perlin.c

/* Coherent noise function over 1, 2 or 3 dimensions */
/* (copyright Ken Perlin) */

#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "perlin.h"

static int p[B + B + 2];
static double g3[B + B + 2][3];
static double g2[B + B + 2][2];
static double g1[B + B + 2];
static int start = 1;

double noise1(double arg)
{
   int bx0, bx1;
   double rx0, rx1, sx, t, u, v, vec[1];

   vec[0] = arg;
   if (start) {
      start = 0;
      init();
   }

   setup(0,bx0,bx1,rx0,rx1);

   sx = s_curve(rx0);
   u = rx0 * g1[ p[ bx0 ] ];
   v = rx1 * g1[ p[ bx1 ] ];

   return(lerp(sx, u, v));
}

double noise2(double vec[2])
{
   int bx0, bx1, by0, by1, b00, b10, b01, b11;
   double rx0, rx1, ry0, ry1, *q, sx, sy, a, b, t, u, v;
   int i, j;

   if (start) {
      start = 0;
      init();
   }

   setup(0, bx0,bx1, rx0,rx1);
   setup(1, by0,by1, ry0,ry1);

   i = p[ bx0 ];
   j = p[ bx1 ];

   b00 = p[ i + by0 ];
   b10 = p[ j + by0 ];
   b01 = p[ i + by1 ];
   b11 = p[ j + by1 ];

   sx = s_curve(rx0);
   sy = s_curve(ry0);

   q = g2[ b00 ] ; u = at2(rx0,ry0);
   q = g2[ b10 ] ; v = at2(rx1,ry0);
   a = lerp(sx, u, v);

   q = g2[ b01 ] ; u = at2(rx0,ry1);
   q = g2[ b11 ] ; v = at2(rx1,ry1);
   b = lerp(sx, u, v);

   return lerp(sy, a, b);
}

double noise3(double vec[3])
{
   int bx0, bx1, by0, by1, bz0, bz1, b00, b10, b01, b11;
   double rx0, rx1, ry0, ry1, rz0, rz1, *q, sy, sz, a, b, c, d, t, u, v;
   int i, j;

   if (start) {
      start = 0;
      init();
   }

   setup(0, bx0,bx1, rx0,rx1);
   setup(1, by0,by1, ry0,ry1);
   setup(2, bz0,bz1, rz0,rz1);

   i = p[ bx0 ];
   j = p[ bx1 ];

   b00 = p[ i + by0 ];
   b10 = p[ j + by0 ];
   b01 = p[ i + by1 ];
   b11 = p[ j + by1 ];

   t  = s_curve(rx0);
   sy = s_curve(ry0);
   sz = s_curve(rz0);

   q = g3[ b00 + bz0 ] ; u = at3(rx0,ry0,rz0);
   q = g3[ b10 + bz0 ] ; v = at3(rx1,ry0,rz0);
   a = lerp(t, u, v);

   q = g3[ b01 + bz0 ] ; u = at3(rx0,ry1,rz0);
   q = g3[ b11 + bz0 ] ; v = at3(rx1,ry1,rz0);
   b = lerp(t, u, v);

   c = lerp(sy, a, b);

   q = g3[ b00 + bz1 ] ; u = at3(rx0,ry0,rz1);
   q = g3[ b10 + bz1 ] ; v = at3(rx1,ry0,rz1);
   a = lerp(t, u, v);

   q = g3[ b01 + bz1 ] ; u = at3(rx0,ry1,rz1);
   q = g3[ b11 + bz1 ] ; v = at3(rx1,ry1,rz1);
   b = lerp(t, u, v);

   d = lerp(sy, a, b);

   return lerp(sz, c, d);
}

void normalize2(double v[2])
{
   double s;

   s = sqrt(v[0] * v[0] + v[1] * v[1]);
   v[0] = v[0] / s;
   v[1] = v[1] / s;
}

void normalize3(double v[3])
{
   double s;

   s = sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
   v[0] = v[0] / s;
   v[1] = v[1] / s;
   v[2] = v[2] / s;
}

void init(void)
{
   int i, j, k;

   for (i = 0 ; i < B ; i++) {
      p[i] = i;
      g1[i] = (double)((random() % (B + B)) - B) / B;

      for (j = 0 ; j < 2 ; j++)
         g2[i][j] = (double)((random() % (B + B)) - B) / B;
      normalize2(g2[i]);

      for (j = 0 ; j < 3 ; j++)
         g3[i][j] = (double)((random() % (B + B)) - B) / B;
      normalize3(g3[i]);
   }

   while (--i) {
      k = p[i];
      p[i] = p[j = random() % B];
      p[j] = k;
   }

   for (i = 0 ; i < B + 2 ; i++) {
      p[B + i] = p[i];
      g1[B + i] = g1[i];
      for (j = 0 ; j < 2 ; j++)
         g2[B + i][j] = g2[i][j];
      for (j = 0 ; j < 3 ; j++)
         g3[B + i][j] = g3[i][j];
   }
}

/* --- My harmonic summing functions - PDB --------------------------*/

/*
   In what follows "alpha" is the weight when the sum is formed.
   Typically it is 2, As this approaches 1 the function is noisier.
   "beta" is the harmonic scaling/spacing, typically 2.
*/

double PerlinNoise1D(double x,double alpha,double beta,int n)
{
   int i;
   double val,sum = 0;
   double p,scale = 1;

   p = x;
   for (i=0;i<n;i++) {
      val = noise1(p);
      sum += val / scale;
      scale *= alpha;
      p *= beta;
   }
   return(sum);
}

double PerlinNoise2D(double x,double y,double alpha,double beta,int n)
{
   int i;
   double val,sum = 0;
   double p[2],scale = 1;

   p[0] = x;
   p[1] = y;
   for (i=0;i<n;i++) {
      val = noise2(p);
      sum += val / scale;
      scale *= alpha;
      p[0] *= beta;
      p[1] *= beta;
   }
   return(sum);
}

double PerlinNoise3D(double x,double y,double z,double alpha,double beta,int n)
{
   int i;
   double val,sum = 0;
   double p[3],scale = 1;

   p[0] = x;
   p[1] = y;
   p[2] = z;
   for (i=0;i<n;i++) {
      val = noise3(p);
      sum += val / scale;
      scale *= alpha;
      p[0] *= beta;
      p[1] *= beta;
      p[2] *= beta;
   }
   return(sum);
}