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 */


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[3];
        double  spt[2];
        double  xd, yd, zd;
        double  b2;
        double  phi;
        register int  i;

        if (rayorigin(&ar, r, AMBIENT, AVGREFL) < 0)
                return(-1);
        hlist[0] = r->rno;
        hlist[1] = dp->t;
        hlist[2] = dp->p;
        multisamp(spt, 2, urand(ilhash(hlist,3)+dp->n));
        zd = sqrt((dp->t + spt[0])/h->nt);
        phi = 2.0*PI * (dp->p + spt[1])/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 > FTINY && 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, wt, pg, dg)          /* compute ambient component */
COLOR  acol;
RAY  *r;
double  wt;
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, wt);
        ndivs = hemi.nt * hemi.np;
        if (ndivs == 0)
                return(0.0);
                                        /* set number of super-samples */
        ns = ambssamp * wt + 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;
                        arad += dp->r;
                        if (div != NULL)
                                dp++;
                        else
                                addcolor(acol, dp->v);
                }
        if (ns > 0 && arad > FTINY && ndivs/arad < minarad)
                ns = 0;                 /* close enough */
        else if (ns > 0) {              /* else 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) {
                arad = 0.0;
                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 = maxarad;
        else
                arad = (ndivs+ns)/arad;
        if (pg != NULL) {               /* reduce radius if gradient large */
                d = DOT(pg,pg);
                if (d*arad*arad > 1.0)
                        arad = 1.0/sqrt(d);
        }
        if (arad < minarad) {
                arad = minarad;
                if (pg != NULL && d*arad*arad > 1.0) {  /* cap gradient */
                        d = 1.0/arad/sqrt(d);
                        for (i = 0; i < 3; i++)
                                pg[i] *= d;
                }
        }
        if ((arad /= sqrt(wt)) > maxarad)
                arad = maxarad;
        return(arad);
oopsy:
        if (div != NULL)
                free((char *)div);
        return(0.0);
}


inithemi(hp, r, wt)             /* initialize sampling hemisphere */
register AMBHEMI  *hp;
RAY  *r;
double  wt;
{
        register int  i;
                                        /* set number of divisions */
        if (wt < (.25*PI)/ambdiv+FTINY) {
                hp->nt = hp->np = 0;
                return;                 /* zero samples */
        }
        hp->nt = sqrt(ambdiv * wt / PI) + 0.5;
        hp->np = PI * hp->nt + 0.5;
                                        /* 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 */
register AMBHEMI  *hp;
{
        register int  i, j;
        double  nextsine, lastsine, 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;
                lastsine = 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;
                                                        /* sin(t)*cos(t)^2 */
                                d *= lastsine * (1.0 - (double)i/hp->nt);
                                mag0 += d*(b - bright(dp[-hp->np].v));
                        }
                        nextsine = sqrt((double)(i+1)/hp->nt);
                        if (j > 0) {
                                d = dp[-1].r;
                                if (dp[0].r > d) d = dp[0].r;
                                mag1 += d * (nextsine - lastsine) *
                                                (b - bright(dp[-1].v));
                        } else {
                                d = dp[hp->np-1].r;
                                if (dp[0].r > d) d = dp[0].r;
                                mag1 += d * (nextsine - lastsine) *
                                                (b - bright(dp[hp->np-1].v));
                        }
                        dp += hp->np;
                        lastsine = nextsine;
                }
                mag0 *= 2.0*PI / hp->np;
                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 */
register 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
                                                        /* tan(t) */
                        mag += bright(dp->v)/sqrt(hp->nt/(i+.5) - 1.0);
                        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])/(hp->nt*hp->np);
}
Revision:	2.6
Committed:	Tue Apr 23 11:06:54 1996 UTC (28 years ago) by greg
Content type:	text/plain
Branch:	MAIN
Changes since 2.5:	+3 -3 lines
Log Message:	fixed bug in super-sampling test which resulted in unnec. sampling
#	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
31			static int
32			ambcmp(d1, d2) /* decreasing order */
33			AMBSAMP d1, d2;
34			{
35			if (d1->k < d2->k)
36			return(1);
37			if (d1->k > d2->k)
38			return(-1);
39			return(0);
40			}
41
42
43			static int
44			ambnorm(d1, d2) /* standard order */
45			AMBSAMP d1, d2;
46			{
47			register int c;
48
49			if (c = d1->t - d2->t)
50			return(c);
51			return(d1->p - d2->p);
52			}
53
54
55			divsample(dp, h, r) /* sample a division */
56			register AMBSAMP *dp;
57			AMBHEMI *h;
58			RAY *r;
59			{
60			RAY ar;
61	greg	1.11	int hlist[3];
62			double spt[2];
63	greg	1.1	double xd, yd, zd;
64			double b2;
65			double phi;
66	greg	1.2	register int i;
67	greg	1.1
68	greg	1.12	if (rayorigin(&ar, r, AMBIENT, AVGREFL) < 0)
69	greg	1.4	return(-1);
70	greg	1.1	hlist[0] = r->rno;
71			hlist[1] = dp->t;
72			hlist[2] = dp->p;
73	greg	1.13	multisamp(spt, 2, urand(ilhash(hlist,3)+dp->n));
74	greg	1.11	zd = sqrt((dp->t + spt[0])/h->nt);
75			phi = 2.0PI (dp->p + spt[1])/h->np;
76	greg	1.1	xd = cos(phi) * zd;
77			yd = sin(phi) * zd;
78			zd = sqrt(1.0 - zd*zd);
79	greg	1.2	for (i = 0; i < 3; i++)
80			ar.rdir[i] = xd*h->ux[i] +
81			yd*h->uy[i] +
82			zd*h->uz[i];
83			dimlist[ndims++] = dp->t*h->np + dp->p + 90171;
84	greg	1.1	rayvalue(&ar);
85			ndims--;
86			addcolor(dp->v, ar.rcol);
87	greg	1.8	if (ar.rt > FTINY && ar.rt < FHUGE)
88	greg	1.4	dp->r += 1.0/ar.rt;
89	greg	1.1	/* (re)initialize error */
90			if (dp->n++) {
91			b2 = bright(dp->v)/dp->n - bright(ar.rcol);
92			b2 = b2b2 + dp->k((dp->n-1)*(dp->n-1));
93			dp->k = b2/(dp->n*dp->n);
94			} else
95			dp->k = 0.0;
96	greg	1.4	return(0);
97	greg	1.1	}
98
99
100			double
101	greg	1.12	doambient(acol, r, wt, pg, dg) /* compute ambient component */
102	greg	1.1	COLOR acol;
103			RAY *r;
104	greg	1.12	double wt;
105	greg	1.1	FVECT pg, dg;
106			{
107			double b, d;
108			AMBHEMI hemi;
109			AMBSAMP *div;
110			AMBSAMP dnew;
111			register AMBSAMP *dp;
112			double arad;
113			int ndivs, ns;
114			register int i, j;
115			/* initialize color */
116			setcolor(acol, 0.0, 0.0, 0.0);
117			/* initialize hemisphere */
118	greg	1.12	inithemi(&hemi, r, wt);
119	greg	1.1	ndivs = hemi.nt * hemi.np;
120			if (ndivs == 0)
121			return(0.0);
122			/* set number of super-samples */
123	greg	1.12	ns = ambssamp * wt + 0.5;
124	greg	1.1	if (ns > 0 \|\| pg != NULL \|\| dg != NULL) {
125			div = (AMBSAMP )malloc(ndivssizeof(AMBSAMP));
126			if (div == NULL)
127			error(SYSTEM, "out of memory in doambient");
128			} else
129			div = NULL;
130			/* sample the divisions */
131			arad = 0.0;
132			if ((dp = div) == NULL)
133			dp = &dnew;
134			for (i = 0; i < hemi.nt; i++)
135			for (j = 0; j < hemi.np; j++) {
136			dp->t = i; dp->p = j;
137			setcolor(dp->v, 0.0, 0.0, 0.0);
138	greg	1.2	dp->r = 0.0;
139	greg	1.1	dp->n = 0;
140	greg	1.4	if (divsample(dp, &hemi, r) < 0)
141	greg	1.1	goto oopsy;
142	greg	2.6	arad += dp->r;
143	greg	1.1	if (div != NULL)
144			dp++;
145	greg	2.6	else
146	greg	1.1	addcolor(acol, dp->v);
147			}
148	greg	2.5	if (ns > 0 && arad > FTINY && ndivs/arad < minarad)
149			ns = 0; /* close enough */
150			else if (ns > 0) { /* else 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	greg	2.6	arad = 0.0;
173	greg	1.3	for (i = ndivs, dp = div; i-- > 0; dp++) {
174			arad += dp->r;
175			if (dp->n > 1) {
176			b = 1.0/dp->n;
177			scalecolor(dp->v, b);
178			dp->r *= b;
179			dp->n = 1;
180			}
181			addcolor(acol, dp->v);
182			}
183	greg	1.5	b = bright(acol);
184	greg	1.6	if (b > FTINY) {
185	greg	1.5	b = ndivs/b;
186	greg	1.6	if (pg != NULL) {
187			posgradient(pg, div, &hemi);
188			for (i = 0; i < 3; i++)
189			pg[i] *= b;
190			}
191			if (dg != NULL) {
192			dirgradient(dg, div, &hemi);
193			for (i = 0; i < 3; i++)
194			dg[i] *= b;
195			}
196			} else {
197			if (pg != NULL)
198			for (i = 0; i < 3; i++)
199			pg[i] = 0.0;
200			if (dg != NULL)
201			for (i = 0; i < 3; i++)
202			dg[i] = 0.0;
203	greg	1.5	}
204	greg	1.1	free((char *)div);
205	greg	1.3	}
206	greg	1.1	b = 1.0/ndivs;
207			scalecolor(acol, b);
208			if (arad <= FTINY)
209	greg	1.16	arad = maxarad;
210	greg	2.3	else
211	greg	1.1	arad = (ndivs+ns)/arad;
212	greg	1.15	if (pg != NULL) { /* reduce radius if gradient large */
213			d = DOT(pg,pg);
214			if (daradarad > 1.0)
215			arad = 1.0/sqrt(d);
216			}
217	greg	1.16	if (arad < minarad) {
218	greg	1.1	arad = minarad;
219	greg	1.16	if (pg != NULL && daradarad > 1.0) { /* cap gradient */
220			d = 1.0/arad/sqrt(d);
221			for (i = 0; i < 3; i++)
222			pg[i] *= d;
223			}
224			}
225	greg	2.3	if ((arad /= sqrt(wt)) > maxarad)
226			arad = maxarad;
227			return(arad);
228	greg	1.1	oopsy:
229			if (div != NULL)
230			free((char *)div);
231			return(0.0);
232			}
233
234
235	greg	1.12	inithemi(hp, r, wt) /* initialize sampling hemisphere */
236	greg	1.1	register AMBHEMI *hp;
237			RAY *r;
238	greg	1.12	double wt;
239	greg	1.1	{
240	greg	1.2	register int i;
241	greg	1.1	/* set number of divisions */
242	greg	1.14	if (wt < (.25*PI)/ambdiv+FTINY) {
243			hp->nt = hp->np = 0;
244			return; /* zero samples */
245			}
246	greg	1.12	hp->nt = sqrt(ambdiv * wt / PI) + 0.5;
247	greg	1.14	hp->np = PI * hp->nt + 0.5;
248	greg	1.1	/* make axes */
249			VCOPY(hp->uz, r->ron);
250			hp->uy[0] = hp->uy[1] = hp->uy[2] = 0.0;
251	greg	1.2	for (i = 0; i < 3; i++)
252			if (hp->uz[i] < 0.6 && hp->uz[i] > -0.6)
253	greg	1.1	break;
254	greg	1.2	if (i >= 3)
255	greg	1.1	error(CONSISTENCY, "bad ray direction in inithemi");
256	greg	1.2	hp->uy[i] = 1.0;
257	greg	1.3	fcross(hp->ux, hp->uy, hp->uz);
258			normalize(hp->ux);
259			fcross(hp->uy, hp->uz, hp->ux);
260	greg	1.1	}
261
262
263			comperrs(da, hp) /* compute initial error estimates */
264	greg	1.2	AMBSAMP da; / assumes standard ordering */
265	greg	1.1	register AMBHEMI *hp;
266			{
267			double b, b2;
268			int i, j;
269			register AMBSAMP *dp;
270			/* sum differences from neighbors */
271			dp = da;
272			for (i = 0; i < hp->nt; i++)
273			for (j = 0; j < hp->np; j++) {
274	greg	1.6	#ifdef DEBUG
275			if (dp->t != i \|\| dp->p != j)
276			error(CONSISTENCY,
277			"division order in comperrs");
278			#endif
279	greg	1.1	b = bright(dp[0].v);
280			if (i > 0) { /* from above */
281			b2 = bright(dp[-hp->np].v) - b;
282			b2 = b2 0.25;
283			dp[0].k += b2;
284			dp[-hp->np].k += b2;
285			}
286			if (j > 0) { /* from behind */
287			b2 = bright(dp[-1].v) - b;
288			b2 = b2 0.25;
289			dp[0].k += b2;
290			dp[-1].k += b2;
291	greg	1.4	} else { /* around */
292			b2 = bright(dp[hp->np-1].v) - b;
293	greg	1.1	b2 = b2 0.25;
294			dp[0].k += b2;
295	greg	1.4	dp[hp->np-1].k += b2;
296	greg	1.1	}
297			dp++;
298			}
299			/* divide by number of neighbors */
300			dp = da;
301			for (j = 0; j < hp->np; j++) /* top row */
302			(dp++)->k *= 1.0/3.0;
303			if (hp->nt < 2)
304			return;
305			for (i = 1; i < hp->nt-1; i++) /* central region */
306			for (j = 0; j < hp->np; j++)
307			(dp++)->k *= 0.25;
308			for (j = 0; j < hp->np; j++) /* bottom row */
309			(dp++)->k *= 1.0/3.0;
310			}
311
312
313			posgradient(gv, da, hp) /* compute position gradient */
314			FVECT gv;
315	greg	1.2	AMBSAMP da; / assumes standard ordering */
316	greg	2.2	register AMBHEMI *hp;
317	greg	1.1	{
318	greg	1.2	register int i, j;
319	greg	2.2	double nextsine, lastsine, b, d;
320	greg	1.2	double mag0, mag1;
321			double phi, cosp, sinp, xd, yd;
322			register AMBSAMP *dp;
323
324			xd = yd = 0.0;
325			for (j = 0; j < hp->np; j++) {
326			dp = da + j;
327			mag0 = mag1 = 0.0;
328	greg	2.2	lastsine = 0.0;
329	greg	1.2	for (i = 0; i < hp->nt; i++) {
330			#ifdef DEBUG
331			if (dp->t != i \|\| dp->p != j)
332			error(CONSISTENCY,
333			"division order in posgradient");
334			#endif
335			b = bright(dp->v);
336			if (i > 0) {
337			d = dp[-hp->np].r;
338			if (dp[0].r > d) d = dp[0].r;
339	greg	2.2	/* sin(t)cos(t)^2 /
340			d = lastsine (1.0 - (double)i/hp->nt);
341	greg	1.2	mag0 += d*(b - bright(dp[-hp->np].v));
342			}
343	greg	2.2	nextsine = sqrt((double)(i+1)/hp->nt);
344	greg	1.2	if (j > 0) {
345			d = dp[-1].r;
346			if (dp[0].r > d) d = dp[0].r;
347	greg	2.2	mag1 += d * (nextsine - lastsine) *
348			(b - bright(dp[-1].v));
349	greg	1.2	} else {
350			d = dp[hp->np-1].r;
351			if (dp[0].r > d) d = dp[0].r;
352	greg	2.2	mag1 += d * (nextsine - lastsine) *
353			(b - bright(dp[hp->np-1].v));
354	greg	1.2	}
355			dp += hp->np;
356	greg	2.2	lastsine = nextsine;
357	greg	1.2	}
358	greg	2.2	mag0 = 2.0PI / hp->np;
359	greg	1.2	phi = 2.0PI (double)j/hp->np;
360			cosp = cos(phi); sinp = sin(phi);
361			xd += mag0cosp - mag1sinp;
362			yd += mag0sinp + mag1cosp;
363			}
364			for (i = 0; i < 3; i++)
365	greg	1.5	gv[i] = (xdhp->ux[i] + ydhp->uy[i])/PI;
366	greg	1.1	}
367
368
369			dirgradient(gv, da, hp) /* compute direction gradient */
370			FVECT gv;
371	greg	1.2	AMBSAMP da; / assumes standard ordering */
372	greg	2.2	register AMBHEMI *hp;
373	greg	1.1	{
374	greg	1.2	register int i, j;
375			double mag;
376			double phi, xd, yd;
377			register AMBSAMP *dp;
378
379			xd = yd = 0.0;
380			for (j = 0; j < hp->np; j++) {
381			dp = da + j;
382			mag = 0.0;
383			for (i = 0; i < hp->nt; i++) {
384			#ifdef DEBUG
385			if (dp->t != i \|\| dp->p != j)
386			error(CONSISTENCY,
387			"division order in dirgradient");
388			#endif
389	greg	2.2	/* tan(t) */
390			mag += bright(dp->v)/sqrt(hp->nt/(i+.5) - 1.0);
391	greg	1.2	dp += hp->np;
392			}
393			phi = 2.0PI (j+.5)/hp->np + PI/2.0;
394			xd += mag * cos(phi);
395			yd += mag * sin(phi);
396			}
397			for (i = 0; i < 3; i++)
398	greg	2.2	gv[i] = (xdhp->ux[i] + ydhp->uy[i])/(hp->nt*hp->np);
399	greg	1.1	}