/// <summary>
/// 3D Perlin Noise Function
/// </summary>
public double Noise(double X, double Y, double Z)
{
X += OffsetX;
Y += OffsetY;
Z += OffsetZ;
int XFloored = NoiseUtils.FastFloor(X);
int YFloored = NoiseUtils.FastFloor(Y);
int ZFloored = NoiseUtils.FastFloor(Z);
int _XFloored = XFloored & 255;
int _YFloored = YFloored & 255;
int _ZFloored = ZFloored & 255;
double FX = Fade(X);
double FY = Fade(Y);
double FZ = Fade(Z);
int A = Permutations[_XFloored] + _YFloored;
int AA = Permutations[A] + _ZFloored;
int AB = Permutations[A + 1] + _ZFloored;
int B = Permutations[_XFloored + 1] + _YFloored;
int BA = Permutations[B] + _ZFloored;
int BB = Permutations[B + 1] + _ZFloored;
return(Lerp(FZ, Lerp(FY, Lerp(FX, Gradient(Permutations[AA], _XFloored, _YFloored, _ZFloored),
Gradient(Permutations[BA], _XFloored - 1, _YFloored, _ZFloored)),
Lerp(FY, Gradient(Permutations[AB], _XFloored, _YFloored - 1, _ZFloored),
Gradient(Permutations[BB], _XFloored - 1, _YFloored - 1, _ZFloored))),
Lerp(FY, Lerp(FX, Gradient(Permutations[AA + 1], _XFloored, _YFloored, _ZFloored - 1),
Gradient(Permutations[BA + 1], _XFloored - 1, _YFloored, _ZFloored - 1)),
Lerp(FY, Gradient(Permutations[AB + 1], _XFloored, _YFloored - 1, _ZFloored - 1),
Gradient(Permutations[BB + 1], _XFloored - 1, _YFloored - 1, _ZFloored - 1)))));
}
/// <summary>
/// 3D Simplex Noise.
/// </summary>
public static float Noise(float xin, float yin, float zin)
{
xin += OffsetX;
yin += OffsetY;
zin += OffsetZ;
float n0, n1, n2, n3; // Noise contributions from the four corners
// Skew the input space to determine which simplex cell we're in
float F3 = 1.0f / 3.0f;
float s = (xin + yin + zin) * F3; // Very nice and simple skew factor for 3D
int i = NoiseUtils.FastFloor(xin + s);
int j = NoiseUtils.FastFloor(yin + s);
int k = NoiseUtils.FastFloor(zin + s);
float G3 = 1.0f / 6.0f; // Very nice and simple unskew factor, too
float t = (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 = xin - X0; // The x,y,z distances from the cell origin
float y0 = yin - Y0;
float 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.
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;
// 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 = Permutations[ii + Permutations[jj + Permutations[kk]]] % 12;
int gi1 = Permutations[ii + i1 + Permutations[jj + j1 + Permutations[kk + k1]]] % 12;
int gi2 = Permutations[ii + i2 + Permutations[jj + j2 + Permutations[kk + k2]]] % 12;
int gi3 = Permutations[ii + 1 + Permutations[jj + 1 + Permutations[kk + 1]]] % 12;
// Calculate the contribution from the four corners
float t0 = 0.6f - x0 * x0 - y0 * y0 - z0 * z0;
if (t0 < 0)
{
n0 = 0.0f;
}
else
{
t0 *= t0;
n0 = t0 * t0 * Dot(Grad3[gi0], x0, y0, z0);
}
float t1 = 0.6f - x1 * x1 - y1 * y1 - z1 * z1;
if (t1 < 0)
{
n1 = 0.0f;
}
else
{
t1 *= t1;
n1 = t1 * t1 * Dot(Grad3[gi1], x1, y1, z1);
}
float t2 = 0.6f - x2 * x2 - y2 * y2 - z2 * z2;
if (t2 < 0)
{
n2 = 0.0f;
}
else
{
t2 *= t2;
n2 = t2 * t2 * Dot(Grad3[gi2], x2, y2, z2);
}
float t3 = 0.6f - x3 * x3 - y3 * y3 - z3 * z3;
if (t3 < 0)
{
n3 = 0.0f;
}
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(32.0f * (n0 + n1 + n2 + n3));
}
/// <summary>
/// 2D Simplex Noise
/// </summary>
public static float Noise(float xin, float yin)
{
xin += OffsetX;
yin += OffsetY;
float n0, n1, n2; // Noise contributions from the three corners
// Skew the input space to determine which simplex cell we're in
float F2 = (float)(0.5 * (Math.Sqrt(3.0) - 1.0));
float s = (xin + yin) * F2; // Hairy factor for 2D
int i = NoiseUtils.FastFloor(xin + s);
int j = NoiseUtils.FastFloor(yin + s);
float g2 = (float)((3.0 - Math.Sqrt(3.0)) / 6.0);
float t = (i + j) * g2;
float X0 = i - t; // Unskew the cell origin back to (x,y) space
float Y0 = j - t;
float x0 = xin - X0; // The x,y distances from the cell origin
float y0 = yin - 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;
// Work out the hashed gradient indices of the three simplex corners
int ii = i & 255;
int jj = j & 255;
int gi0 = Permutations[ii + Permutations[jj]] % 12;
int gi1 = Permutations[ii + i1 + Permutations[jj + j1]] % 12;
int gi2 = Permutations[ii + 1 + Permutations[jj + 1]] % 12;
// Calculate the contribution from the three corners
float t0 = 0.5f - x0 * x0 - y0 * y0;
if (t0 < 0)
{
n0 = 0.0f;
}
else
{
t0 *= t0;
n0 = t0 * t0 * Dot(Grad3[gi0], x0, y0); // (x,y) of Grad3 used for 2D gradient
}
float t1 = 0.5f - x1 * x1 - y1 * y1;
if (t1 < 0)
{
n1 = 0.0f;
}
else
{
t1 *= t1;
n1 = t1 * t1 * Dot(Grad3[gi1], x1, y1);
}
float t2 = 0.5f - x2 * x2 - y2 * y2;
if (t2 < 0)
{
n2 = 0.0f;
}
else
{
t2 *= t2;
n2 = t2 * t2 * Dot(Grad3[gi2], 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].
float returnNoise = 70.0f * (n0 + n1 + n2);
// make it range from 0 to 1;
return((returnNoise + 1.0f) * 0.5f);
}