package cn.nukkit.level.generator.noise; import cn.nukkit.math.NukkitRandom; /** * author: MagicDroidX * Nukkit Project */ public class Simplex extends Perlin { protected static double SQRT_3; protected static double SQRT_5; protected static double F2; protected static double G2; protected static double G22; protected static double F3; protected static double G3; protected static double F4; protected static double G4; protected static double G42; protected static double G43; protected static double G44; protected static int[][] grad4 = {{0, 1, 1, 1}, {0, 1, 1, -1}, {0, 1, -1, 1}, {0, 1, -1, -1}, {0, -1, 1, 1}, {0, -1, 1, -1}, {0, -1, -1, 1}, {0, -1, -1, -1}, {1, 0, 1, 1}, {1, 0, 1, -1}, {1, 0, -1, 1}, {1, 0, -1, -1}, {-1, 0, 1, 1}, {-1, 0, 1, -1}, {-1, 0, -1, 1}, {-1, 0, -1, -1}, {1, 1, 0, 1}, {1, 1, 0, -1}, {1, -1, 0, 1}, {1, -1, 0, -1}, {-1, 1, 0, 1}, {-1, 1, 0, -1}, {-1, -1, 0, 1}, {-1, -1, 0, -1}, {1, 1, 1, 0}, {1, 1, -1, 0}, {1, -1, 1, 0}, {1, -1, -1, 0}, {-1, 1, 1, 0}, {-1, 1, -1, 0}, {-1, -1, 1, 0}, {-1, -1, -1, 0}}; protected static int[][] simplex = { {0, 1, 2, 3}, {0, 1, 3, 2}, {0, 0, 0, 0}, {0, 2, 3, 1}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {1, 2, 3, 0}, {0, 2, 1, 3}, {0, 0, 0, 0}, {0, 3, 1, 2}, {0, 3, 2, 1}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {1, 3, 2, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {1, 2, 0, 3}, {0, 0, 0, 0}, {1, 3, 0, 2}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {2, 3, 0, 1}, {2, 3, 1, 0}, {1, 0, 2, 3}, {1, 0, 3, 2}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {2, 0, 3, 1}, {0, 0, 0, 0}, {2, 1, 3, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {2, 0, 1, 3}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {3, 0, 1, 2}, {3, 0, 2, 1}, {0, 0, 0, 0}, {3, 1, 2, 0}, {2, 1, 0, 3}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {3, 1, 0, 2}, {0, 0, 0, 0}, {3, 2, 0, 1}, {3, 2, 1, 0}}; protected final double offsetW; public Simplex(NukkitRandom random, double octaves, double persistence) { super(random, octaves, persistence); this.offsetW = random.nextDouble() * 256; SQRT_3 = Math.sqrt(3); SQRT_5 = Math.sqrt(5); F2 = 0.5 * (SQRT_3 - 1); G2 = (3 - SQRT_3) / 6; G22 = G2 * 2.0 - 1; F3 = 1.0 / 3.0; G3 = 1.0 / 6.0; F4 = (SQRT_5 - 1.0) / 4.0; G4 = (5.0 - SQRT_5) / 20.0; G42 = G4 * 2.0; G43 = G4 * 3.0; G44 = G4 * 4.0 - 1.0; } public Simplex(NukkitRandom random, double octaves, double persistence, double expansion) { super(random, octaves, persistence, expansion); this.offsetW = random.nextDouble() * 256; SQRT_3 = Math.sqrt(3); SQRT_5 = Math.sqrt(5); F2 = 0.5 * (SQRT_3 - 1); G2 = (3 - SQRT_3) / 6; G22 = G2 * 2.0 - 1; F3 = 1.0 / 3.0; G3 = 1.0 / 6.0; F4 = (SQRT_5 - 1.0) / 4.0; G4 = (5.0 - SQRT_5) / 20.0; G42 = G4 * 2.0; G43 = G4 * 3.0; G44 = G4 * 4.0 - 1.0; } protected static double dot2D(int[] g, double x, double y) { return g[0] * x + g[1] * y; } protected static double dot3D(int[] g, double x, double y, double z) { return g[0] * x + g[1] * y + g[2] * z; } protected static double dot4D(int[] g, double x, double y, double z, double w) { return g[0] * x + g[1] * y + g[2] * z + g[3] * w; } @Override public double getNoise3D(double x, double y, double z) { x += this.offsetX; y += this.offsetY; z += this.offsetZ; // Skew the input space to determine which simplex cell we're in double s = (x + y + z) * F3; // Very nice and simple skew factor for 3D int i = (int) (x + s); int j = (int) (y + s); int k = (int) (z + s); double t = (i + j + k) * G3; // Unskew the cell origin back to (x,y,z) space double x0 = x - (i - t); // The x,y,z distances from the cell origin double y0 = y - (j - t); double z0 = z - (k - t); // For the 3D case, the simplex shape is a slightly irregular tetrahedron. int i1 = 0; int j1 = 0; int k1 = 0; int i2 = 0; int j2 = 0; int k2 = 0; // Determine which simplex we are in. 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; double n = 0; // Calculate the contribution from the four corners double t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0; if (t0 > 0) { int[] gi0 = grad3[this.perm[ii + this.perm[jj + this.perm[kk]]] % 12]; n += t0 * t0 * t0 * t0 * (gi0[0] * x0 + gi0[1] * y0 + gi0[2] * z0); } double t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1; if (t1 > 0) { int[] gi1 = grad3[this.perm[ii + i1 + this.perm[jj + j1 + this.perm[kk + k1]]] % 12]; n += t1 * t1 * t1 * t1 * (gi1[0] * x1 + gi1[1] * y1 + gi1[2] * z1); } double t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2; if (t2 > 0) { int[] gi2 = grad3[this.perm[ii + i2 + this.perm[jj + j2 + this.perm[kk + k2]]] % 12]; n += t2 * t2 * t2 * t2 * (gi2[0] * x2 + gi2[1] * y2 + gi2[2] * z2); } double t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3; if (t3 > 0) { int[] gi3 = grad3[this.perm[ii + 1 + this.perm[jj + 1 + this.perm[kk + 1]]] % 12]; n += t3 * t3 * t3 * t3 * (gi3[0] * x3 + gi3[1] * y3 + gi3[2] * z3); } // Add contributions from each corner to get the noise value. // The result is scaled to stay just inside [-1,1] return 32.0 * n; } @Override public double getNoise2D(double x, double y) { x += this.offsetX; y += this.offsetY; // Skew the input space to determine which simplex cell we're in double s = (x + y) * F2; // Hairy factor for 2D int i = (int) (x + s); int j = (int) (y + s); double t = (i + j) * G2; // Unskew the cell origin back to (x,y) space double x0 = x - (i - t); // The x,y distances from the cell origin double y0 = y - (j - t); // For the 2D case, the simplex shape is an equilateral triangle. int i1 = 0; int j1 = 0; // Determine which simplex we are in. 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 + G22; // Offsets for last corner in (x,y) unskewed coords double y2 = y0 + G22; // Work out the hashed gradient indices of the three simplex corners int ii = i & 255; int jj = j & 255; double n = 0; // Calculate the contribution from the three corners double t0 = 0.5 - x0 * x0 - y0 * y0; if (t0 > 0) { int[] gi0 = grad3[this.perm[ii + this.perm[jj]] % 12]; n += t0 * t0 * t0 * t0 * (gi0[0] * x0 + gi0[1] * y0); // (x,y) of grad3 used for 2D gradient } double t1 = 0.5 - x1 * x1 - y1 * y1; if (t1 > 0) { int[] gi1 = grad3[this.perm[ii + i1 + this.perm[jj + j1]] % 12]; n += t1 * t1 * t1 * t1 * (gi1[0] * x1 + gi1[1] * y1); } double t2 = 0.5 - x2 * x2 - y2 * y2; if (t2 > 0) { int[] gi2 = grad3[this.perm[ii + 1 + this.perm[jj + 1]] % 12]; n += t2 * t2 * t2 * t2 * (gi2[0] * x2 + gi2[1] * y2); } // Add contributions from each corner to get the noise value. // The result is scaled to return values in the interval [-1,1]. return 70.0 * n; } }