protected override double SingleNoise(double x, double y)
{
int ix = MathX.FastFloor(x);
double fx0 = x - ix;
double fx1 = fx0 - 1;
int jx = ix & 255;
int iy = MathX.FastFloor(y);
double fy0 = y - iy;
double fy1 = fy0 - 1;
int jy = iy & 255;
var py = Perm[jy];
int index = PermMod12[jx + py];
int index1 = PermMod12[jx + 1 + py];
var g0 = Gradients[index];
var g1 = Gradients[index1];
double vx0 = g0.x * fx0 + g0.y * fy0;
double vx1 = g1.x * fx1 + g1.y * fy0;
double vy0 = vx0 + fx0 * (vx1 - vx0);
var py1 = Perm[jy + 1];
int index2 = PermMod12[jx + py1];
int index3 = PermMod12[jx + 1 + py1];
var g2 = Gradients[index2];
var g3 = Gradients[index3];
vx0 = g2.x * fx0 + g2.y * fy1;
vx1 = g3.x * fx1 + g3.y * fy1;
double vy1 = vx0 + fx0 * (vx1 - vx0);
return(vy0 + fy0 * (vy1 - vy0));
}
protected double SingleNoise(double x)
{
int ix = MathX.FastFloor(x);
double fx0 = x - ix;
double fx1 = fx0 - 1;
int jx = ix & 255;
int index = PermMod12[jx];
int index1 = PermMod12[jx + 1];
var g0 = Gradients[index];
var g1 = Gradients[index1];
double vx0 = g0.x * fx0;
double vx1 = g1.x * fx1;
return(vx0 + fx0 * (vx1 - vx0));
}
protected override double SingleNoise(double x, double y, double z)
{
int ix = MathX.FastFloor(x);
double fx0 = x - ix;
double fx1 = fx0 - 1;
int jx = ix & 255;
int iy = MathX.FastFloor(y);
double fy0 = y - iy;
double fy1 = fy0 - 1;
int jy = iy & 255;
int iz = MathX.FastFloor(z);
double fz0 = z - iz;
double fz1 = fz0 - 1;
int jz = iz & 255;
var pz = Perm[jz];
var pyz = Perm[jy + pz];
int index = PermMod12[jx + pyz];
int index1 = PermMod12[jx + 1 + pyz];
var g0 = Gradients[index];
var g1 = Gradients[index1];
double vx0 = g0.x * fx0 + g0.y * fy0 + g0.z * fz0;
double vx1 = g1.x * fx1 + g1.y * fy0 + g1.z * fz0;
double vy0 = vx0 + fx0 * (vx1 - vx0);
var py1z = Perm[jy + 1 + pz];
int index2 = PermMod12[jx + py1z];
int index3 = PermMod12[jx + 1 + py1z];
var g2 = Gradients[index2];
var g3 = Gradients[index3];
vx0 = g2.x * fx0 + g2.y * fy1 + g2.z * fz0;
vx1 = g3.x * fx1 + g3.y * fy1 + g3.z * fz0;
double vy1 = vx0 + fx0 * (vx1 - vx0);
double vz0 = vy0 + fy0 * (vy1 - vy0);
var pz1 = Perm[jz + 1];
var pzy1 = Perm[jy + pz1];
int index4 = PermMod12[jx + pzy1];
int index5 = PermMod12[jx + 1 + pzy1];
var g4 = Gradients[index4];
var g5 = Gradients[index5];
vx0 = g4.x * fx0 + g4.y * fy0 + g4.z * fz1;
vx1 = g5.x * fx1 + g5.y * fy0 + g5.z * fz1;
vy0 = vx0 + fx0 * (vx1 - vx0);
var py1z1 = Perm[jy + 1 + pz1];
int index6 = PermMod12[jx + py1z1];
int index7 = PermMod12[jx + 1 + py1z1];
var g6 = Gradients[index6];
var g7 = Gradients[index7];
vx0 = g6.x * fx0 + g6.y * fy1 + g6.z * fz1;
vx1 = g7.x * fx1 + g7.y * fy1 + g7.z * fz1;
vy1 = vx0 + fx0 * (vx1 - vx0);
double vz1 = vy0 + fy0 * (vy1 - vy0);
return(vz0 + fz0 * (vz1 - vz0));
}
protected override double SingleNoise(double xin, double yin)
{
// Skew the input space to determine which simplex cell we're in
double s = (xin + yin) * F2; // Hairy factor for 2D
int i = MathX.FastFloor(xin + s);
int j = MathX.FastFloor(yin + s);
double t = (i + j) * G2;
double X0 = i - t; // Unskew the cell origin back to (x,y) space
double Y0 = j - t;
double x0 = xin - X0; // The x,y distances from the cell origin
double y0 = yin - Y0;
// For the 2D case, the simplex shape is an equilateral triangle.
// Determine which simplex we are in.
int i1 = 0, j1 = 1; // 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)
// 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
double x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
double y1 = y0 - j1 + G2;
double x2 = x0 - 1.0 + 2.0 * G2; // Offsets for last corner in (x,y) unskewed coords
double y2 = y0 - 1.0 + 2.0 * G2;
// Work out the hashed gradient indices of the three simplex corners
int ii = i & 255;
int jj = j & 255;
int gi0 = PermMod12[ii + Perm[jj]];
int gi1 = PermMod12[ii + i1 + Perm[jj + j1]];
int gi2 = PermMod12[ii + 1 + Perm[jj + 1]];
// Calculate the contribution from the three corners
double t0 = 0.5 - x0 * x0 - y0 * y0;
double n0 = 0.0;
if (t0 >= 0)
{
t0 *= t0;
var g = Gradients[gi0];
n0 = t0 * t0 * (g.x * x0 + g.y * y0); // (x,y) of Grad3 used for 2D gradient
}
double t1 = 0.5 - x1 * x1 - y1 * y1;
double n1 = 0.0;
if (t1 >= 0)
{
t1 *= t1;
var g = Gradients[gi1];
n1 = t1 * t1 * (g.x * x1 + g.y * y1);
}
double t2 = 0.5 - x2 * x2 - y2 * y2;
double n2 = 0.0;
if (t2 >= 0)
{
t2 *= t2;
var g = Gradients[gi2];
n2 = t2 * t2 * (g.x * x2 + g.y * y2);
}
// Add contributions from each corner to get the readonly noise value.
// The result is scaled to return values in the interval [-1,1].
return(70.0 * (n0 + n1 + n2));
}
protected override double SingleNoise(double xin, double yin, double zin)
{
// Skew the input space to determine which simplex cell we're in
double s = (xin + yin + zin) * F3; // Very nice and simple skew factor for 3D
int i = MathX.FastFloor(xin + s);
int j = MathX.FastFloor(yin + s);
int k = MathX.FastFloor(zin + s);
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; 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.
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 = PermMod12[ii + Perm[jj + Perm[kk]]];
int gi1 = PermMod12[ii + i1 + Perm[jj + j1 + Perm[kk + k1]]];
int gi2 = PermMod12[ii + i2 + Perm[jj + j2 + Perm[kk + k2]]];
int gi3 = PermMod12[ii + 1 + Perm[jj + 1 + Perm[kk + 1]]];
// Calculate the contribution from the four corners
double t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0;
double n0 = 0.0;
if (t0 >= 0)
{
t0 *= t0;
var g = Gradients[gi0];
n0 = t0 * t0 * (g.x * x0 + g.y * y0 + g.z * z0);
}
double t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1;
double n1 = 0.0;
if (t1 >= 0)
{
t1 *= t1;
var g = Gradients[gi1];
n1 = t1 * t1 * (g.x * x1 + g.y * y1 + g.z * z1);
}
double t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2;
double n2 = 0.0;
if (t2 >= 0)
{
t2 *= t2;
var g = Gradients[gi2];
n2 = t2 * t2 * (g.x * x2 + g.y * y2 + g.z * z2);
}
double t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3;
double n3 = 0.0;
if (t3 >= 0)
{
t3 *= t3;
var g = Gradients[gi3];
n3 = t3 * t3 * (g.x * x3 + g.y * y3 + g.z * z3);
}
// Add contributions from each corner to get the readonly noise value.
// The result is scaled to stay just inside [-1,1]
return(32.0 * (n0 + n1 + n2 + n3));
}
