/*-------------------------------------------------------------------- Simplex Noise C++ implementation Based on a public domain code by Stefan Gustavson. (The original header is below) --------------------------------------------------------------------*/ /*-- start of the original header --*/ /* * A speed-improved simplex noise algorithm for 2D, 3D and 4D in Java. * * Based on example code by Stefan Gustavson (stegu@itn.liu.se). * Optimisations by Peter Eastman (peastman@drizzle.stanford.edu). * Better rank ordering method by Stefan Gustavson in 2012. * * This could be speeded up even further, but it's useful as it is. * * Version 2012-03-09 * * This code was placed in the public domain by its original author, * Stefan Gustavson. You may use it as you see fit, but * attribution is appreciated. * */ /*-- end of the original header --*/ #include "iwa_simplexnoise.h" #include //sqrt #include namespace { static Grad grad3[] = {Grad(1, 1, 0), Grad(-1, 1, 0), Grad(1, -1, 0), Grad(-1, -1, 0), Grad(1, 0, 1), Grad(-1, 0, 1), Grad(1, 0, -1), Grad(-1, 0, -1), Grad(0, 1, 1), Grad(0, -1, 1), Grad(0, 1, -1), Grad(0, -1, -1)}; static Grad grad4[] = { Grad(0, 1, 1, 1), Grad(0, 1, 1, -1), Grad(0, 1, -1, 1), Grad(0, 1, -1, -1), Grad(0, -1, 1, 1), Grad(0, -1, 1, -1), Grad(0, -1, -1, 1), Grad(0, -1, -1, -1), Grad(1, 0, 1, 1), Grad(1, 0, 1, -1), Grad(1, 0, -1, 1), Grad(1, 0, -1, -1), Grad(-1, 0, 1, 1), Grad(-1, 0, 1, -1), Grad(-1, 0, -1, 1), Grad(-1, 0, -1, -1), Grad(1, 1, 0, 1), Grad(1, 1, 0, -1), Grad(1, -1, 0, 1), Grad(1, -1, 0, -1), Grad(-1, 1, 0, 1), Grad(-1, 1, 0, -1), Grad(-1, -1, 0, 1), Grad(-1, -1, 0, -1), Grad(1, 1, 1, 0), Grad(1, 1, -1, 0), Grad(1, -1, 1, 0), Grad(1, -1, -1, 0), Grad(-1, 1, 1, 0), Grad(-1, 1, -1, 0), Grad(-1, -1, 1, 0), Grad(-1, -1, -1, 0)}; // To remove the need for index wrapping, double the permutation table length static short perm[512] = { 151, 160, 137, 91, 90, 15, 131, 13, 201, 95, 96, 53, 194, 233, 7, 225, 140, 36, 103, 30, 69, 142, 8, 99, 37, 240, 21, 10, 23, 190, 6, 148, 247, 120, 234, 75, 0, 26, 197, 62, 94, 252, 219, 203, 117, 35, 11, 32, 57, 177, 33, 88, 237, 149, 56, 87, 174, 20, 125, 136, 171, 168, 68, 175, 74, 165, 71, 134, 139, 48, 27, 166, 77, 146, 158, 231, 83, 111, 229, 122, 60, 211, 133, 230, 220, 105, 92, 41, 55, 46, 245, 40, 244, 102, 143, 54, 65, 25, 63, 161, 1, 216, 80, 73, 209, 76, 132, 187, 208, 89, 18, 169, 200, 196, 135, 130, 116, 188, 159, 86, 164, 100, 109, 198, 173, 186, 3, 64, 52, 217, 226, 250, 124, 123, 5, 202, 38, 147, 118, 126, 255, 82, 85, 212, 207, 206, 59, 227, 47, 16, 58, 17, 182, 189, 28, 42, 223, 183, 170, 213, 119, 248, 152, 2, 44, 154, 163, 70, 221, 153, 101, 155, 167, 43, 172, 9, 129, 22, 39, 253, 19, 98, 108, 110, 79, 113, 224, 232, 178, 185, 112, 104, 218, 246, 97, 228, 251, 34, 242, 193, 238, 210, 144, 12, 191, 179, 162, 241, 81, 51, 145, 235, 249, 14, 239, 107, 49, 192, 214, 31, 181, 199, 106, 157, 184, 84, 204, 176, 115, 121, 50, 45, 127, 4, 150, 254, 138, 236, 205, 93, 222, 114, 67, 29, 24, 72, 243, 141, 128, 195, 78, 66, 215, 61, 156, 180, 151, 160, 137, 91, 90, 15, 131, 13, 201, 95, 96, 53, 194, 233, 7, 225, 140, 36, 103, 30, 69, 142, 8, 99, 37, 240, 21, 10, 23, 190, 6, 148, 247, 120, 234, 75, 0, 26, 197, 62, 94, 252, 219, 203, 117, 35, 11, 32, 57, 177, 33, 88, 237, 149, 56, 87, 174, 20, 125, 136, 171, 168, 68, 175, 74, 165, 71, 134, 139, 48, 27, 166, 77, 146, 158, 231, 83, 111, 229, 122, 60, 211, 133, 230, 220, 105, 92, 41, 55, 46, 245, 40, 244, 102, 143, 54, 65, 25, 63, 161, 1, 216, 80, 73, 209, 76, 132, 187, 208, 89, 18, 169, 200, 196, 135, 130, 116, 188, 159, 86, 164, 100, 109, 198, 173, 186, 3, 64, 52, 217, 226, 250, 124, 123, 5, 202, 38, 147, 118, 126, 255, 82, 85, 212, 207, 206, 59, 227, 47, 16, 58, 17, 182, 189, 28, 42, 223, 183, 170, 213, 119, 248, 152, 2, 44, 154, 163, 70, 221, 153, 101, 155, 167, 43, 172, 9, 129, 22, 39, 253, 19, 98, 108, 110, 79, 113, 224, 232, 178, 185, 112, 104, 218, 246, 97, 228, 251, 34, 242, 193, 238, 210, 144, 12, 191, 179, 162, 241, 81, 51, 145, 235, 249, 14, 239, 107, 49, 192, 214, 31, 181, 199, 106, 157, 184, 84, 204, 176, 115, 121, 50, 45, 127, 4, 150, 254, 138, 236, 205, 93, 222, 114, 67, 29, 24, 72, 243, 141, 128, 195, 78, 66, 215, 61, 156, 180}; static short permMod12[512] = { 7, 4, 5, 7, 6, 3, 11, 1, 9, 11, 0, 5, 2, 5, 7, 9, 8, 0, 7, 6, 9, 10, 8, 3, 1, 0, 9, 10, 11, 10, 6, 4, 7, 0, 6, 3, 0, 2, 5, 2, 10, 0, 3, 11, 9, 11, 11, 8, 9, 9, 9, 4, 9, 5, 8, 3, 6, 8, 5, 4, 3, 0, 8, 7, 2, 9, 11, 2, 7, 0, 3, 10, 5, 2, 2, 3, 11, 3, 1, 2, 0, 7, 1, 2, 4, 9, 8, 5, 7, 10, 5, 4, 4, 6, 11, 6, 5, 1, 3, 5, 1, 0, 8, 1, 5, 4, 0, 7, 4, 5, 6, 1, 8, 4, 3, 10, 8, 8, 3, 2, 8, 4, 1, 6, 5, 6, 3, 4, 4, 1, 10, 10, 4, 3, 5, 10, 2, 3, 10, 6, 3, 10, 1, 8, 3, 2, 11, 11, 11, 4, 10, 5, 2, 9, 4, 6, 7, 3, 2, 9, 11, 8, 8, 2, 8, 10, 7, 10, 5, 9, 5, 11, 11, 7, 4, 9, 9, 10, 3, 1, 7, 2, 0, 2, 7, 5, 8, 4, 10, 5, 4, 8, 2, 6, 1, 0, 11, 10, 2, 1, 10, 6, 0, 0, 11, 11, 6, 1, 9, 3, 1, 7, 9, 2, 11, 11, 1, 0, 10, 7, 1, 7, 10, 1, 4, 0, 0, 8, 7, 1, 2, 9, 7, 4, 6, 2, 6, 8, 1, 9, 6, 6, 7, 5, 0, 0, 3, 9, 8, 3, 6, 6, 11, 1, 0, 0, 7, 4, 5, 7, 6, 3, 11, 1, 9, 11, 0, 5, 2, 5, 7, 9, 8, 0, 7, 6, 9, 10, 8, 3, 1, 0, 9, 10, 11, 10, 6, 4, 7, 0, 6, 3, 0, 2, 5, 2, 10, 0, 3, 11, 9, 11, 11, 8, 9, 9, 9, 4, 9, 5, 8, 3, 6, 8, 5, 4, 3, 0, 8, 7, 2, 9, 11, 2, 7, 0, 3, 10, 5, 2, 2, 3, 11, 3, 1, 2, 0, 7, 1, 2, 4, 9, 8, 5, 7, 10, 5, 4, 4, 6, 11, 6, 5, 1, 3, 5, 1, 0, 8, 1, 5, 4, 0, 7, 4, 5, 6, 1, 8, 4, 3, 10, 8, 8, 3, 2, 8, 4, 1, 6, 5, 6, 3, 4, 4, 1, 10, 10, 4, 3, 5, 10, 2, 3, 10, 6, 3, 10, 1, 8, 3, 2, 11, 11, 11, 4, 10, 5, 2, 9, 4, 6, 7, 3, 2, 9, 11, 8, 8, 2, 8, 10, 7, 10, 5, 9, 5, 11, 11, 7, 4, 9, 9, 10, 3, 1, 7, 2, 0, 2, 7, 5, 8, 4, 10, 5, 4, 8, 2, 6, 1, 0, 11, 10, 2, 1, 10, 6, 0, 0, 11, 11, 6, 1, 9, 3, 1, 7, 9, 2, 11, 11, 1, 0, 10, 7, 1, 7, 10, 1, 4, 0, 0, 8, 7, 1, 2, 9, 7, 4, 6, 2, 6, 8, 1, 9, 6, 6, 7, 5, 0, 0, 3, 9, 8, 3, 6, 6, 11, 1, 0, 0}; }; //---------------------------------------- // 2D simplex noise //---------------------------------------- double SimplexNoise::noise(double xin, double yin) { // Skewing and unskewing factors for 2 dimensions static const double F2 = 0.5 * (sqrt(3.0) - 1.0); static const double G2 = (3.0 - sqrt(3.0)) / 6.0; 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) * F2; // Hairy factor for 2D int i = fastfloor(xin + s); int j = 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, 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 + 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; if (t0 < 0) n0 = 0.0; else { t0 *= t0; n0 = t0 * t0 * dot(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(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(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); } //---------------------------------------- // 3D simplex noise //---------------------------------------- double SimplexNoise::noise(double xin, double yin, double zin) { // Skewing and unskewing factors for 3 dimensions static const double F3 = 1.0 / 3.0; static const double G3 = 1.0 / 6.0; 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 = fastfloor(xin + s); int j = fastfloor(yin + s); int k = 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) rankx++; else ranky++; if (x0 > z0) rankx++; else rankz++; if (x0 > w0) rankx++; else rankw++; if (y0 > z0) ranky++; else rankz++; if (y0 > w0) ranky++; else rankw++; if (z0 > w0) rankz++; else rankw++; 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= 3 ? 1 : 0; j1 = ranky >= 3 ? 1 : 0; k1 = rankz >= 3 ? 1 : 0; l1 = rankw >= 3 ? 1 : 0; // Rank 2 denotes the second largest coordinate. i2 = rankx >= 2 ? 1 : 0; j2 = ranky >= 2 ? 1 : 0; k2 = rankz >= 2 ? 1 : 0; l2 = rankw >= 2 ? 1 : 0; // Rank 1 denotes the second smallest coordinate. i3 = rankx >= 1 ? 1 : 0; j3 = ranky >= 1 ? 1 : 0; k3 = rankz >= 1 ? 1 : 0; l3 = rankw >= 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 = perm[ii + perm[jj + perm[kk + perm[ll]]]] % 32; int gi1 = perm[ii + i1 + perm[jj + j1 + perm[kk + k1 + perm[ll + l1]]]] % 32; int gi2 = perm[ii + i2 + perm[jj + j2 + perm[kk + k2 + perm[ll + l2]]]] % 32; int gi3 = perm[ii + i3 + perm[jj + j3 + perm[kk + k3 + perm[ll + l3]]]] % 32; int gi4 = perm[ii + 1 + perm[jj + 1 + perm[kk + 1 + perm[ll + 1]]]] % 32; /*- パラメータ調整 -*/ double range = 0.66; // double range = 0.6; // Calculate the contribution from the five corners double t0 = range - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0; if (t0 < 0) n0 = 0.0; else { t0 *= t0; n0 = t0 * t0 * dot(grad4[gi0], x0, y0, z0, w0); } double t1 = range - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1; if (t1 < 0) n1 = 0.0; else { t1 *= t1; n1 = t1 * t1 * dot(grad4[gi1], x1, y1, z1, w1); } double t2 = range - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2; if (t2 < 0) n2 = 0.0; else { t2 *= t2; n2 = t2 * t2 * dot(grad4[gi2], x2, y2, z2, w2); } double t3 = range - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3; if (t3 < 0) n3 = 0.0; else { t3 *= t3; n3 = t3 * t3 * dot(grad4[gi3], x3, y3, z3, w3); } double t4 = range - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4; if (t4 < 0) n4 = 0.0; else { t4 *= t4; n4 = t4 * t4 * dot(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); } /*---------------------------------------- セルまたぎを防ぐために、現在の所属セルを得る ----------------------------------------*/ CellIds SimplexNoise::getCellIds(double xin, double yin, double zin) { // Skew the input space to determine which simplex cell we're in const double F3 = 1.0 / 3.0; double s = (xin + yin + zin) * F3; // Very nice and simple skew factor for 3D int i = fastfloor(xin + s); int j = fastfloor(yin + s); int k = fastfloor(zin + s); const double G3 = 1.0 / 6.0; // Very nice and simple unskew factor, too 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