path: root/crawl-ref/source/perlin.cc

/*
 * This is a C++ port of version Stefan Gustavson's public domain
 * implementation of simplex noise (Version 2012-03-09), which can be
 * found at <http://webstaff.itn.liu.se/~stegu/simplexnoise/>.
 *
 * (Simplex Noise is a new (2001) algorithm created by Ken Perlin to
 * replace his classic "Perlin" noise algorithm.)
 *
 * It was ported by Brendan Hickey (brendan@bhickey.net) and released on
 * 2012-09-16.
 *
 * It is made available under the Creative Commons CC0 license.
 *
 * A speed-improved simplex noise algorithm for 2D, 3D and 4D in C++.
 *
 * 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.
 *
 * Clumsily ported to some horrendous C/C++ mix by
 *      Brendan Hickey (brendan@bhickey.net)
 *
 * Version 2012-09-16
 *
 * 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.
 *
 */

#include "AppHdr.h"

#include "perlin.h"
#include <cmath>
#include <stdint.h>

namespace perlin
{
    // Inner class to speed upp gradient computations
    // ([in Java,] array access is a lot slower than member access)
    class Grad
    {
        public:
            const double x, y, z, w;
            Grad(double _x, double _y, double _z) : x(_x), y(_y), z(_z), w(0) {}
            Grad(double _x, double _y, double _z, double _w) : x(_x), y(_y), z(_z), w(_w) {}
    };

    static const 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 const 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)
    };

    static const uint8_t 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,
        // wrap
        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 IMMUTABLE uint8_t permMod12(const uint32_t x)
    {
        return perm[x] % 12;
    }

    // Skewing and unskewing factors for 2, 3, and 4 dimensions
    static const double F2 = 0.5 * (sqrt(3.0) - 1.0);
    static const double G2 = (3.0 - sqrt(3.0)) / 6.0;
    static const double F3 = 1.0 / 3.0;
    static const double G3 = 1.0 / 6.0;
    static const double F4 = (sqrt(5.0) - 1.0) / 4.0;
    static const double G4 = (5.0 - sqrt(5.0)) / 20.0;

    // Use uint64_t so that noise() can work sensibly for
    // coordinates from the full range of uint32_t; otherwise scaling,
    // signedness, and skew will give us considerably less than that.
    static uint64_t fastfloor(const double x)
    {
        uint64_t xi = (uint64_t) x;
        return x < xi ? xi-1 : xi;
    }

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


    // 2D simplex noise
    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
        double s = (xin+yin)*F2; // Hairy factor for 2D
        uint64_t i = fastfloor(xin+s);
        uint64_t 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 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
        double s = (xin+yin+zin)*F3; // Very nice and simple skew factor for 3D
        uint64_t i = fastfloor(xin+s);
        uint64_t j = fastfloor(yin+s);
        uint64_t 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 = permMod12(ii+perm[jj+perm[kk]]);
        int gi1 = permMod12(ii+i1+perm[jj+j1+perm[kk+k1]]);
        int gi2 = permMod12(ii+i2+perm[jj+j2+perm[kk+k2]]);
        int gi3 = permMod12(ii+1+perm[jj+1+perm[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 * 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);
    }


    // 4D simplex noise, better simplex rank ordering method 2012-03-09
    double noise(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
        uint64_t i = fastfloor(x + s);
        uint64_t j = fastfloor(y + s);
        uint64_t k = fastfloor(z + s);
        uint64_t 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;
        ++(x0 > y0 ? rankx : ranky);
        ++(x0 > z0 ? rankx : rankz);
        ++(x0 > w0 ? rankx : rankw);
        ++(y0 > z0 ? ranky : rankz);
        ++(y0 > w0 ? ranky : rankw);
        ++(z0 > w0 ? rankz : 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 = 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);
    }

    // This is *not* in Stefan Gustavson's Java original
    // FIXME: what does it do?
    double fBM(double x, double y, double z, uint32_t octaves)
    {
        if (octaves < 1)
            return 0.0;
        if (octaves == 1)
            return noise(x, y, z);

        uint32_t divisor = 1;
        double norm = 0.0;
        double value = 0;
        double xi = x;
        double yi = y;
        double zi = z;
        for (uint32_t octave = 0; octave < octaves; ++octave)
        {
            value += noise(xi / divisor, yi / divisor, zi / divisor) / divisor;
            norm += 1 / divisor;
            divisor *= 2;
            double xt = yi * sin(1.41421356) + cos(1.41421356);
            yi = yi * cos(1.41421356) + sin(1.41421356);
            xi = xt;
            zi += 1.7;
        }
        return value / norm;
    }
}