SimplexNoise.cs

using System;

namespace Noise
{
    public static class SimplexNoise
    {
        private static double F2 = 0.5 * (Math.Sqrt(3.0) - 1.0);
        private static double G2 = (3.0 - Math.Sqrt(3.0)) / 6.0;

        private static double F3 = 1.0 / 3.0;
        private static double G3 = 1.0 / 6.0; // Very nice and simple unskew factor, too

        private static double F4 = (Math.Sqrt(5.0) - 1.0) / 4.0;
        private static double G4 = (5.0 - Math.Sqrt(5.0)) / 20.0;

        // Simplex noise in 2D and 3D
        private static int[][] grad3 = new int[][]
        {
            new int[] {1,1,0}, new int[] {-1,1,0}, new int[] {1,-1,0}, new int[] {-1,-1,0},
            new int[] {1,0,1}, new int[] {-1,0,1}, new int[] {1,0,-1}, new int[] {-1,0,-1},
            new int[] {0,1,1}, new int[] {0,-1,1}, new int[] {0,1,-1}, new int[] {0,-1,-1}
        };

        // Simplex noise in 4D
        private static int[][] grad4 = new int[][] {
                   new int[] {0,1,1,1},  new int[] {0,1,1,-1},  new int[] {0,1,-1,1},  new int[] {0,1,-1,-1},
                   new int[] {0,-1,1,1}, new int[] {0,-1,1,-1}, new int[] {0,-1,-1,1}, new int[] {0,-1,-1,-1},
                   new int[] {1,0,1,1},  new int[] {1,0,1,-1},  new int[] {1,0,-1,1},  new int[] {1,0,-1,-1},
                   new int[] {-1,0,1,1}, new int[] {-1,0,1,-1}, new int[] {-1,0,-1,1}, new int[] {-1,0,-1,-1},
                   new int[] {1,1,0,1},  new int[] {1,1,0,-1},  new int[] {1,-1,0,1},  new int[] {1,-1,0,-1},
                   new int[] {-1,1,0,1}, new int[] {-1,1,0,-1}, new int[] {-1,-1,0,1}, new int[] {-1,-1,0,-1},
                   new int[] {1,1,1,0},  new int[] {1,1,-1,0},  new int[] {1,-1,1,0},  new int[] {1,-1,-1,0},
                   new int[] {-1,1,1,0}, new int[] {-1,1,-1,0}, new int[] {-1,-1,1,0}, new int[] {-1,-1,-1,0}};

        private static int[] perm =
        {
            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
        };

        // A lookup table to traverse the simplex around a given point in 4D.
        // Details can be found where this table is used, in the 4D noise method.
        private static int[][] simplex = new int[][]
        {
            new int[] {0,1,2,3}, new int[] {0,1,3,2}, new int[] {0,0,0,0}, new int[] {0,2,3,1}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {1,2,3,0},
            new int[] {0,2,1,3}, new int[] {0,0,0,0}, new int[] {0,3,1,2}, new int[] {0,3,2,1}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {1,3,2,0},
            new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0},
            new int[] {1,2,0,3}, new int[] {0,0,0,0}, new int[] {1,3,0,2}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {2,3,0,1}, new int[] {2,3,1,0},
            new int[] {1,0,2,3}, new int[] {1,0,3,2}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {2,0,3,1}, new int[] {0,0,0,0}, new int[] {2,1,3,0},
            new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0},
            new int[] {2,0,1,3}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {3,0,1,2}, new int[] {3,0,2,1}, new int[] {0,0,0,0}, new int[] {3,1,2,0},
            new int[] {2,1,0,3}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {3,1,0,2}, new int[] {0,0,0,0}, new int[] {3,2,0,1}, new int[] {3,2,1,0}
        };

        // This method is a *lot* faster than using (int)Math.floor(x)
        private static int fastfloor(double x)
        {
            return x > 0 ? (int)x : (int)x - 1;
        }

        private static double dot(int[] g, double x, double y)
        {
            return g[0] * x + g[1] * y;
        }

        private static double dot(int[] g, double x, double y, double z)
        {
            return g[0] * x + g[1] * y + g[2] * z;
        }

        private static double dot(int[] g, double x, double y, double z, double w)
        {
            return g[0] * x + g[1] * y + g[2] * z + g[3] * w;
        }

        // 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
            /*final*/
            double s = (xin + yin) * F2; // Hairy factor for 2D
            int i = fastfloor(xin + s);
            int j = fastfloor(yin + s);
            /*final*/
            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 = perm[ii + perm[jj]] % 12;
            int gi1 = perm[ii + i1 + perm[jj + j1]] % 12;
            int 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 * 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
        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
            /*final*/
            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);
            /*final*/
            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 = 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 * dot(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(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(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(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);
        }

        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 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
            double xs = x + s;
            double ys = y + s;
            double zs = z + s;
            double ws = w + s;
            int i = fastfloor(xs);
            int j = fastfloor(ys);
            int k = fastfloor(zs);
            int l = fastfloor(ws);

            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;

            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<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.
            i1 = simplex[c][0] >= 3 ? 1 : 0;
            j1 = simplex[c][1] >= 3 ? 1 : 0;
            k1 = simplex[c][2] >= 3 ? 1 : 0;
            l1 = simplex[c][3] >= 3 ? 1 : 0;

            // The number 2 in the "simplex" array is at the second largest coordinate.
            i2 = simplex[c][0] >= 2 ? 1 : 0;
            j2 = simplex[c][1] >= 2 ? 1 : 0;
            k2 = simplex[c][2] >= 2 ? 1 : 0;
            l2 = simplex[c][3] >= 2 ? 1 : 0;

            // The number 1 in the "simplex" array is at the second smallest coordinate.
            i3 = simplex[c][0] >= 1 ? 1 : 0;
            j3 = simplex[c][1] >= 1 ? 1 : 0;
            k3 = simplex[c][2] >= 1 ? 1 : 0;
            l3 = 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 + 3.0f * G4; // Offsets for fourth corner in (x,y,z,w) coords
            double y3 = y0 - j3 + 3.0f * G4;
            double z3 = z0 - k3 + 3.0f * G4;
            double w3 = w0 - l3 + 3.0f * 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;

            // 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(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(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(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(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(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);
        }
    }
}