public static Double SimplexNoise(Double x, Double y, Int32 seed, InterpolationDelegate interp)
{
Double s = (x + y)*F2;
int i = FastFloor(x + s);
int j = FastFloor(y + s);
Double t = (i + j)*G2;
Double X0 = i - t;
Double Y0 = j - t;
Double x0 = x - X0;
Double y0 = y - Y0;
int i1, j1;
if (x0 > y0)
{
i1 = 1;
j1 = 0;
}
else
{
i1 = 0;
j1 = 1;
}
Double x1 = x0 - (Double) i1 + G2;
Double y1 = y0 - (Double) j1 + G2;
Double x2 = x0 - 1.0 + 2.0*G2;
Double y2 = y0 - 1.0 + 2.0*G2;
// Hash the triangle coordinates to index the gradient table
uint h0 = HashCoordinates(i, j, (int) seed);
uint h1 = HashCoordinates(i + i1, j + j1, (int) seed);
uint h2 = HashCoordinates(i + 1, j + 1, (int) seed);
// Now, index the tables
Double[] g0 = {NoiseLookupTable.Gradient2D[h0, 0], NoiseLookupTable.Gradient2D[h0, 1]};
Double[] g1 = {NoiseLookupTable.Gradient2D[h1, 0], NoiseLookupTable.Gradient2D[h1, 1]};
Double[] g2 = {NoiseLookupTable.Gradient2D[h2, 0], NoiseLookupTable.Gradient2D[h2, 1]};
Double n0, n1, n2;
// Calculate the contributions from the 3 corners
Double t0 = 0.5 - x0*x0 - y0*y0;
if (t0 < 0) n0 = 0;
else
{
t0 *= t0;
n0 = t0*t0*ArrayDot(g0, x0, y0);
}
Double t1 = 0.5 - x1*x1 - y1*y1;
if (t1 < 0) n1 = 0;
else
{
t1 *= t1;
n1 = t1*t1*ArrayDot(g1, x1, y1);
}
Double t2 = 0.5 - x2*x2 - y2*y2;
if (t2 < 0) n2 = 0;
else
{
t2 *= t2;
n2 = t2*t2*ArrayDot(g2, x2, y2);
}
// Add contributions together
return (70.0*(n0 + n1 + n2))*1.42188695 + 0.001054489;
}
public static void TimeInterpolate(int duration, decimal start, decimal end, bool reverse, InterpolationDelegate step)
{
var stepDelta = (end - start) / duration;
if (reverse)
{
var tmp = start;
start = end;
end = tmp;
stepDelta *= -1;
}
var val = start;
for (var sec = 0; sec <= duration; sec += StepInterval)
{
step(val, ((decimal)(reverse ? (duration - sec) : sec) / duration));
val += stepDelta * StepInterval;
Thread.Sleep(StepInterval * 1000);
}
}
public static Double GradientValueNoise(Double x, Double y, Double z, Double w, Double u, Double v, Int32 seed, InterpolationDelegate interp)
{
return ValueNoise(x, y, z, w, u, v, seed, interp) + GradientNoise(x, y, z, w, u, v, seed, interp);
}
public static Double WhiteNoise(Double x, Double y, Double z, Double w, Double u, Double v, Int32 seed, InterpolationDelegate interp)
{
return NoiseLookupTable.WhiteNoise[(Byte)HashCoordinates(x, y, z, w, u, v, seed)];
}
public static Double GradientNoise(Double x, Double y, Double z, Double w, Int32 seed, InterpolationDelegate interp)
{
var x0 = FastFloor(x);
var y0 = FastFloor(y);
var z0 = FastFloor(z);
var w0 = FastFloor(w);
var x1 = x0 + 1;
var y1 = y0 + 1;
var z1 = z0 + 1;
var w1 = w0 + 1;
var xs = interp((x - x0));
var ys = interp((y - y0));
var zs = interp((z - z0));
var ws = interp((w - w0));
return interpolate_XYZW_4(x, y, z, w, xs, ys, zs, ws, x0, x1, y0, y1, z0, z1, w0, w1, seed, InternalGradientNoise);
}
public static Double GradientNoise(Double x, Double y, Double z, Double w, Double u, Double v, Int32 seed, InterpolationDelegate interp)
{
var x0 = FastFloor(x);
var y0 = FastFloor(y);
var z0 = FastFloor(z);
var w0 = FastFloor(w);
var u0 = FastFloor(u);
var v0 = FastFloor(v);
var x1 = x0 + 1;
var y1 = y0 + 1;
var z1 = z0 + 1;
var w1 = w0 + 1;
var u1 = u0 + 1;
var v1 = v0 + 1;
var xs = interp((x - x0));
var ys = interp((y - y0));
var zs = interp((z - z0));
var ws = interp((w - w0));
var us = interp((u - u0));
var vs = interp((v - v0));
return interpolate_XYZWUV_6(x, y, z, w, u, v, xs, ys, zs, ws, us, vs, x0, x1, y0, y1, z0, z1, w0, w1, u0, u1, v0, v1, seed, InternalGradientNoise);
}
public static Double ValueNoise(Double x, Double y, Double z, Int32 seed, InterpolationDelegate interp)
{
var x0 = FastFloor(x);
var y0 = FastFloor(y);
var z0 = FastFloor(z);
var x1 = x0 + 1;
var y1 = y0 + 1;
var z1 = z0 + 1;
var xs = interp((x - x0));
var ys = interp((y - y0));
var zs = interp((z - z0));
return interpolate_XYZ_3(x, y, z, xs, ys, zs, x0, x1, y0, y1, z0, z1, seed, InternalValueNoise);
}
public static Double GradientNoise(Double x, Double y, Int32 seed, InterpolationDelegate interp)
{
var x0 = FastFloor(x);
var y0 = FastFloor(y);
var x1 = x0 + 1;
var y1 = y0 + 1;
var xs = interp((x - x0));
var ys = interp((y - y0));
return interpolate_XY_2(x, y, xs, ys, x0, x1, y0, y1, seed, InternalGradientNoise);
}
public static Double SimplexNoise(Double x, Double y, Double z, Double w, Double u, Double v, Int32 seed, InterpolationDelegate interp)
{
// Skew
var f4 = (Math.Sqrt(7.0) - 1.0) / 6.0;
// Unskew
var g4 = f4/(1.0 + 6.0*f4);
var sideLength = Math.Sqrt(6.0)/(6.0*f4 + 1.0);
var a = Math.Sqrt((sideLength * sideLength) - ((sideLength / 2.0) * (sideLength / 2.0)));
var cornerFace = Math.Sqrt(a * a + (a / 2.0) * (a / 2.0));
var cornerFaceSqrd = cornerFace * cornerFace;
var valueScaler = Math.Pow(5.0, -0.5);
valueScaler *= Math.Pow(5.0, -3.5) * 100 + 13;
var loc = new[] { x, y, z, w, u, v };
var s = 0.00;
for (var c = 0; c < 6; ++c)
s += loc[c];
s *= f4;
var skewLoc = new[]{
FastFloor(x + s), FastFloor(y + s), FastFloor(z + s),
FastFloor(w + s), FastFloor(u + s), FastFloor(v + s)
};
var intLoc = new[]{
FastFloor(x + s), FastFloor(y + s), FastFloor(z + s),
FastFloor(w + s), FastFloor(u + s), FastFloor(v + s)
};
var unskew = 0.0;
for (var c = 0; c < 6; ++c)
unskew += skewLoc[c];
unskew *= g4;
var cellDist = new[]
{
loc[0] - skewLoc[0] + unskew, loc[1] - skewLoc[1] + unskew,
loc[2] - skewLoc[2] + unskew, loc[3] - skewLoc[3] + unskew,
loc[4] - skewLoc[4] + unskew, loc[5] - skewLoc[5] + unskew
};
var distOrder = new[] { 0, 1, 2, 3, 4, 5 };
SortBy6(cellDist, distOrder);
var newDistOrder = new[]
{
-1, distOrder[0], distOrder[1], distOrder[2], distOrder[3], distOrder[4], distOrder[5]
};
var n = 0.00;
var skewOffset = 0.00;
for (var c = 0; c < 7; ++c)
{
var i = newDistOrder[c];
if (i != -1)
intLoc[i] += 1;
var uu = new Double[6];
for (var d = 0; d < 6; ++d)
{
uu[d] = cellDist[d] - (intLoc[d] - skewLoc[d]) + skewOffset;
}
var t = cornerFaceSqrd;
for (var d = 0; d < 6; ++d)
{
t -= uu[d]*uu[d];
}
if (t > 0.0)
{
var h = HashCoordinates(intLoc[0], intLoc[1], intLoc[2], intLoc[3], intLoc[4], intLoc[5], seed);
var gr = 0.00;
gr += NoiseLookupTable.Gradient6D[h, 0]*uu[0];
gr += NoiseLookupTable.Gradient6D[h, 1]*uu[1];
gr += NoiseLookupTable.Gradient6D[h, 2]*uu[2];
gr += NoiseLookupTable.Gradient6D[h, 3]*uu[3];
gr += NoiseLookupTable.Gradient6D[h, 4]*uu[4];
gr += NoiseLookupTable.Gradient6D[h, 5]*uu[5];
n += gr*t*t*t*t;
}
skewOffset += g4;
}
n *= valueScaler;
return n;
}
public static Double NewSimplexNoise4D(Double x, Double y, Double z, Double w, Int32 seed, InterpolationDelegate interp)
{
var f4 = (Math.Sqrt(5.0) - 1.0)/4.0;
var sideLength = 2.0/(4.0*f4 + 1.0);
var a = Math.Sqrt((sideLength*sideLength) - ((sideLength/2.0)*(sideLength/2.0)));
var cornerToFace = Math.Sqrt((a*a + (a/2.0)*(a/2.0)));
var cornerToFaceSquared = cornerToFace*cornerToFace;
var valueScaler = Math.Pow(3.0, -0.5);
var g4 = f4/(1.0 + 4.0*f4);
valueScaler *= Math.Pow(3.0, -3.5)*100.0 + 13.0;
Double[] loc = {x, y, z, w};
Double s = 0;
for (var c = 0; c < 4; ++c)
s += loc[c];
s *= f4;
var skewLoc = new[] {FastFloor(x + s), FastFloor(y + s), FastFloor(z + s), FastFloor(w + s)};
var intLoc = new[] {FastFloor(x + s), FastFloor(y + s), FastFloor(z + s), FastFloor(w + s)};
var unskew = 0.00;
for (var c = 0; c < 4; ++c)
unskew += skewLoc[c];
unskew *= g4;
var cellDist = new[]
{
loc[0] - skewLoc[0] + unskew, loc[1] - skewLoc[1] + unskew,
loc[2] - skewLoc[2] + unskew, loc[3] - skewLoc[3] + unskew
};
var distOrder = new[] {0, 1, 2, 3};
SortBy4(cellDist, distOrder);
var newDistOrder = new[] {-1, distOrder[0], distOrder[1], distOrder[2], distOrder[3]};
var n = 0.00;
var skewOffset = 0.00;
for (var c = 0; c < 5; ++c)
{
var i = newDistOrder[c];
if (i != -1)
intLoc[i] += 1;
var u = new Double[4];
for (var d = 0; d < 4; ++d)
{
u[d] = cellDist[d] - (intLoc[d] - skewLoc[d]) + skewOffset;
}
var t = cornerToFaceSquared;
for (var d = 0; d < 4; ++d)
{
t -= u[d]*u[d];
}
if (t > 0.0)
{
var h = HashCoordinates(intLoc[0], intLoc[1], intLoc[2], intLoc[3], seed);
var gr = 0.00;
for (var d = 0; d < 4; ++d)
{
gr += NoiseLookupTable.Gradient4D[h, d]*u[d];
}
n += gr*t*t*t*t;
}
skewOffset += g4;
}
n *= valueScaler;
return n;
}
public static Double SimplexNoise(Double x, Double y, Double z, Double w, Int32 seed, InterpolationDelegate interp)
{
Double F4 = (Math.Sqrt(5.0) - 1.0)/4.0;
Double G4 = (5.0 - Math.Sqrt(5.0))/20.0;
Double 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
Double s = (x + y + z + w)*F4; // Factor for 4D skewing
int i = FastFloor(x + s);
int j = FastFloor(y + s);
int k = FastFloor(z + s);
int l = FastFloor(w + s);
Double t = (i + j + k + l)*G4; // Factor for 4D unskewing
Double X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
Double Y0 = j - t;
Double Z0 = k - t;
Double W0 = l - t;
Double x0 = x - X0; // The x,y,z,w distances from the cell origin
Double y0 = y - Y0;
Double z0 = z - Z0;
Double 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.
Double x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
Double y1 = y0 - j1 + G4;
Double z1 = z0 - k1 + G4;
Double w1 = w0 - l1 + G4;
Double x2 = x0 - i2 + 2.0*G4; // Offsets for third corner in (x,y,z,w) coords
Double y2 = y0 - j2 + 2.0*G4;
Double z2 = z0 - k2 + 2.0*G4;
Double w2 = w0 - l2 + 2.0*G4;
Double x3 = x0 - i3 + 3.0*G4; // Offsets for fourth corner in (x,y,z,w) coords
Double y3 = y0 - j3 + 3.0*G4;
Double z3 = z0 - k3 + 3.0*G4;
Double w3 = w0 - l3 + 3.0*G4;
Double x4 = x0 - 1.0 + 4.0*G4; // Offsets for last corner in (x,y,z,w) coords
Double y4 = y0 - 1.0 + 4.0*G4;
Double z4 = z0 - 1.0 + 4.0*G4;
Double w4 = w0 - 1.0 + 4.0*G4;
// Work out the hashed gradient indices of the five simplex corners
uint h0 = HashCoordinates(i, j, k, l, (int) seed);
uint h1 = HashCoordinates(i + i1, j + j1, k + k1, l + l1, (int) seed);
uint h2 = HashCoordinates(i + i2, j + j2, k + k2, l + l2, (int) seed);
uint h3 = HashCoordinates(i + i3, j + j3, k + k3, l + l3, (int) seed);
uint h4 = HashCoordinates(i + 1, j + 1, k + 1, l + 1, (int) seed);
Double[] g0 = {
NoiseLookupTable.Gradient4D[h0, 0], NoiseLookupTable.Gradient4D[h0, 1],
NoiseLookupTable.Gradient4D[h0, 2], NoiseLookupTable.Gradient4D[h0, 3]
};
Double[] g1 = {
NoiseLookupTable.Gradient4D[h1, 0], NoiseLookupTable.Gradient4D[h1, 1],
NoiseLookupTable.Gradient4D[h1, 2], NoiseLookupTable.Gradient4D[h1, 3]
};
Double[] g2 = {
NoiseLookupTable.Gradient4D[h2, 0], NoiseLookupTable.Gradient4D[h2, 1],
NoiseLookupTable.Gradient4D[h2, 2], NoiseLookupTable.Gradient4D[h2, 3]
};
Double[] g3 = {
NoiseLookupTable.Gradient4D[h3, 0], NoiseLookupTable.Gradient4D[h3, 1],
NoiseLookupTable.Gradient4D[h3, 2], NoiseLookupTable.Gradient4D[h3, 3]
};
Double[] g4 = {
NoiseLookupTable.Gradient4D[h4, 0], NoiseLookupTable.Gradient4D[h4, 1],
NoiseLookupTable.Gradient4D[h4, 2], NoiseLookupTable.Gradient4D[h4, 3]
};
// Calculate the contribution from the five corners
Double t0 = 0.6 - x0*x0 - y0*y0 - z0*z0 - w0*w0;
if (t0 < 0) n0 = 0.0;
else
{
t0 *= t0;
n0 = t0*t0*ArrayDot(g0, x0, y0, z0, w0);
}
Double t1 = 0.6 - x1*x1 - y1*y1 - z1*z1 - w1*w1;
if (t1 < 0) n1 = 0.0;
else
{
t1 *= t1;
n1 = t1*t1*ArrayDot(g1, x1, y1, z1, w1);
}
Double t2 = 0.6 - x2*x2 - y2*y2 - z2*z2 - w2*w2;
if (t2 < 0) n2 = 0.0;
else
{
t2 *= t2;
n2 = t2*t2*ArrayDot(g2, x2, y2, z2, w2);
}
Double t3 = 0.6 - x3*x3 - y3*y3 - z3*z3 - w3*w3;
if (t3 < 0) n3 = 0.0;
else
{
t3 *= t3;
n3 = t3*t3*ArrayDot(g3, x3, y3, z3, w3);
}
Double t4 = 0.6 - x4*x4 - y4*y4 - z4*z4 - w4*w4;
if (t4 < 0) n4 = 0.0;
else
{
t4 *= t4;
n4 = t4*t4*ArrayDot(g4, x4, y4, z4, w4);
}
// Sum up and scale the result to cover the range [-1,1]
return 27.0*(n0 + n1 + n2 + n3 + n4);
}
public static Double SimplexNoise(Double x, Double y, Double z, Int32 seed, InterpolationDelegate interp)
{
//static Double F3 = 1.0/3.0;
//static Double G3 = 1.0/6.0;
Double n0, n1, n2, n3;
Double s = (x + y + z)*F3;
int i = FastFloor(x + s);
int j = FastFloor(y + s);
int k = FastFloor(z + s);
Double t = (i + j + k)*G3;
Double X0 = i - t;
Double Y0 = j - t;
Double Z0 = k - t;
Double x0 = x - X0;
Double y0 = y - Y0;
Double z0 = z - Z0;
int i1, j1, k1;
int i2, j2, k2;
if (x0 >= y0)
{
if (y0 >= z0)
{
i1 = 1;
j1 = 0;
k1 = 0;
i2 = 1;
j2 = 1;
k2 = 0;
}
else if (x0 >= z0)
{
i1 = 1;
j1 = 0;
k1 = 0;
i2 = 1;
j2 = 0;
k2 = 1;
}
else
{
i1 = 0;
j1 = 0;
k1 = 1;
i2 = 1;
j2 = 0;
k2 = 1;
}
}
else
{
if (y0 < z0)
{
i1 = 0;
j1 = 0;
k1 = 1;
i2 = 0;
j2 = 1;
k2 = 1;
}
else if (x0 < z0)
{
i1 = 0;
j1 = 1;
k1 = 0;
i2 = 0;
j2 = 1;
k2 = 1;
}
else
{
i1 = 0;
j1 = 1;
k1 = 0;
i2 = 1;
j2 = 1;
k2 = 0;
}
}
var x1 = x0 - i1 + G3;
var y1 = y0 - j1 + G3;
var z1 = z0 - k1 + G3;
var x2 = x0 - i2 + 2.0 * G3;
var y2 = y0 - j2 + 2.0 * G3;
var z2 = z0 - k2 + 2.0 * G3;
var x3 = x0 - 1.0 + 3.0 * G3;
var y3 = y0 - 1.0 + 3.0 * G3;
var z3 = z0 - 1.0 + 3.0 * G3;
var h0 = HashCoordinates(i, j, k, (int) seed);
var h1 = HashCoordinates(i + i1, j + j1, k + k1, (int) seed);
var h2 = HashCoordinates(i + i2, j + j2, k + k2, (int) seed);
var h3 = HashCoordinates(i + 1, j + 1, k + 1, (int) seed);
Double[] g0 = {
NoiseLookupTable.Gradient3D[h0, 0], NoiseLookupTable.Gradient3D[h0, 1],
NoiseLookupTable.Gradient3D[h0, 2]
};
Double[] g1 = {
NoiseLookupTable.Gradient3D[h1, 0], NoiseLookupTable.Gradient3D[h1, 1],
NoiseLookupTable.Gradient3D[h1, 2]
};
Double[] g2 = {
NoiseLookupTable.Gradient3D[h2, 0], NoiseLookupTable.Gradient3D[h2, 1],
NoiseLookupTable.Gradient3D[h2, 2]
};
Double[] g3 = {
NoiseLookupTable.Gradient3D[h3, 0], NoiseLookupTable.Gradient3D[h3, 1],
NoiseLookupTable.Gradient3D[h3, 2]
};
var t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0;
if (t0 < 0.0) n0 = 0.0;
else
{
t0 *= t0;
n0 = t0*t0*ArrayDot(g0, x0, y0, z0);
}
var t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1;
if (t1 < 0.0) n1 = 0.0;
else
{
t1 *= t1;
n1 = t1*t1*ArrayDot(g1, x1, y1, z1);
}
var t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2;
if (t2 < 0) n2 = 0.0;
else
{
t2 *= t2;
n2 = t2*t2*ArrayDot(g2, x2, y2, z2);
}
var t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3;
if (t3 < 0) n3 = 0.0;
else
{
t3 *= t3;
n3 = t3*t3*ArrayDot(g3, x3, y3, z3);
}
return (32.0*(n0 + n1 + n2 + n3))*1.25086885 + 0.0003194984;
}
public CustomInterpolator(InterpolationDelegate interpolationFunction)
{
InterpolationFunction = interpolationFunction;
}