22 = t2 = n2 = gx2 = gy2 = 0.0f; /* No influence */
else {
grad2( perm[ii + 1 + perm[jj + 1]], &gx2, &gy2 );
t22 = t2 * t2;
t42 = t22 * t22;
n2 = t42 * ( gx2 * x2 + gy2 * y2 );
}
/* Add contributions from each corner to get the final noise value.
* The result is scaled to return values in the interval [-1,1]. */
float noise = 40.0f * ( n0 + n1 + n2 );
/* Compute derivative, if requested by supplying non-null pointers
* for the last two arguments */
if( ( dnoise_dx != 0 ) && ( dnoise_dy != 0 ) )
{
/* A straight, unoptimised calculation would be like:
* *dnoise_dx = -8.0f * t20 * t0 * x0 * ( gx0 * x0 + gy0 * y0 ) + t40 * gx0;
* *dnoise_dy = -8.0f * t20 * t0 * y0 * ( gx0 * x0 + gy0 * y0 ) + t40 * gy0;
* *dnoise_dx += -8.0f * t21 * t1 * x1 * ( gx1 * x1 + gy1 * y1 ) + t41 * gx1;
* *dnoise_dy += -8.0f * t21 * t1 * y1 * ( gx1 * x1 + gy1 * y1 ) + t41 * gy1;
* *dnoise_dx += -8.0f * t22 * t2 * x2 * ( gx2 * x2 + gy2 * y2 ) + t42 * gx2;
* *dnoise_dy += -8.0f * t22 * t2 * y2 * ( gx2 * x2 + gy2 * y2 ) + t42 * gy2;
*/
float temp0 = t20 * t0 * ( gx0* x0 + gy0 * y0 );
*dnoise_dx = temp0 * x0;
*dnoise_dy = temp0 * y0;
float temp1 = t21 * t1 * ( gx1 * x1 + gy1 * y1 );
*dnoise_dx += temp1 * x1;
*dnoise_dy += temp1 * y1;
float temp2 = t22 * t2 * ( gx2* x2 + gy2 * y2 );
*dnoise_dx += temp2 * x2;
*dnoise_dy += temp2 * y2;
*dnoise_dx *= -8.0f;
*dnoise_dy *= -8.0f;
*dnoise_dx += t40 * gx0 + t41 * gx1 + t42 * gx2;
*dnoise_dy += t40 * gy0 + t41 * gy1 + t42 * gy2;
*dnoise_dx *= 40.0f; /* Scale derivative to match the noise scaling */
*dnoise_dy *= 40.0f;
}
return noise;
}
