/// <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)); }