prosperon/source/engine/simplex.c

/*

C source for simplex noise generation, 
Original Java Source from: http://staffwww.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf
Published originally as a Garrysmod Lua Extension under the pseudonym Levybreak

*/

#include <math.h>
#include "simplex.h"

double Noise(genericNoise func, int len, double inputs[])
{
    switch (len){
        case 2:
            return func.p2(inputs[0], inputs[1]);
        case 3:
            return func.p3(inputs[0], inputs[1], inputs[2]);
        case 4:
            return func.p4(inputs[0], inputs[1], inputs[2], inputs[3]);
        default:
            return func.pn(len, inputs);
    }
}

double TurbulentNoise(genericNoise func, int dir, int iter, int len, double inputs[])
{
    double ret = fabs(Noise(func, len, inputs));

    int i = 0;
    for (i = 0 ; i < iter ; i++){
        double num = pow(2,iter);
        double scaled[len];
        int j = 0;
        for (j = 0; j < len; j++) {
            scaled[j] = inputs[len]*(num/i);
        }
        ret = ret + (i/num)*fabs(Noise(func, len, scaled));
    }
    
    return (double)sin(inputs[dir]+ret);
}

double FractalSumNoise(genericNoise func, int iter, int len, double inputs[])
{
    double ret = Noise(func, len, inputs);

    int i = 0;
    for (i = 0 ; i < iter ; i++){
        double num = pow(2,iter);
        double scaled[len];
        int j = 0;
        for (j = 0; j < len; j++) {
            scaled[j] = inputs[len]*(num/i);
        }
        ret = ret + (i/num)*(Noise(func, len, scaled));
    }
    
    return ret;
}

double FractalSumAbsNoise(genericNoise func, int iter, int len, double inputs[])
{
    double ret = fabs(Noise(func, len, inputs));

    int i = 0;
    for (i = 0 ; i < iter ; i++){
        double num = pow(2,iter);
        double scaled[len];
        int j = 0;
        for (j = 0; j < len; j++) {
            scaled[j] = inputs[len]*(num/i);
        }
        ret = ret + (i/num)*fabs(Noise(func, len, scaled));
    }
    
    return ret;
}


int gradients3d[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}};
int gradients4d[32][4] = {{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}};
int p[256] = {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};

int perm[512];

static void con() __attribute__((constructor));

void con() {
    int i = 0;
    for (i = 0 ; i < 255 ; i++) {
        perm[i] = p[i];
        perm[i+256] = p[i];
    }
}


int simplex[64][4] = {
{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}};

const double e = 2.71828182845904523536;
const double PI = 3.14159265358979323846;

double Dot2D(int tbl[],double x,double y)
{
    return tbl[0]*x + tbl[1]*y; 
}

double Dot3D(int tbl[],double x,double y,double z)
{
    return tbl[0]*x + tbl[1]*y + tbl[2]*z;
}

double Dot4D(int tbl[],double x,double y,double z,double w) 
{
    return tbl[0]*x + tbl[1]*y + tbl[2]*z + tbl[3]*w;
}

double Noise2D(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 F2 = 0.5*(sqrt(3.0)-1.0);
    double s = (xin+yin)*F2; // Hairy factor for 2D
    int i = floor(xin+s);
    int j = floor(yin+s);
    double G2 = (3.0-sqrt(3.0))/6.0;
    
    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 * t0;
        n0 = t0 * t0 * Dot2D(gradients3d[gi0], x0, y0); // (x,y) of Gradients3D used for 2D gradient
    }
    
    double t1 = 0.5 - x1*x1-y1*y1;
    if (t1<0){
        n1 = 0.0;
    }
    else{
        t1 = t1*t1;
        n1 = t1 * t1 * Dot2D(gradients3d[gi1], x1, y1);
    }
    
    double t2 = 0.5 - x2*x2-y2*y2;
    if (t2<0){
        n2 = 0.0;
    }
    else{
        t2 = t2*t2;
        n2 = t2 * t2 * Dot2D(gradients3d[gi2], x2, y2);
    }
    
    // Add contributions from each corner to get the final noise value.
    // The result is scaled to return values in the localerval [-1,1].
    double ret = (70.0 * (n0 + n1 + n2));

    return ret;
}

double Noise3D(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 F3 = 1.0/3.0;
    double s = (xin+yin+zin)*F3; // Very nice and simple skew factor for 3D
    int i = floor(xin+s);
    int j = floor(yin+s);
    int k = floor(zin+s);
    
    double G3 = 1.0/6.0; // Very nice and simple unskew factor, too
    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 = 0.5 - x0*x0 - y0*y0 - z0*z0;
    
    if (t0<0){
        n0 = 0.0;
    }
    else {
        t0 = t0*t0;
        n0 = t0 * t0 * Dot3D(gradients3d[gi0], x0, y0, z0);
    }
    
    double t1 = 0.5 - x1*x1 - y1*y1 - z1*z1;
    
    if (t1<0){ 
        n1 = 0.0;
    }
    else{
        t1 = t1*t1;
        n1 = t1 * t1 * Dot3D(gradients3d[gi1], x1, y1, z1);
    }
    
    double t2 = 0.5 - x2*x2 - y2*y2 - z2*z2;
    
    if (t2<0){
        n2 = 0.0;
    }
    else{
        t2 = t2*t2;
        n2 = t2 * t2 * Dot3D(gradients3d[gi2], x2, y2, z2);
    }
    
    double t3 = 0.5 - x3*x3 - y3*y3 - z3*z3;
    
    if (t3<0){
        n3 = 0.0;
    }
    else{
        t3 = t3*t3;
        n3 = t3 * t3 * Dot3D(gradients3d[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]
    double retval = 32.0*(n0 + n1 + n2 + n3);
    
    return retval;
}

double Noise4D(double x,double y,double z,double w)
{
    // The skewing and unskewing factors are hairy again for the 4D case
    double F4 = (sqrt(5.0)-1.0)/4.0;
    double G4 = (5.0-sqrt(5.0))/20.0;
    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 = floor(x + s);
    int j = floor(y + s);
    int k = floor(z + s);
    int l = floor(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.
    // 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 localeger index.
    int c1 = (x0 > y0) ? 32 : 1;
    int c2 = (x0 > z0) ? 16 : 1;
    int c3 = (y0 > z0) ? 8 : 1;
    int c4 = (x0 > w0) ? 4 : 1;
    int c5 = (y0 > w0) ? 2 : 1;
    int c6 = (z0 > w0) ? 1 : 1;
    int c = c1 + c2 + c3 + c4 + c5 + c6;
    int i1, j1, k1, l1; // The localeger offsets for the second simplex corner
    int i2, j2, k2, l2; // The localeger offsets for the third simplex corner
    int i3, j3, k3, l3; // The localeger 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 co:dinate.
    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 co:dinate.
    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 + 3.0*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 = 0.5 - x0*x0 - y0*y0 - z0*z0 - w0*w0;
    if (t0<0){
        n0 = 0.0;
    }
    else{
        t0 = t0*t0;
        n0 = t0 * t0 * Dot4D(gradients4d[gi0], x0, y0, z0, w0);
    }
    
    double t1 = 0.5 - x1*x1 - y1*y1 - z1*z1 - w1*w1;
    if (t1<0){
        n1 = 0.0;
    }
    else{
        t1 = t1*t1;
        n1 = t1 * t1 * Dot4D(gradients4d[gi1], x1, y1, z1, w1);
    }
    
    double t2 = 0.5 - x2*x2 - y2*y2 - z2*z2 - w2*w2;
    if (t2<0){
        n2 = 0.0;
    }
    else{
        t2 = t2*t2;
        n2 = t2 * t2 * Dot4D(gradients4d[gi2], x2, y2, z2, w2);
    }
    
    double t3 = 0.5 - x3*x3 - y3*y3 - z3*z3 - w3*w3;
    if (t3<0){
        n3 = 0.0;
    }
    else {
        t3 = t3*t3;
        n3 = t3 * t3 * Dot4D(gradients4d[gi3], x3, y3, z3, w3);
    }
    
    double t4 = 0.5 - x4*x4 - y4*y4 - z4*z4 - w4*w4;
    if (t4<0){
        n4 = 0.0;
    }
    else{
        t4 = t4*t4;
        n4 = t4 * t4 * Dot4D(gradients4d[gi4], x4, y4, z4, w4);
    }
    
    // Sum up and scale the result to cover the range [-1,1]
    
    double retval = 27.0 * (n0 + n1 + n2 + n3 + n4);
    
    return retval;
}

double GBlur2D(double stdDev, double x, double y)
{
    if (fabs(stdDev)<=0.0) { return 0; }
    
    double pwr = ((pow(x,2)+pow(y,2))/(2*pow(stdDev,2)))*-1;
    double ret = (1/(2*PI*pow(stdDev,2)))*pow(e, pwr);
    
    return ret;
}


double GBlur1D(double stdDev, double x)
{
    if (fabs(stdDev)<=0.0) { return 0; }
    
    double pwr = (pow(x,2)/(2*pow(stdDev,2)))*-1;
    double ret = (1/(sqrt(2*PI)*stdDev))*pow(e, pwr);

    return ret;
}

double octave_3d(double x, double y, double z, int octaves, double persistence)
{
  double total = 0;
  double frequency = 1;
  double amplitude = 1;
  double max = 0;
  for (int i = 0; i < octaves; i++) {
    total += Noise3D(x*frequency, y*frequency, z*frequency) * amplitude;
    max += amplitude;
    amplitude *= persistence;
    frequency *= 2;
  }
  return total/max;
}