/** * Jingga * * @package Utils * @copyright Jingga * @license OMS License 2.0 * @version 1.0.0 * @link https://jingga.app */ #ifndef COMS_NOISE_SIMPLEX_H #define COMS_NOISE_SIMPLEX_H #include #define SIMPLEX_NOISE_F2 0.5 * (sqrt(3.0) - 1.0) #define SIMPLEX_NOISE_G2 (3.0 - sqrt(3.0)) / 6.0 static const int perm[512] = { 151,160,137,91,90,15, 131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142, 151,160,137,91,90,15, 131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142, }; static const int grad3_2[12][2] = { {1,1}, {-1,1}, {1,-1}, {-1,-1}, {1,0}, {-1,0}, {1,0}, {-1,0}, {0,1}, {0,-1}, {0,1}, {0,-1} }; static const int grad3_3[12][3] = { {1,1,0}, {-1,1,0}, {1,-1,0}, {-1,-1,0}, {1,0,1}, {-1,0,1}, {1,0,-1}, {-1,0,-1}, {0,1,1}, {0,-1,1}, {0,1,-1}, {0,-1,-1} }; static inline double simplex_noise_dot2(const int32* g, double x, double y) { return g[0] * x + g[1] * y; } static inline double simplex_noise_dot3(const int32* g, double x, double y, double z) { return g[0] * x + g[1] * y + g[2] * z; } double simplex_noise_2d(double x, double y) { double n0, n1, n2; // Noise contributions from the three corners // Skew the input space to determine which simplex cell we're in double s = (x + y) * SIMPLEX_NOISE_F2; // Hairy factor for 2D int32 i = floor(x + s); int32 j = floor(y + s); double t = (i + j) * SIMPLEX_NOISE_G2; double X0 = i - t; // Unskew the cell origin back to (x, y) space double Y0 = j - t; double x0 = x - X0; // The x, y distances from the cell origin double y0 = y - Y0; // For the 2D case, the simplex shape is an equilateral triangle. // Determine which simplex we are in. int32 i1, j1; // Offsets for the second (middle) corner of simplex in (i, j) if (x0 > y0) { i1 = 1; j1 = 0; // Lower triangle, XY order } else { i1 = 0; j1 = 1; // Upper triangle, YX order } // 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 + SIMPLEX_NOISE_G2; // Offsets for middle corner in (x, y) unskewed coords double y1 = y0 - j1 + SIMPLEX_NOISE_G2; double x2 = x0 - 1.0 + 2.0 * SIMPLEX_NOISE_G2; // Offsets for last corner in (x, y) unskewed coords double y2 = y0 - 1.0 + 2.0 * SIMPLEX_NOISE_G2; // Work out the hashed gradient indices of the three simplex corners int32 ii = i & 255; int32 jj = j & 255; int32 gi0 = perm[ii + perm[jj]] % 12; int32 gi1 = perm[ii + i1 + perm[jj + j1]] % 12; int32 gi2 = perm[ii + 1 + 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 * simplex_noise_dot2(grad3_2[gi0], x0, y0); // (x,y) of grad3_2 used for 2D gradient } double t1 = 0.5 - x1 * x1 - y1 * y1; if (t1 < 0) { n1 = 0.0; } else { t1 *= t1; n1 = t1 * t1 * simplex_noise_dot2(grad3_2[gi1], x1, y1); } double t2 = 0.5 - x2 * x2 - y2 * y2; if (t2 < 0) { n2 = 0.0; } else { t2 *= t2; n2 = t2 * t2 * simplex_noise_dot2(grad3_2[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); } double simplex_noise_3d(double x, double y, double z) { 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 = (x + y + z) * SIMPLEX_NOISE_F2; // Skew factor for 3D int i = floor(x + s); int j = floor(y + s); int k = floor(z + s); double t = (i + j + k) * SIMPLEX_NOISE_G2; double X0 = i - t; // Unskew the cell origin back to (x, y, z) space double Y0 = j - t; double Z0 = k - t; double x0 = x - X0; // The x, y, z distances from the cell origin double y0 = y - Y0; double z0 = z - 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) int i2, j2, k2; // Offsets for third corner of simplex in (i, j, k) if (x0 >= y0) { if (y0 >= z0) { i1 = 1; j1 = 0; k1 = 0; // X Y Z order i2 = 1; j2 = 1; k2 = 0; } else if (x0 >= z0) { i1 = 1; j1 = 0; k1 = 0; // X Z Y order i2 = 1; j2 = 0; k2 = 1; } else { i1 = 0; j1 = 0; k1 = 1; // Z X Y order i2 = 1; j2 = 0; k2 = 1; } } else { // x0 < y0 if (y0 < z0) { i1 = 0; j1 = 0; k1 = 1; // Z Y X order i2 = 0; j2 = 1; k2 = 1; } else if (x0 < z0) { i1 = 0; j1 = 1; k1 = 0; // Y Z X order i2 = 0; j2 = 1; k2 = 1; } else { i1 = 0; j1 = 1; k1 = 0; // Y X Z order i2 = 1; j2 = 1; k2 = 0; } } // Offsets for second corner in (x, y, z) unskewed coords double x1 = x0 - i1 + SIMPLEX_NOISE_G2; double y1 = y0 - j1 + SIMPLEX_NOISE_G2; double z1 = z0 - k1 + SIMPLEX_NOISE_G2; // Offsets for third corner in (x, y, z) unskewed coords double x2 = x0 - i2 + 2.0 * SIMPLEX_NOISE_G2; double y2 = y0 - j2 + 2.0 * SIMPLEX_NOISE_G2; double z2 = z0 - k2 + 2.0 * SIMPLEX_NOISE_G2; // Offsets for last corner in (x, y, z) unskewed coords double x3 = x0 - 1.0 + 3.0 * SIMPLEX_NOISE_G2; double y3 = y0 - 1.0 + 3.0 * SIMPLEX_NOISE_G2; double z3 = z0 - 1.0 + 3.0 * SIMPLEX_NOISE_G2; // 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 = perm[ii + perm[jj + perm[kk]]] % 12; int gi1 = perm[ii + i1 + perm[jj + j1 + perm[kk + k1]]] % 12; int gi2 = perm[ii + i2 + perm[jj + j2 + perm[kk + k2]]] % 12; int gi3 = perm[ii + 1 + perm[jj + 1 + 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 * simplex_noise_dot3(grad3_3[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 * simplex_noise_dot3(grad3_3[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 * simplex_noise_dot3(grad3_3[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 * simplex_noise_dot3(grad3_3[gi3], x3, y3, z3); } // Add contributions from each corner to get the final noise value. // The result is scaled to return values in the interval [-1,1]. return 32.0 * (n0 + n1 + n2 + n3); } #endif