paysages3d/lib_paysages/simplexnoise.c

#include "simplexnoise.h"

/*
 * Simplex noise implementation.
 * 
 * Based on Stefan Gustavson implementation.
 */

#include <stdlib.h>
#include <math.h>
#include <string.h>

typedef struct
{
    double x;
    double y;
    double z;
} Grad3;

typedef struct
{
    double x;
    double y;
    double z;
    double w;
} Grad4;

static Grad3 _grad3[] = {
    {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 Grad4 _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}
};

static short _permutations[] = {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 _permutations2[512];
static short _permutationsMod12[512];

static double _F2;
static double _G2;
static double _F3;
static double _G3;
static double _F4;
static double _G4;

static inline int _fastfloor(double x)
{
    int xi = (int) x;
    return x < xi ? xi - 1 : xi;
}

static double _dot2(Grad3 g, double x, double y)
{
    return g.x * x + g.y * y;
}

static double _dot3(Grad3 g, double x, double y, double z)
{
    return g.x * x + g.y * y + g.z * z;
}

static double _dot4(Grad4 g, double x, double y, double z, double w)
{
    return g.x * x + g.y * y + g.z * z + g.w * w;
}

void simplexNoiseInit()
{
    int i;

    /* To remove the need for index wrapping, double the permutation table length */
    for (i = 0; i < 512; i++)
    {
        _permutations2[i] = _permutations[i & 255];
        _permutationsMod12[i] = (short) (_permutations2[i] % 12);
    }

    /* Skewing and unskewing factors for 2, 3, and 4 dimensions */
    _F2 = 0.5 * (sqrt(3.0) - 1.0);
    _G2 = (3.0 - sqrt(3.0)) / 6.0;
    _F3 = 1.0 / 3.0;
    _G3 = 1.0 / 6.0;
    _F4 = (sqrt(5.0) - 1.0) / 4.0;
    _G4 = (5.0 - sqrt(5.0)) / 20.0;
}

double simplexNoiseGet2DValue(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) * _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 = _permutationsMod12[ii + _permutations2[jj]];
    int gi1 = _permutationsMod12[ii + i1 + _permutations2[jj + j1]];
    int gi2 = _permutationsMod12[ii + 1 + _permutations2[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 * _dot2(_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 * _dot2(_grad3[gi1], x1, y1);
    }
    double t2 = 0.5 - x2 * x2 - y2*y2;
    if (t2 < 0) n2 = 0.0;
    else
    {
        t2 *= t2;
        n2 = t2 * t2 * _dot2(_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);
}

double simplexNoiseGet3DValue(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 = _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 */
        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 = _permutationsMod12[ii + _permutations2[jj + _permutations2[kk]]];
    int gi1 = _permutationsMod12[ii + i1 + _permutations2[jj + j1 + _permutations2[kk + k1]]];
    int gi2 = _permutationsMod12[ii + i2 + _permutations2[jj + j2 + _permutations2[kk + k2]]];
    int gi3 = _permutationsMod12[ii + 1 + _permutations2[jj + 1 + _permutations2[kk + 1]]];
    /* 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 * _dot3(_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 * _dot3(_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 * _dot3(_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 * _dot3(_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);
}

double simplexNoiseGet4DValue(double x, double y, double z, double w)
{
    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 = _fastfloor(x + s);
    int j = _fastfloor(y + s);
    int k = _fastfloor(z + s);
    int l = _fastfloor(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.
       Six pair-wise comparisons are performed between each possible pair
       of the four coordinates, and the results are used to rank the numbers. */
    int rankx = 0;
    int ranky = 0;
    int rankz = 0;
    int rankw = 0;
    if (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<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.
       Rank 3 denotes the largest coordinate. */
    i1 = rankx >= 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 compute that. */
    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 = _permutations2[ii + _permutations2[jj + _permutations2[kk + _permutations2[ll]]]] % 32;
    int gi1 = _permutations2[ii + i1 + _permutations2[jj + j1 + _permutations2[kk + k1 + _permutations2[ll + l1]]]] % 32;
    int gi2 = _permutations2[ii + i2 + _permutations2[jj + j2 + _permutations2[kk + k2 + _permutations2[ll + l2]]]] % 32;
    int gi3 = _permutations2[ii + i3 + _permutations2[jj + j3 + _permutations2[kk + k3 + _permutations2[ll + l3]]]] % 32;
    int gi4 = _permutations2[ii + 1 + _permutations2[jj + 1 + _permutations2[kk + 1 + _permutations2[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 * _dot4(_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 * _dot4(_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 * _dot4(_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 * _dot4(_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 * _dot4(_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);
}