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noise3.c
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#ifndef lint
static const char RCSid[] = "$Id: noise3.c,v 2.14 2018/11/21 20:23:15 greg Exp $";
#endif
/*
* noise3.c - noise functions for random textures.
*
* Credit for the smooth algorithm goes to Ken Perlin, and code
* translation/implementation to Rahul Narain.
* (ref. Improving Noise, Computer Graphics; Vol. 35 No. 3., 2002)
*/
#include "copyright.h"
#include "ray.h"
#include "func.h"
static char noise_name[4][8] = {"noise3x", "noise3y", "noise3z", "noise3"};
static char fnoise_name[] = "fnoise3";
#define EPSILON .0005 /* error allowed in fractal */
#define frand3(x,y,z) frand(17*(x)+23*(y)+29*(z))
static double l_noise3(char *nam);
static double noise3(double xnew[3], int i);
static double noise3partial(double f3, double x[3], int i);
static double perlin_noise (double x, double y, double z);
static double frand(long s);
static double fnoise3(double x[3]);
static double
l_noise3( /* compute a noise function */
char *nam
)
{
int i;
double x[3];
/* get point */
x[0] = argument(1);
x[1] = argument(2);
x[2] = argument(3);
/* make appropriate call */
if (nam == fnoise_name)
return(fnoise3(x));
i = 4;
while (i--)
if (nam == noise_name[i])
return(noise3(x,i));
eputs(nam);
eputs(": called l_noise3!\n");
quit(1);
return 1; /* pro forma return */
}
void
setnoisefuncs(void) /* add noise functions to library */
{
int i;
funset(fnoise_name, 3, ':', l_noise3);
i = 4;
while (i--)
funset(noise_name[i], 3, ':', l_noise3);
}
static double
frand( /* get random number from seed */
long s
)
{
s = s<<13 ^ s;
return(1.0-((s*(s*s*15731+789221)+1376312589)&0x7fffffff)/1073741824.0);
}
static double
fnoise3( /* compute fractal noise function */
double x[3]
)
{
long t[3], v[3], beg[3];
double fval[8], fc;
int branch;
long s;
int i, j;
/* get starting cube */
s = (long)(1.0/EPSILON);
for (i = 0; i < 3; i++) {
t[i] = s*x[i];
beg[i] = s*floor(x[i]);
}
for (j = 0; j < 8; j++) {
for (i = 0; i < 3; i++) {
v[i] = beg[i];
if (j & 1<<i)
v[i] += s;
}
fval[j] = frand3(v[0],v[1],v[2]);
}
/* compute fractal */
for ( ; ; ) {
fc = 0.0;
for (j = 0; j < 8; j++)
fc += fval[j];
fc *= 0.125;
if ((s >>= 1) == 0)
return(fc); /* close enough */
branch = 0;
for (i = 0; i < 3; i++) { /* do center */
v[i] = beg[i] + s;
if (t[i] > v[i]) {
branch |= 1<<i;
}
}
fc += s*EPSILON*frand3(v[0],v[1],v[2]);
fval[~branch & 7] = fc;
for (i = 0; i < 3; i++) { /* do faces */
if (branch & 1<<i)
v[i] += s;
else
v[i] -= s;
fc = 0.0;
for (j = 0; j < 8; j++)
if (~(j^branch) & 1<<i)
fc += fval[j];
fc = 0.25*fc + s*EPSILON*frand3(v[0],v[1],v[2]);
fval[~(branch^1<<i) & 7] = fc;
v[i] = beg[i] + s;
}
for (i = 0; i < 3; i++) { /* do edges */
if ((j = i+1) == 3) j = 0;
if (branch & 1<<j)
v[j] += s;
else
v[j] -= s;
if (++j == 3) j = 0;
if (branch & 1<<j)
v[j] += s;
else
v[j] -= s;
fc = fval[branch & ~(1<<i)];
fc += fval[branch | 1<<i];
fc = 0.5*fc + s*EPSILON*frand3(v[0],v[1],v[2]);
fval[branch^1<<i] = fc;
if ((j = i+1) == 3) j = 0;
v[j] = beg[j] + s;
if (++j == 3) j = 0;
v[j] = beg[j] + s;
}
for (i = 0; i < 3; i++) /* new cube */
if (branch & 1<<i)
beg[i] += s;
}
}
static double
noise3( /* compute the revised Perlin noise function */
double xnew[3], int i
)
{
static int gotV;
static double x[3];
static double f[4];
if (!gotV || xnew[0] != x[0] || (xnew[1] != x[1]) | (xnew[2] != x[2])) {
f[3] = perlin_noise(x[0]=xnew[0], x[1]=xnew[1], x[2]=xnew[2]);
gotV = 0x8;
}
if (!(gotV>>i & 1)) {
f[i] = noise3partial(f[3], x, i);
gotV |= 1<<i;
}
return(f[i]);
}
static double
noise3partial( /* compute partial derivative for ith coordinate */
double f3, double x[3], int i
)
{
double fc;
switch (i) {
case 0:
fc = perlin_noise(x[0]-EPSILON, x[1], x[2]);
break;
case 1:
fc = perlin_noise(x[0], x[1]-EPSILON, x[2]);
break;
case 2:
fc = perlin_noise(x[0], x[1], x[2]-EPSILON);
break;
default:
return(.0);
}
return((f3 - fc)/EPSILON);
}
#define fade(t) ((t)*(t)*(t)*((t)*((t)*6. - 15.) + 10.))
static double lerp(double t, double a, double b) {return a + t*(b - a);}
static double
grad(int hash, double x, double y, double z)
{
int h = hash & 15; // CONVERT LO 4 BITS OF HASH CODE
double u = h<8 ? x : y, // INTO 12 GRADIENT DIRECTIONS.
v = h<4 ? y : h==12|h==14 ? x : z;
return (!(h&1) ? u : -u) + (!(h&2) ? v : -v);
}
static const int permutation[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
};
#define p(i) permutation[(i)&0xff]
static double
perlin_noise(double x, double y, double z)
{
int X, Y, Z;
double u, v, w;
int A, AA, AB, B, BA, BB;
X = (int)x-(x<0); // FIND UNIT CUBE THAT
Y = (int)y-(y<0); // CONTAINS POINT.
Z = (int)z-(z<0);
x -= (double)X; // FIND RELATIVE X,Y,Z
y -= (double)Y; // OF POINT IN CUBE.
z -= (double)Z;
X &= 0xff; Y &= 0xff; Z &= 0xff;
u = fade(x); // COMPUTE FADE CURVES
v = fade(y); // FOR EACH OF X,Y,Z.
w = fade(z);
A = p(X )+Y; AA = p(A)+Z; AB = p(A+1)+Z; // HASH COORDINATES OF
B = p(X+1)+Y; BA = p(B)+Z; BB = p(B+1)+Z; // THE 8 CUBE CORNERS,
return lerp(w, lerp(v, lerp(u, grad(p(AA ), x , y , z ), // AND ADD
grad(p(BA ), x-1, y , z )), // BLENDED
lerp(u, grad(p(AB ), x , y-1, z ), // RESULTS
grad(p(BB ), x-1, y-1, z ))),// FROM 8
lerp(v, lerp(u, grad(p(AA+1), x , y , z-1), // CORNERS
grad(p(BA+1), x-1, y , z-1)), // OF CUBE
lerp(u, grad(p(AB+1), x , y-1, z-1),
grad(p(BB+1), x-1, y-1, z-1))));
}
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