| 1 |
– |
/* Copyright (c) 1988 Regents of the University of California */ |
| 2 |
– |
|
| 1 |
|
#ifndef lint |
| 2 |
< |
static char SCCSid[] = "$SunId$ LBL"; |
| 2 |
> |
static const char RCSid[] = "$Id$"; |
| 3 |
|
#endif |
| 6 |
– |
|
| 4 |
|
/* |
| 5 |
|
* noise3.c - noise functions for random textures. |
| 6 |
|
* |
| 7 |
< |
* Credit for the smooth algorithm goes to Ken Perlin. |
| 8 |
< |
* (ref. SIGGRAPH Vol 19, No 3, pp 287-96) |
| 9 |
< |
* |
| 13 |
< |
* 4/15/86 |
| 14 |
< |
* 5/19/88 Added fractal noise function |
| 7 |
> |
* Credit for the smooth algorithm goes to Ken Perlin, and code |
| 8 |
> |
* translation/implementation to Rahul Narain. |
| 9 |
> |
* (ref. Improving Noise, Computer Graphics; Vol. 35 No. 3., 2002) |
| 10 |
|
*/ |
| 11 |
|
|
| 12 |
+ |
#include "copyright.h" |
| 13 |
|
|
| 14 |
< |
#define A 0 |
| 15 |
< |
#define B 1 |
| 20 |
< |
#define C 2 |
| 21 |
< |
#define D 3 |
| 14 |
> |
#include "ray.h" |
| 15 |
> |
#include "func.h" |
| 16 |
|
|
| 17 |
< |
#define rand3a(x,y,z) frand(67*(x)+59*(y)+71*(z)) |
| 18 |
< |
#define rand3b(x,y,z) frand(73*(x)+79*(y)+83*(z)) |
| 25 |
< |
#define rand3c(x,y,z) frand(89*(x)+97*(y)+101*(z)) |
| 26 |
< |
#define rand3d(x,y,z) frand(103*(x)+107*(y)+109*(z)) |
| 17 |
> |
static char noise_name[4][8] = {"noise3x", "noise3y", "noise3z", "noise3"}; |
| 18 |
> |
static char fnoise_name[] = "fnoise3"; |
| 19 |
|
|
| 20 |
< |
#define hermite(p0,p1,r0,r1,t) ( p0*((2.0*t-3.0)*t*t+1.0) + \ |
| 29 |
< |
p1*(-2.0*t+3.0)*t*t + \ |
| 30 |
< |
r0*((t-2.0)*t+1.0)*t + \ |
| 31 |
< |
r1*(t-1.0)*t*t ) |
| 20 |
> |
#define EPSILON .0005 /* error allowed in fractal */ |
| 21 |
|
|
| 33 |
– |
double *noise3(), noise3coef(), argument(), frand(); |
| 34 |
– |
|
| 35 |
– |
static long xlim[3][2]; |
| 36 |
– |
static double xarg[3]; |
| 37 |
– |
|
| 38 |
– |
#define EPSILON .0001 /* error allowed in fractal */ |
| 39 |
– |
|
| 22 |
|
#define frand3(x,y,z) frand(17*(x)+23*(y)+29*(z)) |
| 23 |
|
|
| 24 |
< |
double fnoise3(); |
| 24 |
> |
static double l_noise3(char *nam); |
| 25 |
> |
static double noise3(double xnew[3], int i); |
| 26 |
> |
static double noise3partial(double f3, double x[3], int i); |
| 27 |
> |
static double perlin_noise (double x, double y, double z); |
| 28 |
> |
static double frand(long s); |
| 29 |
> |
static double fnoise3(double x[3]); |
| 30 |
|
|
| 31 |
|
|
| 45 |
– |
double |
| 46 |
– |
l_noise3() /* compute 3-dimensional noise function */ |
| 47 |
– |
{ |
| 48 |
– |
return(noise3coef(D)); |
| 49 |
– |
} |
| 50 |
– |
|
| 51 |
– |
|
| 52 |
– |
double |
| 53 |
– |
l_noise3a() /* compute x slope of noise function */ |
| 54 |
– |
{ |
| 55 |
– |
return(noise3coef(A)); |
| 56 |
– |
} |
| 57 |
– |
|
| 58 |
– |
|
| 59 |
– |
double |
| 60 |
– |
l_noise3b() /* compute y slope of noise function */ |
| 61 |
– |
{ |
| 62 |
– |
return(noise3coef(B)); |
| 63 |
– |
} |
| 64 |
– |
|
| 65 |
– |
|
| 66 |
– |
double |
| 67 |
– |
l_noise3c() /* compute z slope of noise function */ |
| 68 |
– |
{ |
| 69 |
– |
return(noise3coef(C)); |
| 70 |
– |
} |
| 71 |
– |
|
| 72 |
– |
|
| 73 |
– |
double |
| 74 |
– |
l_fnoise3() /* compute fractal noise function */ |
| 75 |
– |
{ |
| 76 |
– |
double x[3]; |
| 77 |
– |
|
| 78 |
– |
x[0] = argument(1); |
| 79 |
– |
x[1] = argument(2); |
| 80 |
– |
x[2] = argument(3); |
| 81 |
– |
|
| 82 |
– |
return(fnoise3(x)); |
| 83 |
– |
} |
| 84 |
– |
|
| 85 |
– |
|
| 32 |
|
static double |
| 33 |
< |
noise3coef(coef) /* return coefficient of noise function */ |
| 34 |
< |
int coef; |
| 33 |
> |
l_noise3( /* compute a noise function */ |
| 34 |
> |
char *nam |
| 35 |
> |
) |
| 36 |
|
{ |
| 37 |
+ |
int i; |
| 38 |
|
double x[3]; |
| 39 |
< |
|
| 39 |
> |
/* get point */ |
| 40 |
|
x[0] = argument(1); |
| 41 |
|
x[1] = argument(2); |
| 42 |
|
x[2] = argument(3); |
| 43 |
< |
|
| 44 |
< |
return(noise3(x)[coef]); |
| 43 |
> |
/* make appropriate call */ |
| 44 |
> |
if (nam == fnoise_name) |
| 45 |
> |
return(fnoise3(x)); |
| 46 |
> |
i = 4; |
| 47 |
> |
while (i--) |
| 48 |
> |
if (nam == noise_name[i]) |
| 49 |
> |
return(noise3(x,i)); |
| 50 |
> |
eputs(nam); |
| 51 |
> |
eputs(": called l_noise3!\n"); |
| 52 |
> |
quit(1); |
| 53 |
> |
return 1; /* pro forma return */ |
| 54 |
|
} |
| 55 |
|
|
| 56 |
|
|
| 57 |
< |
double * |
| 58 |
< |
noise3(xnew) /* compute the noise function */ |
| 102 |
< |
register double xnew[3]; |
| 57 |
> |
void |
| 58 |
> |
setnoisefuncs(void) /* add noise functions to library */ |
| 59 |
|
{ |
| 60 |
< |
extern double floor(); |
| 105 |
< |
static double x[3] = {-100000.0, -100000.0, -100000.0}; |
| 106 |
< |
static double f[4]; |
| 60 |
> |
int i; |
| 61 |
|
|
| 62 |
< |
if (x[0]==xnew[0] && x[1]==xnew[1] && x[2]==xnew[2]) |
| 63 |
< |
return(f); |
| 64 |
< |
x[0] = xnew[0]; x[1] = xnew[1]; x[2] = xnew[2]; |
| 65 |
< |
xlim[0][0] = floor(x[0]); xlim[0][1] = xlim[0][0] + 1; |
| 112 |
< |
xlim[1][0] = floor(x[1]); xlim[1][1] = xlim[1][0] + 1; |
| 113 |
< |
xlim[2][0] = floor(x[2]); xlim[2][1] = xlim[2][0] + 1; |
| 114 |
< |
xarg[0] = x[0] - xlim[0][0]; |
| 115 |
< |
xarg[1] = x[1] - xlim[1][0]; |
| 116 |
< |
xarg[2] = x[2] - xlim[2][0]; |
| 117 |
< |
interpolate(f, 0, 3); |
| 118 |
< |
return(f); |
| 62 |
> |
funset(fnoise_name, 3, ':', l_noise3); |
| 63 |
> |
i = 4; |
| 64 |
> |
while (i--) |
| 65 |
> |
funset(noise_name[i], 3, ':', l_noise3); |
| 66 |
|
} |
| 67 |
|
|
| 68 |
|
|
| 69 |
< |
static |
| 70 |
< |
interpolate(f, i, n) |
| 71 |
< |
double f[4]; |
| 72 |
< |
register int i, n; |
| 69 |
> |
static double |
| 70 |
> |
frand( /* get random number from seed */ |
| 71 |
> |
long s |
| 72 |
> |
) |
| 73 |
|
{ |
| 127 |
– |
double f0[4], f1[4]; |
| 128 |
– |
|
| 129 |
– |
if (n == 0) { |
| 130 |
– |
f[A] = rand3a(xlim[0][i&1],xlim[1][i>>1&1],xlim[2][i>>2]); |
| 131 |
– |
f[B] = rand3b(xlim[0][i&1],xlim[1][i>>1&1],xlim[2][i>>2]); |
| 132 |
– |
f[C] = rand3c(xlim[0][i&1],xlim[1][i>>1&1],xlim[2][i>>2]); |
| 133 |
– |
f[D] = rand3d(xlim[0][i&1],xlim[1][i>>1&1],xlim[2][i>>2]); |
| 134 |
– |
} else { |
| 135 |
– |
n--; |
| 136 |
– |
interpolate(f0, i, n); |
| 137 |
– |
interpolate(f1, i | 1<<n, n); |
| 138 |
– |
f[A] = (1.0-xarg[n])*f0[A] + xarg[n]*f1[A]; |
| 139 |
– |
f[B] = (1.0-xarg[n])*f0[B] + xarg[n]*f1[B]; |
| 140 |
– |
f[C] = (1.0-xarg[n])*f0[C] + xarg[n]*f1[C]; |
| 141 |
– |
f[D] = hermite(f0[D], f1[D], f0[n], f1[n], xarg[n]); |
| 142 |
– |
} |
| 143 |
– |
} |
| 144 |
– |
|
| 145 |
– |
|
| 146 |
– |
double |
| 147 |
– |
frand(s) /* get random number from seed */ |
| 148 |
– |
register long s; |
| 149 |
– |
{ |
| 74 |
|
s = s<<13 ^ s; |
| 75 |
|
return(1.0-((s*(s*s*15731+789221)+1376312589)&0x7fffffff)/1073741824.0); |
| 76 |
|
} |
| 77 |
|
|
| 78 |
|
|
| 79 |
< |
double |
| 80 |
< |
l_hermite() /* library call for hermite interpolation */ |
| 79 |
> |
static double |
| 80 |
> |
fnoise3( /* compute fractal noise function */ |
| 81 |
> |
double x[3] |
| 82 |
> |
) |
| 83 |
|
{ |
| 84 |
< |
double t; |
| 159 |
< |
|
| 160 |
< |
t = argument(5); |
| 161 |
< |
return( hermite(argument(1), argument(2), |
| 162 |
< |
argument(3), argument(4), t) ); |
| 163 |
< |
} |
| 164 |
< |
|
| 165 |
< |
|
| 166 |
< |
double |
| 167 |
< |
fnoise3(p) /* compute fractal noise function */ |
| 168 |
< |
double p[3]; |
| 169 |
< |
{ |
| 170 |
< |
double floor(); |
| 171 |
< |
long t[3], v[3], beg[3], s; |
| 84 |
> |
long t[3], v[3], beg[3]; |
| 85 |
|
double fval[8], fc; |
| 86 |
|
int branch; |
| 87 |
< |
register int i, j; |
| 87 |
> |
long s; |
| 88 |
> |
int i, j; |
| 89 |
|
/* get starting cube */ |
| 90 |
|
s = (long)(1.0/EPSILON); |
| 91 |
|
for (i = 0; i < 3; i++) { |
| 92 |
< |
t[i] = s*p[i]; |
| 93 |
< |
beg[i] = s*floor(p[i]); |
| 92 |
> |
t[i] = s*x[i]; |
| 93 |
> |
beg[i] = s*floor(x[i]); |
| 94 |
|
} |
| 95 |
|
for (j = 0; j < 8; j++) { |
| 96 |
|
for (i = 0; i < 3; i++) { |
| 102 |
|
} |
| 103 |
|
/* compute fractal */ |
| 104 |
|
for ( ; ; ) { |
| 105 |
< |
s >>= 1; |
| 105 |
> |
fc = 0.0; |
| 106 |
> |
for (j = 0; j < 8; j++) |
| 107 |
> |
fc += fval[j]; |
| 108 |
> |
fc *= 0.125; |
| 109 |
> |
if ((s >>= 1) == 0) |
| 110 |
> |
return(fc); /* close enough */ |
| 111 |
|
branch = 0; |
| 112 |
|
for (i = 0; i < 3; i++) { /* do center */ |
| 113 |
|
v[i] = beg[i] + s; |
| 115 |
|
branch |= 1<<i; |
| 116 |
|
} |
| 117 |
|
} |
| 199 |
– |
fc = 0.0; |
| 200 |
– |
for (j = 0; j < 8; j++) |
| 201 |
– |
fc += fval[j]; |
| 202 |
– |
fc *= 0.125; |
| 203 |
– |
if (s < 1) |
| 204 |
– |
return(fc); /* close enough */ |
| 118 |
|
fc += s*EPSILON*frand3(v[0],v[1],v[2]); |
| 119 |
|
fval[~branch & 7] = fc; |
| 120 |
|
for (i = 0; i < 3; i++) { /* do faces */ |
| 131 |
|
v[i] = beg[i] + s; |
| 132 |
|
} |
| 133 |
|
for (i = 0; i < 3; i++) { /* do edges */ |
| 134 |
< |
j = (i+1)%3; |
| 134 |
> |
if ((j = i+1) == 3) j = 0; |
| 135 |
|
if (branch & 1<<j) |
| 136 |
|
v[j] += s; |
| 137 |
|
else |
| 138 |
|
v[j] -= s; |
| 139 |
< |
j = (i+2)%3; |
| 139 |
> |
if (++j == 3) j = 0; |
| 140 |
|
if (branch & 1<<j) |
| 141 |
|
v[j] += s; |
| 142 |
|
else |
| 145 |
|
fc += fval[branch | 1<<i]; |
| 146 |
|
fc = 0.5*fc + s*EPSILON*frand3(v[0],v[1],v[2]); |
| 147 |
|
fval[branch^1<<i] = fc; |
| 148 |
< |
j = (i+1)%3; |
| 148 |
> |
if ((j = i+1) == 3) j = 0; |
| 149 |
|
v[j] = beg[j] + s; |
| 150 |
< |
j = (i+2)%3; |
| 150 |
> |
if (++j == 3) j = 0; |
| 151 |
|
v[j] = beg[j] + s; |
| 152 |
|
} |
| 153 |
|
for (i = 0; i < 3; i++) /* new cube */ |
| 154 |
|
if (branch & 1<<i) |
| 155 |
|
beg[i] += s; |
| 156 |
|
} |
| 157 |
+ |
} |
| 158 |
+ |
|
| 159 |
+ |
|
| 160 |
+ |
static double |
| 161 |
+ |
noise3( /* compute the revised Perlin noise function */ |
| 162 |
+ |
double xnew[3], int i |
| 163 |
+ |
) |
| 164 |
+ |
{ |
| 165 |
+ |
static int gotV; |
| 166 |
+ |
static double x[3]; |
| 167 |
+ |
static double f[4]; |
| 168 |
+ |
|
| 169 |
+ |
if (gotV && x[0]==xnew[0] && (x[1]==xnew[1]) & (x[2]==xnew[2])) { |
| 170 |
+ |
if (!(gotV>>i & 1)) { |
| 171 |
+ |
f[i] = noise3partial(f[3], x, i); |
| 172 |
+ |
gotV |= 1<<i; |
| 173 |
+ |
} |
| 174 |
+ |
return(f[i]); |
| 175 |
+ |
} |
| 176 |
+ |
gotV = 0x8; |
| 177 |
+ |
return(f[3] = perlin_noise(x[0]=xnew[0], x[1]=xnew[1], x[2]=xnew[2])); |
| 178 |
+ |
} |
| 179 |
+ |
|
| 180 |
+ |
static double |
| 181 |
+ |
noise3partial( /* compute partial derivative for ith coordinate */ |
| 182 |
+ |
double f3, double x[3], int i |
| 183 |
+ |
) |
| 184 |
+ |
{ |
| 185 |
+ |
double fc; |
| 186 |
+ |
|
| 187 |
+ |
switch (i) { |
| 188 |
+ |
case 0: |
| 189 |
+ |
fc = perlin_noise(x[0]-EPSILON, x[1], x[2]); |
| 190 |
+ |
break; |
| 191 |
+ |
case 1: |
| 192 |
+ |
fc = perlin_noise(x[0], x[1]-EPSILON, x[2]); |
| 193 |
+ |
break; |
| 194 |
+ |
case 2: |
| 195 |
+ |
fc = perlin_noise(x[0], x[1], x[2]-EPSILON); |
| 196 |
+ |
break; |
| 197 |
+ |
default: |
| 198 |
+ |
return(.0); |
| 199 |
+ |
} |
| 200 |
+ |
return((f3 - fc)/EPSILON); |
| 201 |
+ |
} |
| 202 |
+ |
|
| 203 |
+ |
#define fade(t) ((t)*(t)*(t)*((t)*((t)*6. - 15.) + 10.)) |
| 204 |
+ |
|
| 205 |
+ |
static double lerp(double t, double a, double b) {return a + t*(b - a);} |
| 206 |
+ |
|
| 207 |
+ |
static double |
| 208 |
+ |
grad(int hash, double x, double y, double z) |
| 209 |
+ |
{ |
| 210 |
+ |
int h = hash & 15; // CONVERT LO 4 BITS OF HASH CODE |
| 211 |
+ |
double u = h<8 ? x : y, // INTO 12 GRADIENT DIRECTIONS. |
| 212 |
+ |
v = h<4 ? y : h==12|h==14 ? x : z; |
| 213 |
+ |
return (!(h&1) ? u : -u) + (!(h&2) ? v : -v); |
| 214 |
+ |
} |
| 215 |
+ |
|
| 216 |
+ |
static const int permutation[256] = {151,160,137,91,90,15, |
| 217 |
+ |
131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23, |
| 218 |
+ |
190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33, |
| 219 |
+ |
88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166, |
| 220 |
+ |
77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244, |
| 221 |
+ |
102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196, |
| 222 |
+ |
135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123, |
| 223 |
+ |
5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42, |
| 224 |
+ |
223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9, |
| 225 |
+ |
129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228, |
| 226 |
+ |
251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107, |
| 227 |
+ |
49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254, |
| 228 |
+ |
138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180 |
| 229 |
+ |
}; |
| 230 |
+ |
|
| 231 |
+ |
#define p(i) permutation[(i)&0xff] |
| 232 |
+ |
|
| 233 |
+ |
static double |
| 234 |
+ |
perlin_noise(double x, double y, double z) |
| 235 |
+ |
{ |
| 236 |
+ |
int X, Y, Z; |
| 237 |
+ |
double u, v, w; |
| 238 |
+ |
int A, AA, AB, B, BA, BB; |
| 239 |
+ |
|
| 240 |
+ |
X = (int)x-(x<0); // FIND UNIT CUBE THAT |
| 241 |
+ |
Y = (int)y-(y<0); // CONTAINS POINT. |
| 242 |
+ |
Z = (int)z-(z<0); |
| 243 |
+ |
x -= (double)X; // FIND RELATIVE X,Y,Z |
| 244 |
+ |
y -= (double)Y; // OF POINT IN CUBE. |
| 245 |
+ |
z -= (double)Z; |
| 246 |
+ |
X &= 0xff; Y &= 0xff; Z &= 0xff; |
| 247 |
+ |
|
| 248 |
+ |
u = fade(x); // COMPUTE FADE CURVES |
| 249 |
+ |
v = fade(y); // FOR EACH OF X,Y,Z. |
| 250 |
+ |
w = fade(z); |
| 251 |
+ |
|
| 252 |
+ |
A = p(X )+Y; AA = p(A)+Z; AB = p(A+1)+Z; // HASH COORDINATES OF |
| 253 |
+ |
B = p(X+1)+Y; BA = p(B)+Z; BB = p(B+1)+Z; // THE 8 CUBE CORNERS, |
| 254 |
+ |
|
| 255 |
+ |
return lerp(w, lerp(v, lerp(u, grad(p(AA ), x , y , z ), // AND ADD |
| 256 |
+ |
grad(p(BA ), x-1, y , z )), // BLENDED |
| 257 |
+ |
lerp(u, grad(p(AB ), x , y-1, z ), // RESULTS |
| 258 |
+ |
grad(p(BB ), x-1, y-1, z ))),// FROM 8 |
| 259 |
+ |
lerp(v, lerp(u, grad(p(AA+1), x , y , z-1), // CORNERS |
| 260 |
+ |
grad(p(BA+1), x-1, y , z-1)), // OF CUBE |
| 261 |
+ |
lerp(u, grad(p(AB+1), x , y-1, z-1), |
| 262 |
+ |
grad(p(BB+1), x-1, y-1, z-1)))); |
| 263 |
|
} |
