/// <summary>
/// Provides the patch and patch delta for the given path delta.
/// </summary>
/// <param name="pointA">Point a.</param>
/// <param name="pointB">Point b.</param>
/// <param name="patchDelta">Patch delta.</param>
/// <param name="delta">Delta.</param>
private void PatchForDelta(out BezierPointAttribute pointA, out BezierPointAttribute pointB, out float patchDelta,
float delta)
{
int patches = m_Points.Length - 1;
if (m_Closed)
{
patches++;
}
if (patches < 1)
{
throw new Exception("No patches in the path!");
}
delta = Mathf.Repeat(delta, 1.0f);
int patchIndex = HydraMathUtils.FloorToInt(delta * patches);
pointA = m_Points[patchIndex];
pointB = GetNextPoint(patchIndex);
float singlePatchDelta = 1.0f / patches;
patchDelta = delta - (patchIndex * singlePatchDelta);
patchDelta *= patches;
}
/// <summary>
/// 4D simplex noise
/// </summary>
/// <param name="x">The x coordinate.</param>
/// <param name="y">The y coordinate.</param>
/// <param name="z">The z coordinate.</param>
/// <param name="w">The w coordinate.</param>
public static double Noise(double x, double y, double z, double w)
{
// The skewing and unskewing factors are hairy again for the 4D case
double F4 = (s_Root5 - 1.0) / 4.0;
double G4 = (5.0 - s_Root5) / 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 = HydraMathUtils.FloorToInt(x + s);
int j = HydraMathUtils.FloorToInt(y + s);
int k = HydraMathUtils.FloorToInt(z + s);
int l = HydraMathUtils.FloorToInt(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;
// 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.
int i1 = s_Simplex[c][0] >= 3 ? 1 : 0;
int j1 = s_Simplex[c][1] >= 3 ? 1 : 0;
int k1 = s_Simplex[c][2] >= 3 ? 1 : 0;
int l1 = s_Simplex[c][3] >= 3 ? 1 : 0;
// The number 2 in the "simplex" array is at the second largest coordinate.
int i2 = s_Simplex[c][0] >= 2 ? 1 : 0;
int j2 = s_Simplex[c][1] >= 2 ? 1 : 0;
int k2 = s_Simplex[c][2] >= 2 ? 1 : 0;
int l2 = s_Simplex[c][3] >= 2 ? 1 : 0;
// The number 1 in the "simplex" array is at the second smallest coordinate.
int i3 = s_Simplex[c][0] >= 1 ? 1 : 0;
int j3 = s_Simplex[c][1] >= 1 ? 1 : 0;
int k3 = s_Simplex[c][2] >= 1 ? 1 : 0;
int l3 = s_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
int ii = i & 255;
int jj = j & 255;
int kk = k & 255;
int ll = l & 255;
int gi0 = s_Perm[ii + s_Perm[jj + s_Perm[kk + s_Perm[ll]]]] % 32;
int gi1 = s_Perm[ii + i1 + s_Perm[jj + j1 + s_Perm[kk + k1 + s_Perm[ll + l1]]]] % 32;
int gi2 = s_Perm[ii + i2 + s_Perm[jj + j2 + s_Perm[kk + k2 + s_Perm[ll + l2]]]] % 32;
int gi3 = s_Perm[ii + i3 + s_Perm[jj + j3 + s_Perm[kk + k3 + s_Perm[ll + l3]]]] % 32;
int gi4 = s_Perm[ii + 1 + s_Perm[jj + 1 + s_Perm[kk + 1 + s_Perm[ll + 1]]]] % 32;
// 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 * Dot(s_Grad4[gi0], 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 * Dot(s_Grad4[gi1], 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 * Dot(s_Grad4[gi2], 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 * Dot(s_Grad4[gi3], 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 * Dot(s_Grad4[gi4], x4, y4, z4, w4);
}
// Sum up and scale the result to cover the range [-1,1]
return(27.0 * (n0 + n1 + n2 + n3 + n4));
}
// 3D simplex noise
public static double 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 s = (xin + yin + zin) * F3; // Very nice and simple skew factor for 3D
int i = HydraMathUtils.FloorToInt(xin + s);
int j = HydraMathUtils.FloorToInt(yin + s);
int k = HydraMathUtils.FloorToInt(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 = s_Perm[ii + s_Perm[jj + s_Perm[kk]]] % 12;
int gi1 = s_Perm[ii + i1 + s_Perm[jj + j1 + s_Perm[kk + k1]]] % 12;
int gi2 = s_Perm[ii + i2 + s_Perm[jj + j2 + s_Perm[kk + k2]]] % 12;
int gi3 = s_Perm[ii + 1 + s_Perm[jj + 1 + s_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(s_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(s_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(s_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(s_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));
}
// 2D simplex noise
public static double Noise(double xin, double yin)
{
double n0, n1, n2; // Noise contributions from the three corners
// Skew the input space to determine which simplex cell we're in
double s = (xin + yin) * s_F2; // Hairy factor for 2D
int i = HydraMathUtils.FloorToInt(xin + s);
int j = HydraMathUtils.FloorToInt(yin + s);
double t = (i + j) * s_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, 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
double x1 = x0 - i1 + s_G2; // Offsets for middle corner in (x,y) unskewed coords
double y1 = y0 - j1 + s_G2;
double x2 = x0 - 1.0 + 2.0 * s_G2; // Offsets for last corner in (x,y) unskewed coords
double y2 = y0 - 1.0 + 2.0 * s_G2;
// Work out the hashed gradient indices of the three simplex corners
int ii = i & 255;
int jj = j & 255;
int gi0 = s_Perm[ii + s_Perm[jj]] % 12;
int gi1 = s_Perm[ii + i1 + s_Perm[jj + j1]] % 12;
int gi2 = s_Perm[ii + 1 + s_Perm[jj + 1]] % 12;
// Calculate the contribution from the three corners
double t0 = 0.5 - x0 * x0 - y0 * y0;
if (t0 < 0)
{
n0 = 0.0;
}
else
{
t0 *= t0;
n0 = t0 * t0 * Dot(s_Grad3[gi0], x0, y0); // (x,y) of grad3 used for 2D gradient
}
double t1 = 0.5 - x1 * x1 - y1 * y1;
if (t1 < 0)
{
n1 = 0.0;
}
else
{
t1 *= t1;
n1 = t1 * t1 * Dot(s_Grad3[gi1], x1, y1);
}
double t2 = 0.5 - x2 * x2 - y2 * y2;
if (t2 < 0)
{
n2 = 0.0;
}
else
{
t2 *= t2;
n2 = t2 * t2 * Dot(s_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].
return(70.0 * (n0 + n1 + n2));
}
/// <summary>
/// Returns an int in the min-max range, min inclusive.
/// </summary>
/// <param name="min">Minimum.</param>
/// <param name="max">Maximum.</param>
public int Range(int min, int max)
{
float range = Range((float)min, (float)max);
return(HydraMathUtils.FloorToInt(range));
}
