src/rt/ambcomp.c

/* Copyright (c) 1991 Regents of the University of California */

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

/*
 * Routines to compute "ambient" values using Monte Carlo
 */

#include  "ray.h"

#include  "ambient.h"

#include  "random.h"

typedef struct {
        short  t, p;            /* theta, phi indices */
        COLOR  v;               /* value sum */
        float  r;               /* 1/distance sum */
        float  k;               /* variance for this division */
        int  n;                 /* number of subsamples */
}  AMBSAMP;             /* ambient sample division */

typedef struct {
        FVECT  ux, uy, uz;      /* x, y and z axis directions */
        short  nt, np;          /* number of theta and phi directions */
}  AMBHEMI;             /* ambient sample hemisphere */

extern double  sin(), cos(), sqrt();


static int
ambcmp(d1, d2)                          /* decreasing order */
AMBSAMP  *d1, *d2;
{
        if (d1->k < d2->k)
                return(1);
        if (d1->k > d2->k)
                return(-1);
        return(0);
}


static int
ambnorm(d1, d2)                         /* standard order */
AMBSAMP  *d1, *d2;
{
        register int  c;

        if (c = d1->t - d2->t)
                return(c);
        return(d1->p - d2->p);
}


divsample(dp, h, r)                     /* sample a division */
register AMBSAMP  *dp;
AMBHEMI  *h;
RAY  *r;
{
        RAY  ar;
        int  hlist[4];
        double  xd, yd, zd;
        double  b2;
        double  phi;
        register int  i;

        if (rayorigin(&ar, r, AMBIENT, 0.5) < 0)
                return(-1);
        hlist[0] = r->rno;
        hlist[1] = dp->t;
        hlist[2] = dp->p;
        hlist[3] = 0;
        zd = sqrt((dp->t+urand(ilhash(hlist,4)+dp->n))/h->nt);
        hlist[3] = 1;
        phi = 2.0*PI * (dp->p+urand(ilhash(hlist,4)+dp->n))/h->np;
        xd = cos(phi) * zd;
        yd = sin(phi) * zd;
        zd = sqrt(1.0 - zd*zd);
        for (i = 0; i < 3; i++)
                ar.rdir[i] =    xd*h->ux[i] +
                                yd*h->uy[i] +
                                zd*h->uz[i];
        dimlist[ndims++] = dp->t*h->np + dp->p + 90171;
        rayvalue(&ar);
        ndims--;
        addcolor(dp->v, ar.rcol);
        if (ar.rt < FHUGE)
                dp->r += 1.0/ar.rt;
                                        /* (re)initialize error */
        if (dp->n++) {
                b2 = bright(dp->v)/dp->n - bright(ar.rcol);
                b2 = b2*b2 + dp->k*((dp->n-1)*(dp->n-1));
                dp->k = b2/(dp->n*dp->n);
        } else
                dp->k = 0.0;
        return(0);
}


double
doambient(acol, r, pg, dg)              /* compute ambient component */
COLOR  acol;
RAY  *r;
FVECT  pg, dg;
{
        double  b, d;
        AMBHEMI  hemi;
        AMBSAMP  *div;
        AMBSAMP  dnew;
        register AMBSAMP  *dp;
        double  arad;
        int  ndivs, ns;
        register int  i, j;
                                        /* initialize color */
        setcolor(acol, 0.0, 0.0, 0.0);
                                        /* initialize hemisphere */
        inithemi(&hemi, r);
        ndivs = hemi.nt * hemi.np;
        if (ndivs == 0)
                return(0.0);
                                        /* set number of super-samples */
        ns = ambssamp * r->rweight + 0.5;
        if (ns > 0 || pg != NULL || dg != NULL) {
                div = (AMBSAMP *)malloc(ndivs*sizeof(AMBSAMP));
                if (div == NULL)
                        error(SYSTEM, "out of memory in doambient");
        } else
                div = NULL;
                                        /* sample the divisions */
        arad = 0.0;
        if ((dp = div) == NULL)
                dp = &dnew;
        for (i = 0; i < hemi.nt; i++)
                for (j = 0; j < hemi.np; j++) {
                        dp->t = i; dp->p = j;
                        setcolor(dp->v, 0.0, 0.0, 0.0);
                        dp->r = 0.0;
                        dp->n = 0;
                        if (divsample(dp, &hemi, r) < 0)
                                goto oopsy;
                        if (div != NULL)
                                dp++;
                        else {
                                addcolor(acol, dp->v);
                                arad += dp->r;
                        }
                }
        if (ns > 0) {                   /* perform super-sampling */
                comperrs(div, &hemi);                   /* compute errors */
                qsort(div, ndivs, sizeof(AMBSAMP), ambcmp);     /* sort divs */
                                                /* super-sample */
                for (i = ns; i > 0; i--) {
                        copystruct(&dnew, div);
                        if (divsample(&dnew, &hemi, r) < 0)
                                goto oopsy;
                                                        /* reinsert */
                        dp = div;
                        j = ndivs < i ? ndivs : i;
                        while (--j > 0 && dnew.k < dp[1].k) {
                                copystruct(dp, dp+1);
                                dp++;
                        }
                        copystruct(dp, &dnew);
                }
                if (pg != NULL || dg != NULL)   /* restore order */
                        qsort(div, ndivs, sizeof(AMBSAMP), ambnorm);
        }
                                        /* compute returned values */
        if (div != NULL) {
                for (i = ndivs, dp = div; i-- > 0; dp++) {
                        arad += dp->r;
                        if (dp->n > 1) {
                                b = 1.0/dp->n;
                                scalecolor(dp->v, b);
                                dp->r *= b;
                                dp->n = 1;
                        }
                        addcolor(acol, dp->v);
                }
                b = bright(acol);
                if (b > FTINY) {
                        b = ndivs/b;
                        if (pg != NULL) {
                                posgradient(pg, div, &hemi);
                                for (i = 0; i < 3; i++)
                                        pg[i] *= b;
                        }
                        if (dg != NULL) {
                                dirgradient(dg, div, &hemi);
                                for (i = 0; i < 3; i++)
                                        dg[i] *= b;
                        }
                } else {
                        if (pg != NULL)
                                for (i = 0; i < 3; i++)
                                        pg[i] = 0.0;
                        if (dg != NULL)
                                for (i = 0; i < 3; i++)
                                        dg[i] = 0.0;
                }
                free((char *)div);
        }
        b = 1.0/ndivs;
        scalecolor(acol, b);
        if (arad <= FTINY)
                arad = FHUGE;
        else
                arad = (ndivs+ns)/arad;
        if (arad > maxarad)
                arad = maxarad;
        else if (arad < minarad)
                arad = minarad;
        arad /= sqrt(r->rweight);
        return(arad);
oopsy:
        if (div != NULL)
                free((char *)div);
        return(0.0);
}


inithemi(hp, r)                 /* initialize sampling hemisphere */
register AMBHEMI  *hp;
RAY  *r;
{
        register int  i;
                                        /* set number of divisions */
        hp->nt = sqrt(ambdiv * r->rweight * 0.5) + 0.5;
        hp->np = 2 * hp->nt;
                                        /* make axes */
        VCOPY(hp->uz, r->ron);
        hp->uy[0] = hp->uy[1] = hp->uy[2] = 0.0;
        for (i = 0; i < 3; i++)
                if (hp->uz[i] < 0.6 && hp->uz[i] > -0.6)
                        break;
        if (i >= 3)
                error(CONSISTENCY, "bad ray direction in inithemi");
        hp->uy[i] = 1.0;
        fcross(hp->ux, hp->uy, hp->uz);
        normalize(hp->ux);
        fcross(hp->uy, hp->uz, hp->ux);
}


comperrs(da, hp)                /* compute initial error estimates */
AMBSAMP  *da;           /* assumes standard ordering */
register AMBHEMI  *hp;
{
        double  b, b2;
        int  i, j;
        register AMBSAMP  *dp;
                                /* sum differences from neighbors */
        dp = da;
        for (i = 0; i < hp->nt; i++)
                for (j = 0; j < hp->np; j++) {
#ifdef  DEBUG
                        if (dp->t != i || dp->p != j)
                                error(CONSISTENCY,
                                        "division order in comperrs");
#endif
                        b = bright(dp[0].v);
                        if (i > 0) {            /* from above */
                                b2 = bright(dp[-hp->np].v) - b;
                                b2 *= b2 * 0.25;
                                dp[0].k += b2;
                                dp[-hp->np].k += b2;
                        }
                        if (j > 0) {            /* from behind */
                                b2 = bright(dp[-1].v) - b;
                                b2 *= b2 * 0.25;
                                dp[0].k += b2;
                                dp[-1].k += b2;
                        } else {                /* around */
                                b2 = bright(dp[hp->np-1].v) - b;
                                b2 *= b2 * 0.25;
                                dp[0].k += b2;
                                dp[hp->np-1].k += b2;
                        }
                        dp++;
                }
                                /* divide by number of neighbors */
        dp = da;
        for (j = 0; j < hp->np; j++)            /* top row */
                (dp++)->k *= 1.0/3.0;
        if (hp->nt < 2)
                return;
        for (i = 1; i < hp->nt-1; i++)          /* central region */
                for (j = 0; j < hp->np; j++)
                        (dp++)->k *= 0.25;
        for (j = 0; j < hp->np; j++)            /* bottom row */
                (dp++)->k *= 1.0/3.0;
}


posgradient(gv, da, hp)                         /* compute position gradient */
FVECT  gv;
AMBSAMP  *da;                   /* assumes standard ordering */
AMBHEMI  *hp;
{
        register int  i, j;
        double  b, d;
        double  mag0, mag1;
        double  phi, cosp, sinp, xd, yd;
        register AMBSAMP  *dp;

        xd = yd = 0.0;
        for (j = 0; j < hp->np; j++) {
                dp = da + j;
                mag0 = mag1 = 0.0;
                for (i = 0; i < hp->nt; i++) {
#ifdef  DEBUG
                        if (dp->t != i || dp->p != j)
                                error(CONSISTENCY,
                                        "division order in posgradient");
#endif
                        b = bright(dp->v);
                        if (i > 0) {
                                d = dp[-hp->np].r;
                                if (dp[0].r > d) d = dp[0].r;
                                d *= 1.0 - sqrt((double)i/hp->nt);
                                mag0 += d*(b - bright(dp[-hp->np].v));
                        }
                        if (j > 0) {
                                d = dp[-1].r;
                                if (dp[0].r > d) d = dp[0].r;
                                mag1 += d*(b - bright(dp[-1].v));
                        } else {
                                d = dp[hp->np-1].r;
                                if (dp[0].r > d) d = dp[0].r;
                                mag1 += d*(b - bright(dp[hp->np-1].v));
                        }
                        dp += hp->np;
                }
                if (hp->nt > 1) {
                        mag0 /= (double)hp->np;
                        mag1 /= (double)hp->nt;
                }
                phi = 2.0*PI * (double)j/hp->np;
                cosp = cos(phi); sinp = sin(phi);
                xd += mag0*cosp - mag1*sinp;
                yd += mag0*sinp + mag1*cosp;
        }
        for (i = 0; i < 3; i++)
                gv[i] = (xd*hp->ux[i] + yd*hp->uy[i])/PI;
}


dirgradient(gv, da, hp)                         /* compute direction gradient */
FVECT  gv;
AMBSAMP  *da;                   /* assumes standard ordering */
AMBHEMI  *hp;
{
        register int  i, j;
        double  mag;
        double  phi, xd, yd;
        register AMBSAMP  *dp;

        xd = yd = 0.0;
        for (j = 0; j < hp->np; j++) {
                dp = da + j;
                mag = 0.0;
                for (i = 0; i < hp->nt; i++) {
#ifdef  DEBUG
                        if (dp->t != i || dp->p != j)
                                error(CONSISTENCY,
                                        "division order in dirgradient");
#endif
                        mag += sqrt((i+.5)/hp->nt)*bright(dp->v);
                        dp += hp->np;
                }
                phi = 2.0*PI * (j+.5)/hp->np + PI/2.0;
                xd += mag * cos(phi);
                yd += mag * sin(phi);
        }
        for (i = 0; i < 3; i++)
                gv[i] = (xd*hp->ux[i] + yd*hp->uy[i])*PI/(hp->nt*hp->np);
}
Revision:	1.6
Committed:	Thu Jun 13 10:54:00 1991 UTC (32 years, 10 months ago) by greg
Content type:	text/plain
Branch:	MAIN
Changes since 1.5:	+23 -12 lines
Log Message:	made computations of gradients a little more robust
#	User	Rev	Content
1	greg	1.1	/* Copyright (c) 1991 Regents of the University of California */
2
3			#ifndef lint
4			static char SCCSid[] = "$SunId$ LBL";
5			#endif
6
7			/*
8			* Routines to compute "ambient" values using Monte Carlo
9			*/
10
11			#include "ray.h"
12
13			#include "ambient.h"
14
15			#include "random.h"
16
17			typedef struct {
18			short t, p; /* theta, phi indices */
19			COLOR v; /* value sum */
20	greg	1.2	float r; /* 1/distance sum */
21			float k; /* variance for this division */
22	greg	1.1	int n; /* number of subsamples */
23	greg	1.2	} AMBSAMP; /* ambient sample division */
24	greg	1.1
25			typedef struct {
26			FVECT ux, uy, uz; /* x, y and z axis directions */
27			short nt, np; /* number of theta and phi directions */
28			} AMBHEMI; /* ambient sample hemisphere */
29
30			extern double sin(), cos(), sqrt();
31
32
33			static int
34			ambcmp(d1, d2) /* decreasing order */
35			AMBSAMP d1, d2;
36			{
37			if (d1->k < d2->k)
38			return(1);
39			if (d1->k > d2->k)
40			return(-1);
41			return(0);
42			}
43
44
45			static int
46			ambnorm(d1, d2) /* standard order */
47			AMBSAMP d1, d2;
48			{
49			register int c;
50
51			if (c = d1->t - d2->t)
52			return(c);
53			return(d1->p - d2->p);
54			}
55
56
57			divsample(dp, h, r) /* sample a division */
58			register AMBSAMP *dp;
59			AMBHEMI *h;
60			RAY *r;
61			{
62			RAY ar;
63			int hlist[4];
64			double xd, yd, zd;
65			double b2;
66			double phi;
67	greg	1.2	register int i;
68	greg	1.1
69			if (rayorigin(&ar, r, AMBIENT, 0.5) < 0)
70	greg	1.4	return(-1);
71	greg	1.1	hlist[0] = r->rno;
72			hlist[1] = dp->t;
73			hlist[2] = dp->p;
74			hlist[3] = 0;
75			zd = sqrt((dp->t+urand(ilhash(hlist,4)+dp->n))/h->nt);
76			hlist[3] = 1;
77			phi = 2.0PI (dp->p+urand(ilhash(hlist,4)+dp->n))/h->np;
78			xd = cos(phi) * zd;
79			yd = sin(phi) * zd;
80			zd = sqrt(1.0 - zd*zd);
81	greg	1.2	for (i = 0; i < 3; i++)
82			ar.rdir[i] = xd*h->ux[i] +
83			yd*h->uy[i] +
84			zd*h->uz[i];
85			dimlist[ndims++] = dp->t*h->np + dp->p + 90171;
86	greg	1.1	rayvalue(&ar);
87			ndims--;
88			addcolor(dp->v, ar.rcol);
89	greg	1.4	if (ar.rt < FHUGE)
90			dp->r += 1.0/ar.rt;
91	greg	1.1	/* (re)initialize error */
92			if (dp->n++) {
93			b2 = bright(dp->v)/dp->n - bright(ar.rcol);
94			b2 = b2b2 + dp->k((dp->n-1)*(dp->n-1));
95			dp->k = b2/(dp->n*dp->n);
96			} else
97			dp->k = 0.0;
98	greg	1.4	return(0);
99	greg	1.1	}
100
101
102			double
103			doambient(acol, r, pg, dg) /* compute ambient component */
104			COLOR acol;
105			RAY *r;
106			FVECT pg, dg;
107			{
108			double b, d;
109			AMBHEMI hemi;
110			AMBSAMP *div;
111			AMBSAMP dnew;
112			register AMBSAMP *dp;
113			double arad;
114			int ndivs, ns;
115			register int i, j;
116			/* initialize color */
117			setcolor(acol, 0.0, 0.0, 0.0);
118			/* initialize hemisphere */
119			inithemi(&hemi, r);
120			ndivs = hemi.nt * hemi.np;
121			if (ndivs == 0)
122			return(0.0);
123			/* set number of super-samples */
124			ns = ambssamp * r->rweight + 0.5;
125			if (ns > 0 \|\| pg != NULL \|\| dg != NULL) {
126			div = (AMBSAMP )malloc(ndivssizeof(AMBSAMP));
127			if (div == NULL)
128			error(SYSTEM, "out of memory in doambient");
129			} else
130			div = NULL;
131			/* sample the divisions */
132			arad = 0.0;
133			if ((dp = div) == NULL)
134			dp = &dnew;
135			for (i = 0; i < hemi.nt; i++)
136			for (j = 0; j < hemi.np; j++) {
137			dp->t = i; dp->p = j;
138			setcolor(dp->v, 0.0, 0.0, 0.0);
139	greg	1.2	dp->r = 0.0;
140	greg	1.1	dp->n = 0;
141	greg	1.4	if (divsample(dp, &hemi, r) < 0)
142	greg	1.1	goto oopsy;
143			if (div != NULL)
144			dp++;
145	greg	1.2	else {
146	greg	1.1	addcolor(acol, dp->v);
147	greg	1.2	arad += dp->r;
148			}
149	greg	1.1	}
150			if (ns > 0) { /* perform super-sampling */
151	greg	1.4	comperrs(div, &hemi); /* compute errors */
152	greg	1.1	qsort(div, ndivs, sizeof(AMBSAMP), ambcmp); /* sort divs */
153			/* super-sample */
154			for (i = ns; i > 0; i--) {
155			copystruct(&dnew, div);
156	greg	1.4	if (divsample(&dnew, &hemi, r) < 0)
157	greg	1.1	goto oopsy;
158			/* reinsert */
159			dp = div;
160			j = ndivs < i ? ndivs : i;
161			while (--j > 0 && dnew.k < dp[1].k) {
162			copystruct(dp, dp+1);
163			dp++;
164			}
165			copystruct(dp, &dnew);
166			}
167	greg	1.2	if (pg != NULL \|\| dg != NULL) /* restore order */
168	greg	1.1	qsort(div, ndivs, sizeof(AMBSAMP), ambnorm);
169			}
170			/* compute returned values */
171	greg	1.3	if (div != NULL) {
172			for (i = ndivs, dp = div; i-- > 0; dp++) {
173			arad += dp->r;
174			if (dp->n > 1) {
175			b = 1.0/dp->n;
176			scalecolor(dp->v, b);
177			dp->r *= b;
178			dp->n = 1;
179			}
180			addcolor(acol, dp->v);
181			}
182	greg	1.5	b = bright(acol);
183	greg	1.6	if (b > FTINY) {
184	greg	1.5	b = ndivs/b;
185	greg	1.6	if (pg != NULL) {
186			posgradient(pg, div, &hemi);
187			for (i = 0; i < 3; i++)
188			pg[i] *= b;
189			}
190			if (dg != NULL) {
191			dirgradient(dg, div, &hemi);
192			for (i = 0; i < 3; i++)
193			dg[i] *= b;
194			}
195			} else {
196			if (pg != NULL)
197			for (i = 0; i < 3; i++)
198			pg[i] = 0.0;
199			if (dg != NULL)
200			for (i = 0; i < 3; i++)
201			dg[i] = 0.0;
202	greg	1.5	}
203	greg	1.1	free((char *)div);
204	greg	1.3	}
205	greg	1.1	b = 1.0/ndivs;
206			scalecolor(acol, b);
207			if (arad <= FTINY)
208			arad = FHUGE;
209			else
210			arad = (ndivs+ns)/arad;
211			if (arad > maxarad)
212			arad = maxarad;
213			else if (arad < minarad)
214			arad = minarad;
215			arad /= sqrt(r->rweight);
216			return(arad);
217			oopsy:
218			if (div != NULL)
219			free((char *)div);
220			return(0.0);
221			}
222
223
224			inithemi(hp, r) /* initialize sampling hemisphere */
225			register AMBHEMI *hp;
226			RAY *r;
227			{
228	greg	1.2	register int i;
229	greg	1.1	/* set number of divisions */
230			hp->nt = sqrt(ambdiv * r->rweight * 0.5) + 0.5;
231			hp->np = 2 * hp->nt;
232			/* make axes */
233			VCOPY(hp->uz, r->ron);
234			hp->uy[0] = hp->uy[1] = hp->uy[2] = 0.0;
235	greg	1.2	for (i = 0; i < 3; i++)
236			if (hp->uz[i] < 0.6 && hp->uz[i] > -0.6)
237	greg	1.1	break;
238	greg	1.2	if (i >= 3)
239	greg	1.1	error(CONSISTENCY, "bad ray direction in inithemi");
240	greg	1.2	hp->uy[i] = 1.0;
241	greg	1.3	fcross(hp->ux, hp->uy, hp->uz);
242			normalize(hp->ux);
243			fcross(hp->uy, hp->uz, hp->ux);
244	greg	1.1	}
245
246
247			comperrs(da, hp) /* compute initial error estimates */
248	greg	1.2	AMBSAMP da; / assumes standard ordering */
249	greg	1.1	register AMBHEMI *hp;
250			{
251			double b, b2;
252			int i, j;
253			register AMBSAMP *dp;
254			/* sum differences from neighbors */
255			dp = da;
256			for (i = 0; i < hp->nt; i++)
257			for (j = 0; j < hp->np; j++) {
258	greg	1.6	#ifdef DEBUG
259			if (dp->t != i \|\| dp->p != j)
260			error(CONSISTENCY,
261			"division order in comperrs");
262			#endif
263	greg	1.1	b = bright(dp[0].v);
264			if (i > 0) { /* from above */
265			b2 = bright(dp[-hp->np].v) - b;
266			b2 = b2 0.25;
267			dp[0].k += b2;
268			dp[-hp->np].k += b2;
269			}
270			if (j > 0) { /* from behind */
271			b2 = bright(dp[-1].v) - b;
272			b2 = b2 0.25;
273			dp[0].k += b2;
274			dp[-1].k += b2;
275	greg	1.4	} else { /* around */
276			b2 = bright(dp[hp->np-1].v) - b;
277	greg	1.1	b2 = b2 0.25;
278			dp[0].k += b2;
279	greg	1.4	dp[hp->np-1].k += b2;
280	greg	1.1	}
281			dp++;
282			}
283			/* divide by number of neighbors */
284			dp = da;
285			for (j = 0; j < hp->np; j++) /* top row */
286			(dp++)->k *= 1.0/3.0;
287			if (hp->nt < 2)
288			return;
289			for (i = 1; i < hp->nt-1; i++) /* central region */
290			for (j = 0; j < hp->np; j++)
291			(dp++)->k *= 0.25;
292			for (j = 0; j < hp->np; j++) /* bottom row */
293			(dp++)->k *= 1.0/3.0;
294			}
295
296
297			posgradient(gv, da, hp) /* compute position gradient */
298			FVECT gv;
299	greg	1.2	AMBSAMP da; / assumes standard ordering */
300	greg	1.1	AMBHEMI *hp;
301			{
302	greg	1.2	register int i, j;
303			double b, d;
304			double mag0, mag1;
305			double phi, cosp, sinp, xd, yd;
306			register AMBSAMP *dp;
307
308			xd = yd = 0.0;
309			for (j = 0; j < hp->np; j++) {
310			dp = da + j;
311			mag0 = mag1 = 0.0;
312			for (i = 0; i < hp->nt; i++) {
313			#ifdef DEBUG
314			if (dp->t != i \|\| dp->p != j)
315			error(CONSISTENCY,
316			"division order in posgradient");
317			#endif
318			b = bright(dp->v);
319			if (i > 0) {
320			d = dp[-hp->np].r;
321			if (dp[0].r > d) d = dp[0].r;
322			d *= 1.0 - sqrt((double)i/hp->nt);
323			mag0 += d*(b - bright(dp[-hp->np].v));
324			}
325			if (j > 0) {
326			d = dp[-1].r;
327			if (dp[0].r > d) d = dp[0].r;
328			mag1 += d*(b - bright(dp[-1].v));
329			} else {
330			d = dp[hp->np-1].r;
331			if (dp[0].r > d) d = dp[0].r;
332			mag1 += d*(b - bright(dp[hp->np-1].v));
333			}
334			dp += hp->np;
335			}
336			if (hp->nt > 1) {
337	greg	1.4	mag0 /= (double)hp->np;
338	greg	1.2	mag1 /= (double)hp->nt;
339			}
340			phi = 2.0PI (double)j/hp->np;
341			cosp = cos(phi); sinp = sin(phi);
342			xd += mag0cosp - mag1sinp;
343			yd += mag0sinp + mag1cosp;
344			}
345			for (i = 0; i < 3; i++)
346	greg	1.5	gv[i] = (xdhp->ux[i] + ydhp->uy[i])/PI;
347	greg	1.1	}
348
349
350			dirgradient(gv, da, hp) /* compute direction gradient */
351			FVECT gv;
352	greg	1.2	AMBSAMP da; / assumes standard ordering */
353	greg	1.1	AMBHEMI *hp;
354			{
355	greg	1.2	register int i, j;
356			double mag;
357			double phi, xd, yd;
358			register AMBSAMP *dp;
359
360			xd = yd = 0.0;
361			for (j = 0; j < hp->np; j++) {
362			dp = da + j;
363			mag = 0.0;
364			for (i = 0; i < hp->nt; i++) {
365			#ifdef DEBUG
366			if (dp->t != i \|\| dp->p != j)
367			error(CONSISTENCY,
368			"division order in dirgradient");
369			#endif
370			mag += sqrt((i+.5)/hp->nt)*bright(dp->v);
371			dp += hp->np;
372			}
373			phi = 2.0PI (j+.5)/hp->np + PI/2.0;
374			xd += mag * cos(phi);
375			yd += mag * sin(phi);
376			}
377			for (i = 0; i < 3; i++)
378	greg	1.5	gv[i] = (xdhp->ux[i] + ydhp->uy[i])PI/(hp->nthp->np);
379	greg	1.1	}