src/rt/noise3.c

/* Copyright (c) 1988 Regents of the University of California */

#ifndef lint
static char SCCSid[] = "$SunId$ LBL";
#endif

/*
 *  noise3.c - noise functions for random textures.
 *
 *     Credit for the smooth algorithm goes to Ken Perlin.
 *     (ref. SIGGRAPH Vol 19, No 3, pp 287-96)
 *
 *     4/15/86
 *     5/19/88  Added fractal noise function
 */

#include  <math.h>

#define  A              0
#define  B              1
#define  C              2
#define  D              3

#define  rand3a(x,y,z)  frand(67*(x)+59*(y)+71*(z))
#define  rand3b(x,y,z)  frand(73*(x)+79*(y)+83*(z))
#define  rand3c(x,y,z)  frand(89*(x)+97*(y)+101*(z))
#define  rand3d(x,y,z)  frand(103*(x)+107*(y)+109*(z))

#define  hpoly1(t)      ((2.0*t-3.0)*t*t+1.0)
#define  hpoly2(t)      (-2.0*t+3.0)*t*t
#define  hpoly3(t)      ((t-2.0)*t+1.0)*t
#define  hpoly4(t)      (t-1.0)*t*t

#define  hermite(p0,p1,r0,r1,t)  (      p0*hpoly1(t) + \
                                        p1*hpoly2(t) + \
                                        r0*hpoly3(t) + \
                                        r1*hpoly4(t) )

static char  noise_name[4][8] = {"noise3x", "noise3y", "noise3z", "noise3"};
static char  fnoise_name[] = "fnoise3";
static char  hermite_name[] = "hermite";

double  *noise3(), fnoise3(), argument(), frand();
static  interpolate();

static long  xlim[3][2];
static double  xarg[3];

#define  EPSILON        .001            /* error allowed in fractal */

#define  frand3(x,y,z)  frand(17*(x)+23*(y)+29*(z))


static double
l_noise3(nam)                   /* compute a noise function */
register char  *nam;
{
        register 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);
}


double
l_hermite()                     /* library call for hermite interpolation */
{
        double  t;
        
        t = argument(5);
        return( hermite(argument(1), argument(2),
                        argument(3), argument(4), t) );
}


setnoisefuncs()                 /* add noise functions to library */
{
        register int  i;

        funset(hermite_name, 5, ':', l_hermite);
        funset(fnoise_name, 3, ':', l_noise3);
        i = 4;
        while (i--)
                funset(noise_name[i], 3, ':', l_noise3);
}


double *
noise3(xnew)                    /* compute the noise function */
register double  xnew[3];
{
        static double  x[3] = {-100000.0, -100000.0, -100000.0};
        static double  f[4];

        if (x[0]==xnew[0] && x[1]==xnew[1] && x[2]==xnew[2])
                return(f);
        x[0] = xnew[0]; x[1] = xnew[1]; x[2] = xnew[2];
        xlim[0][0] = floor(x[0]); xlim[0][1] = xlim[0][0] + 1;
        xlim[1][0] = floor(x[1]); xlim[1][1] = xlim[1][0] + 1;
        xlim[2][0] = floor(x[2]); xlim[2][1] = xlim[2][0] + 1;
        xarg[0] = x[0] - xlim[0][0];
        xarg[1] = x[1] - xlim[1][0];
        xarg[2] = x[2] - xlim[2][0];
        interpolate(f, 0, 3);
        return(f);
}


static
interpolate(f, i, n)
double  f[4];
register int  i, n;
{
        double  f0[4], f1[4], hp1, hp2;

        if (n == 0) {
                f[A] = rand3a(xlim[0][i&1],xlim[1][i>>1&1],xlim[2][i>>2]);
                f[B] = rand3b(xlim[0][i&1],xlim[1][i>>1&1],xlim[2][i>>2]);
                f[C] = rand3c(xlim[0][i&1],xlim[1][i>>1&1],xlim[2][i>>2]);
                f[D] = rand3d(xlim[0][i&1],xlim[1][i>>1&1],xlim[2][i>>2]);
        } else {
                n--;
                interpolate(f0, i, n);
                interpolate(f1, i | 1<<n, n);
                hp1 = hpoly1(xarg[n]); hp2 = hpoly2(xarg[n]);
                f[A] = f0[A]*hp1 + f1[A]*hp2;
                f[B] = f0[B]*hp1 + f1[B]*hp2;
                f[C] = f0[C]*hp1 + f1[C]*hp2;
                f[D] = f0[D]*hp1 + f1[D]*hp2 +
                                f0[n]*hpoly3(xarg[n]) + f1[n]*hpoly4(xarg[n]);
        }
}


double
frand(s)                        /* get random number from seed */
register long  s;
{
        s = s<<13 ^ s;
        return(1.0-((s*(s*s*15731+789221)+1376312589)&0x7fffffff)/1073741824.0);
}


double
fnoise3(p)                      /* compute fractal noise function */
double  p[3];
{
        long  t[3], v[3], beg[3];
        double  fval[8], fc;
        int  branch;
        register long  s;
        register int  i, j;
                                                /* get starting cube */
        s = (long)(1.0/EPSILON);
        for (i = 0; i < 3; i++) {
                t[i] = s*p[i];
                beg[i] = s*floor(p[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 */
                        j = (i+1)%3;
                        if (branch & 1<<j)
                                v[j] += s;
                        else
                                v[j] -= s;
                        j = (i+2)%3;
                        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;
                        j = (i+1)%3;
                        v[j] = beg[j] + s;
                        j = (i+2)%3;
                        v[j] = beg[j] + s;
                }
                for (i = 0; i < 3; i++)         /* new cube */
                        if (branch & 1<<i)
                                beg[i] += s;
        }
}
Revision:	2.5
Committed:	Thu Oct 31 10:58:36 1996 UTC (28 years ago) by greg
Content type:	text/plain
Branch:	MAIN
Changes since 2.4:	+1 -1 lines
Log Message:	renamed noise3{a,b,c} to noise3{x,y,z}
#	User	Rev	Content
1	greg	1.1	/* Copyright (c) 1988 Regents of the University of California */
2
3			#ifndef lint
4			static char SCCSid[] = "$SunId$ LBL";
5			#endif
6
7			/*
8			* noise3.c - noise functions for random textures.
9			*
10			* Credit for the smooth algorithm goes to Ken Perlin.
11			* (ref. SIGGRAPH Vol 19, No 3, pp 287-96)
12			*
13			* 4/15/86
14			* 5/19/88 Added fractal noise function
15			*/
16
17	greg	2.2	#include <math.h>
18	greg	1.1
19			#define A 0
20			#define B 1
21			#define C 2
22			#define D 3
23
24			#define rand3a(x,y,z) frand(67(x)+59(y)+71*(z))
25			#define rand3b(x,y,z) frand(73(x)+79(y)+83*(z))
26			#define rand3c(x,y,z) frand(89(x)+97(y)+101*(z))
27			#define rand3d(x,y,z) frand(103(x)+107(y)+109*(z))
28
29	greg	1.7	#define hpoly1(t) ((2.0t-3.0)t*t+1.0)
30			#define hpoly2(t) (-2.0t+3.0)t*t
31			#define hpoly3(t) ((t-2.0)t+1.0)t
32			#define hpoly4(t) (t-1.0)tt
33	greg	1.1
34	greg	1.7	#define hermite(p0,p1,r0,r1,t) ( p0*hpoly1(t) + \
35			p1*hpoly2(t) + \
36			r0*hpoly3(t) + \
37			r1*hpoly4(t) )
38
39	greg	2.5	static char noise_name[4][8] = {"noise3x", "noise3y", "noise3z", "noise3"};
40	greg	1.5	static char fnoise_name[] = "fnoise3";
41			static char hermite_name[] = "hermite";
42	greg	1.1
43	greg	1.5	double *noise3(), fnoise3(), argument(), frand();
44	greg	2.3	static interpolate();
45	greg	1.5
46	greg	1.1	static long xlim[3][2];
47			static double xarg[3];
48
49	greg	2.4	#define EPSILON .001 /* error allowed in fractal */
50	greg	1.1
51	greg	1.3	#define frand3(x,y,z) frand(17(x)+23(y)+29*(z))
52	greg	1.1
53
54	greg	1.5	static double
55			l_noise3(nam) /* compute a noise function */
56			register char *nam;
57	greg	1.1	{
58	greg	1.5	register int i;
59			double x[3];
60			/* get point */
61			x[0] = argument(1);
62			x[1] = argument(2);
63			x[2] = argument(3);
64			/* make appropriate call */
65			if (nam == fnoise_name)
66			return(fnoise3(x));
67			i = 4;
68			while (i--)
69			if (nam == noise_name[i])
70			return(noise3(x)[i]);
71	greg	1.6	eputs(nam);
72			eputs(": called l_noise3!\n");
73	greg	1.5	quit(1);
74	greg	1.1	}
75
76
77			double
78	greg	1.5	l_hermite() /* library call for hermite interpolation */
79	greg	1.1	{
80	greg	1.5	double t;
81
82			t = argument(5);
83			return( hermite(argument(1), argument(2),
84			argument(3), argument(4), t) );
85	greg	1.1	}
86
87
88	greg	1.5	setnoisefuncs() /* add noise functions to library */
89	greg	1.1	{
90	greg	1.5	register int i;
91	greg	1.1
92	greg	1.5	funset(hermite_name, 5, ':', l_hermite);
93			funset(fnoise_name, 3, ':', l_noise3);
94			i = 4;
95			while (i--)
96			funset(noise_name[i], 3, ':', l_noise3);
97	greg	1.1	}
98
99
100			double *
101			noise3(xnew) /* compute the noise function */
102			register double xnew[3];
103			{
104			static double x[3] = {-100000.0, -100000.0, -100000.0};
105			static double f[4];
106
107			if (x[0]==xnew[0] && x[1]==xnew[1] && x[2]==xnew[2])
108			return(f);
109			x[0] = xnew[0]; x[1] = xnew[1]; x[2] = xnew[2];
110			xlim[0][0] = floor(x[0]); xlim[0][1] = xlim[0][0] + 1;
111			xlim[1][0] = floor(x[1]); xlim[1][1] = xlim[1][0] + 1;
112			xlim[2][0] = floor(x[2]); xlim[2][1] = xlim[2][0] + 1;
113			xarg[0] = x[0] - xlim[0][0];
114			xarg[1] = x[1] - xlim[1][0];
115			xarg[2] = x[2] - xlim[2][0];
116			interpolate(f, 0, 3);
117			return(f);
118			}
119
120
121			static
122			interpolate(f, i, n)
123			double f[4];
124			register int i, n;
125			{
126	greg	1.7	double f0[4], f1[4], hp1, hp2;
127	greg	1.1
128			if (n == 0) {
129			f[A] = rand3a(xlim[0][i&1],xlim[1][i>>1&1],xlim[2][i>>2]);
130			f[B] = rand3b(xlim[0][i&1],xlim[1][i>>1&1],xlim[2][i>>2]);
131			f[C] = rand3c(xlim[0][i&1],xlim[1][i>>1&1],xlim[2][i>>2]);
132			f[D] = rand3d(xlim[0][i&1],xlim[1][i>>1&1],xlim[2][i>>2]);
133			} else {
134			n--;
135			interpolate(f0, i, n);
136			interpolate(f1, i \| 1<<n, n);
137	greg	1.7	hp1 = hpoly1(xarg[n]); hp2 = hpoly2(xarg[n]);
138			f[A] = f0[A]hp1 + f1[A]hp2;
139			f[B] = f0[B]hp1 + f1[B]hp2;
140			f[C] = f0[C]hp1 + f1[C]hp2;
141			f[D] = f0[D]hp1 + f1[D]hp2 +
142			f0[n]hpoly3(xarg[n]) + f1[n]hpoly4(xarg[n]);
143	greg	1.1	}
144			}
145
146
147			double
148			frand(s) /* get random number from seed */
149			register long s;
150			{
151			s = s<<13 ^ s;
152			return(1.0-((s(ss*15731+789221)+1376312589)&0x7fffffff)/1073741824.0);
153			}
154
155
156			double
157			fnoise3(p) /* compute fractal noise function */
158	greg	1.3	double p[3];
159	greg	1.1	{
160	greg	1.4	long t[3], v[3], beg[3];
161	greg	1.3	double fval[8], fc;
162			int branch;
163	greg	1.4	register long s;
164	greg	1.1	register int i, j;
165			/* get starting cube */
166	greg	1.3	s = (long)(1.0/EPSILON);
167			for (i = 0; i < 3; i++) {
168			t[i] = s*p[i];
169			beg[i] = s*floor(p[i]);
170			}
171	greg	1.1	for (j = 0; j < 8; j++) {
172			for (i = 0; i < 3; i++) {
173			v[i] = beg[i];
174			if (j & 1<<i)
175	greg	1.3	v[i] += s;
176	greg	1.1	}
177			fval[j] = frand3(v[0],v[1],v[2]);
178			}
179			/* compute fractal */
180			for ( ; ; ) {
181	greg	1.4	fc = 0.0;
182			for (j = 0; j < 8; j++)
183			fc += fval[j];
184			fc *= 0.125;
185			if ((s >>= 1) == 0)
186			return(fc); /* close enough */
187	greg	1.1	branch = 0;
188			for (i = 0; i < 3; i++) { /* do center */
189			v[i] = beg[i] + s;
190	greg	1.3	if (t[i] > v[i]) {
191	greg	1.1	branch \|= 1<<i;
192	greg	1.3	}
193	greg	1.1	}
194	greg	1.3	fc += sEPSILONfrand3(v[0],v[1],v[2]);
195	greg	1.1	fval[~branch & 7] = fc;
196			for (i = 0; i < 3; i++) { /* do faces */
197			if (branch & 1<<i)
198			v[i] += s;
199			else
200			v[i] -= s;
201			fc = 0.0;
202			for (j = 0; j < 8; j++)
203			if (~(j^branch) & 1<<i)
204			fc += fval[j];
205	greg	1.3	fc = 0.25fc + sEPSILON*frand3(v[0],v[1],v[2]);
206	greg	1.1	fval[~(branch^1<<i) & 7] = fc;
207			v[i] = beg[i] + s;
208			}
209			for (i = 0; i < 3; i++) { /* do edges */
210			j = (i+1)%3;
211			if (branch & 1<<j)
212			v[j] += s;
213			else
214			v[j] -= s;
215			j = (i+2)%3;
216			if (branch & 1<<j)
217			v[j] += s;
218			else
219			v[j] -= s;
220			fc = fval[branch & ~(1<<i)];
221			fc += fval[branch \| 1<<i];
222	greg	1.3	fc = 0.5fc + sEPSILON*frand3(v[0],v[1],v[2]);
223	greg	1.1	fval[branch^1<<i] = fc;
224			j = (i+1)%3;
225			v[j] = beg[j] + s;
226			j = (i+2)%3;
227			v[j] = beg[j] + s;
228			}
229			for (i = 0; i < 3; i++) /* new cube */
230			if (branch & 1<<i)
231			beg[i] += s;
232			}
233			}