1 |
#ifndef lint |
2 |
static const char RCSid[] = "$Id: noise3.c,v 2.7 2003/02/25 02:47:22 greg Exp $"; |
3 |
#endif |
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 |
*/ |
10 |
|
11 |
#include "copyright.h" |
12 |
|
13 |
#include "calcomp.h" |
14 |
|
15 |
#include <math.h> |
16 |
|
17 |
#define A 0 |
18 |
#define B 1 |
19 |
#define C 2 |
20 |
#define D 3 |
21 |
|
22 |
#define rand3a(x,y,z) frand(67*(x)+59*(y)+71*(z)) |
23 |
#define rand3b(x,y,z) frand(73*(x)+79*(y)+83*(z)) |
24 |
#define rand3c(x,y,z) frand(89*(x)+97*(y)+101*(z)) |
25 |
#define rand3d(x,y,z) frand(103*(x)+107*(y)+109*(z)) |
26 |
|
27 |
#define hpoly1(t) ((2.0*t-3.0)*t*t+1.0) |
28 |
#define hpoly2(t) (-2.0*t+3.0)*t*t |
29 |
#define hpoly3(t) ((t-2.0)*t+1.0)*t |
30 |
#define hpoly4(t) (t-1.0)*t*t |
31 |
|
32 |
#define hermite(p0,p1,r0,r1,t) ( p0*hpoly1(t) + \ |
33 |
p1*hpoly2(t) + \ |
34 |
r0*hpoly3(t) + \ |
35 |
r1*hpoly4(t) ) |
36 |
|
37 |
static char noise_name[4][8] = {"noise3x", "noise3y", "noise3z", "noise3"}; |
38 |
static char fnoise_name[] = "fnoise3"; |
39 |
static char hermite_name[] = "hermite"; |
40 |
|
41 |
double *noise3(), fnoise3(), frand(); |
42 |
static interpolate(); |
43 |
|
44 |
static long xlim[3][2]; |
45 |
static double xarg[3]; |
46 |
|
47 |
#define EPSILON .001 /* error allowed in fractal */ |
48 |
|
49 |
#define frand3(x,y,z) frand(17*(x)+23*(y)+29*(z)) |
50 |
|
51 |
|
52 |
static double |
53 |
l_noise3(nam) /* compute a noise function */ |
54 |
register char *nam; |
55 |
{ |
56 |
register int i; |
57 |
double x[3]; |
58 |
/* get point */ |
59 |
x[0] = argument(1); |
60 |
x[1] = argument(2); |
61 |
x[2] = argument(3); |
62 |
/* make appropriate call */ |
63 |
if (nam == fnoise_name) |
64 |
return(fnoise3(x)); |
65 |
i = 4; |
66 |
while (i--) |
67 |
if (nam == noise_name[i]) |
68 |
return(noise3(x)[i]); |
69 |
eputs(nam); |
70 |
eputs(": called l_noise3!\n"); |
71 |
quit(1); |
72 |
} |
73 |
|
74 |
|
75 |
double |
76 |
l_hermite(char *nm) /* library call for hermite interpolation */ |
77 |
{ |
78 |
double t; |
79 |
|
80 |
t = argument(5); |
81 |
return( hermite(argument(1), argument(2), |
82 |
argument(3), argument(4), t) ); |
83 |
} |
84 |
|
85 |
|
86 |
setnoisefuncs() /* add noise functions to library */ |
87 |
{ |
88 |
register int i; |
89 |
|
90 |
funset(hermite_name, 5, ':', l_hermite); |
91 |
funset(fnoise_name, 3, ':', l_noise3); |
92 |
i = 4; |
93 |
while (i--) |
94 |
funset(noise_name[i], 3, ':', l_noise3); |
95 |
} |
96 |
|
97 |
|
98 |
double * |
99 |
noise3(xnew) /* compute the noise function */ |
100 |
register double xnew[3]; |
101 |
{ |
102 |
static double x[3] = {-100000.0, -100000.0, -100000.0}; |
103 |
static double f[4]; |
104 |
|
105 |
if (x[0]==xnew[0] && x[1]==xnew[1] && x[2]==xnew[2]) |
106 |
return(f); |
107 |
x[0] = xnew[0]; x[1] = xnew[1]; x[2] = xnew[2]; |
108 |
xlim[0][0] = floor(x[0]); xlim[0][1] = xlim[0][0] + 1; |
109 |
xlim[1][0] = floor(x[1]); xlim[1][1] = xlim[1][0] + 1; |
110 |
xlim[2][0] = floor(x[2]); xlim[2][1] = xlim[2][0] + 1; |
111 |
xarg[0] = x[0] - xlim[0][0]; |
112 |
xarg[1] = x[1] - xlim[1][0]; |
113 |
xarg[2] = x[2] - xlim[2][0]; |
114 |
interpolate(f, 0, 3); |
115 |
return(f); |
116 |
} |
117 |
|
118 |
|
119 |
static |
120 |
interpolate(f, i, n) |
121 |
double f[4]; |
122 |
register int i, n; |
123 |
{ |
124 |
double f0[4], f1[4], hp1, hp2; |
125 |
|
126 |
if (n == 0) { |
127 |
f[A] = rand3a(xlim[0][i&1],xlim[1][i>>1&1],xlim[2][i>>2]); |
128 |
f[B] = rand3b(xlim[0][i&1],xlim[1][i>>1&1],xlim[2][i>>2]); |
129 |
f[C] = rand3c(xlim[0][i&1],xlim[1][i>>1&1],xlim[2][i>>2]); |
130 |
f[D] = rand3d(xlim[0][i&1],xlim[1][i>>1&1],xlim[2][i>>2]); |
131 |
} else { |
132 |
n--; |
133 |
interpolate(f0, i, n); |
134 |
interpolate(f1, i | 1<<n, n); |
135 |
hp1 = hpoly1(xarg[n]); hp2 = hpoly2(xarg[n]); |
136 |
f[A] = f0[A]*hp1 + f1[A]*hp2; |
137 |
f[B] = f0[B]*hp1 + f1[B]*hp2; |
138 |
f[C] = f0[C]*hp1 + f1[C]*hp2; |
139 |
f[D] = f0[D]*hp1 + f1[D]*hp2 + |
140 |
f0[n]*hpoly3(xarg[n]) + f1[n]*hpoly4(xarg[n]); |
141 |
} |
142 |
} |
143 |
|
144 |
|
145 |
double |
146 |
frand(s) /* get random number from seed */ |
147 |
register long s; |
148 |
{ |
149 |
s = s<<13 ^ s; |
150 |
return(1.0-((s*(s*s*15731+789221)+1376312589)&0x7fffffff)/1073741824.0); |
151 |
} |
152 |
|
153 |
|
154 |
double |
155 |
fnoise3(p) /* compute fractal noise function */ |
156 |
double p[3]; |
157 |
{ |
158 |
long t[3], v[3], beg[3]; |
159 |
double fval[8], fc; |
160 |
int branch; |
161 |
register long s; |
162 |
register int i, j; |
163 |
/* get starting cube */ |
164 |
s = (long)(1.0/EPSILON); |
165 |
for (i = 0; i < 3; i++) { |
166 |
t[i] = s*p[i]; |
167 |
beg[i] = s*floor(p[i]); |
168 |
} |
169 |
for (j = 0; j < 8; j++) { |
170 |
for (i = 0; i < 3; i++) { |
171 |
v[i] = beg[i]; |
172 |
if (j & 1<<i) |
173 |
v[i] += s; |
174 |
} |
175 |
fval[j] = frand3(v[0],v[1],v[2]); |
176 |
} |
177 |
/* compute fractal */ |
178 |
for ( ; ; ) { |
179 |
fc = 0.0; |
180 |
for (j = 0; j < 8; j++) |
181 |
fc += fval[j]; |
182 |
fc *= 0.125; |
183 |
if ((s >>= 1) == 0) |
184 |
return(fc); /* close enough */ |
185 |
branch = 0; |
186 |
for (i = 0; i < 3; i++) { /* do center */ |
187 |
v[i] = beg[i] + s; |
188 |
if (t[i] > v[i]) { |
189 |
branch |= 1<<i; |
190 |
} |
191 |
} |
192 |
fc += s*EPSILON*frand3(v[0],v[1],v[2]); |
193 |
fval[~branch & 7] = fc; |
194 |
for (i = 0; i < 3; i++) { /* do faces */ |
195 |
if (branch & 1<<i) |
196 |
v[i] += s; |
197 |
else |
198 |
v[i] -= s; |
199 |
fc = 0.0; |
200 |
for (j = 0; j < 8; j++) |
201 |
if (~(j^branch) & 1<<i) |
202 |
fc += fval[j]; |
203 |
fc = 0.25*fc + s*EPSILON*frand3(v[0],v[1],v[2]); |
204 |
fval[~(branch^1<<i) & 7] = fc; |
205 |
v[i] = beg[i] + s; |
206 |
} |
207 |
for (i = 0; i < 3; i++) { /* do edges */ |
208 |
j = (i+1)%3; |
209 |
if (branch & 1<<j) |
210 |
v[j] += s; |
211 |
else |
212 |
v[j] -= s; |
213 |
j = (i+2)%3; |
214 |
if (branch & 1<<j) |
215 |
v[j] += s; |
216 |
else |
217 |
v[j] -= s; |
218 |
fc = fval[branch & ~(1<<i)]; |
219 |
fc += fval[branch | 1<<i]; |
220 |
fc = 0.5*fc + s*EPSILON*frand3(v[0],v[1],v[2]); |
221 |
fval[branch^1<<i] = fc; |
222 |
j = (i+1)%3; |
223 |
v[j] = beg[j] + s; |
224 |
j = (i+2)%3; |
225 |
v[j] = beg[j] + s; |
226 |
} |
227 |
for (i = 0; i < 3; i++) /* new cube */ |
228 |
if (branch & 1<<i) |
229 |
beg[i] += s; |
230 |
} |
231 |
} |