src/rt/ambcomp.c

#ifndef lint
static const char       RCSid[] = "$Id: ambcomp.c,v 2.16 2005/05/31 18:01:09 greg Exp $";
#endif
/*
 * Routines to compute "ambient" values using Monte Carlo
 *
 *  Declarations of external symbols in ambient.h
 */

#include "copyright.h"

#include  "ray.h"

#include  "ambient.h"

#include  "random.h"


void
inithemi(                       /* initialize sampling hemisphere */
        register AMBHEMI  *hp,
        COLOR ac,
        RAY  *r,
        double  wt
)
{
        double  d;
        register int  i;
                                        /* set number of divisions */
        if (ambacc <= FTINY &&
                        wt > (d = 0.8*bright(ac)*r->rweight/(ambdiv*minweight)))
                wt = d;                 /* avoid ray termination */
        hp->nt = sqrt(ambdiv * wt / PI) + 0.5;
        i = ambacc > FTINY ? 3 : 1;     /* minimum number of samples */
        if (hp->nt < i)
                hp->nt = i;
        hp->np = PI * hp->nt + 0.5;
                                        /* set number of super-samples */
        hp->ns = ambssamp * wt + 0.5;
                                        /* assign coefficient */
        copycolor(hp->acoef, ac);
        d = 1.0/(hp->nt*hp->np);
        scalecolor(hp->acoef, d);
                                        /* 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);
}


int
divsample(                              /* 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;
                                        /* ambient coefficient for weight */
        if (ambacc > FTINY)
                setcolor(ar.rcoef, AVGREFL, AVGREFL, AVGREFL);
        else
                copycolor(ar.rcoef, h->acoef);
        if (rayorigin(&ar, AMBIENT, r, ar.rcoef) < 0)
                return(-1);
        if (ambacc > FTINY) {
                multcolor(ar.rcoef, h->acoef);
                scalecolor(ar.rcoef, 1./AVGREFL);
        }
        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 = tcos(phi) * zd;
        yd = tsin(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--;
        multcolor(ar.rcol, ar.rcoef);   /* apply coefficient */
        addcolor(dp->v, ar.rcol);
                                        /* use rt to improve gradient calc */
        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);
}


static int
ambcmp(                                 /* decreasing order */
        const void *p1,
        const void *p2
)
{
        const AMBSAMP   *d1 = (const AMBSAMP *)p1;
        const AMBSAMP   *d2 = (const AMBSAMP *)p2;

        if (d1->k < d2->k)
                return(1);
        if (d1->k > d2->k)
                return(-1);
        return(0);
}


static int
ambnorm(                                /* standard order */
        const void *p1,
        const void *p2
)
{
        const AMBSAMP   *d1 = (const AMBSAMP *)p1;
        const AMBSAMP   *d2 = (const AMBSAMP *)p2;
        register int    c;

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


double
doambient(                              /* compute ambient component */
        COLOR  acol,
        RAY  *r,
        double  wt,
        FVECT  pg,
        FVECT  dg
)
{
        double  b, d;
        AMBHEMI  hemi;
        AMBSAMP  *div;
        AMBSAMP  dnew;
        register AMBSAMP  *dp;
        double  arad;
        int  ndivs;
        register int  i, j;
                                        /* initialize hemisphere */
        inithemi(&hemi, acol, r, wt);
        ndivs = hemi.nt * hemi.np;
                                        /* initialize */
        if (pg != NULL)
                pg[0] = pg[1] = pg[2] = 0.0;
        if (dg != NULL)
                dg[0] = dg[1] = dg[2] = 0.0;
        setcolor(acol, 0.0, 0.0, 0.0);
        if (ndivs == 0)
                return(0.0);
                                        /* allocate super-samples */
        if (hemi.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) {
                                if (div != NULL) dp++;
                                hemi.ns = 0;    /* incomplete sampling */
                                pg = dg = NULL;
                                continue;
                        }
                        arad += dp->r;
                        if (div != NULL)
                                dp++;
                        else
                                addcolor(acol, dp->v);
                }
        if (hemi.ns > 0 && arad > FTINY && ndivs/arad < minarad)
                hemi.ns = 0;            /* close enough */
        else if (hemi.ns > 0) {         /* else perform super-sampling */
                comperrs(div, &hemi);                   /* compute errors */
                qsort(div, ndivs, sizeof(AMBSAMP), ambcmp);     /* sort divs */
                                                /* super-sample */
                for (i = hemi.ns; i > 0; i--) {
                        dnew = *div;
                        if (divsample(&dnew, &hemi, r) < 0) {
                                dp++;
                                continue;
                        }
                        dp = div;               /* reinsert */
                        j = ndivs < i ? ndivs : i;
                        while (--j > 0 && dnew.k < dp[1].k) {
                                *dp = *(dp+1);
                                dp++;
                        }
                        *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 = 1.0/b;      /* compute & normalize gradient(s) */
                        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;
                        }
                }
                free((void *)div);
        }
        if (arad <= FTINY)
                arad = maxarad;
        else
                arad = (ndivs+hemi.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);
}


void
comperrs(                       /* 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;
}


void
posgradient(                                    /* 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 = tcos(phi); sinp = tsin(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])*(hp->nt*hp->np)/PI;
}


void
dirgradient(                                    /* 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 * tcos(phi);
                yd += mag * tsin(phi);
        }
        for (i = 0; i < 3; i++)
                gv[i] = xd*hp->ux[i] + yd*hp->uy[i];
}
Revision:	2.17
Committed:	Sat Jun 4 06:10:12 2005 UTC (18 years, 10 months ago) by greg
Content type:	text/plain
Branch:	MAIN
Changes since 2.16:	+13 -12 lines
Log Message:	Bug fix for -aa 0 -as > 0
#	User	Rev	Content
1	greg	1.1	#ifndef lint
2	greg	2.17	static const char RCSid[] = "$Id: ambcomp.c,v 2.16 2005/05/31 18:01:09 greg Exp $";
3	greg	1.1	#endif
4			/*
5			* Routines to compute "ambient" values using Monte Carlo
6	greg	2.9	*
7			* Declarations of external symbols in ambient.h
8			*/
9
10	greg	2.10	#include "copyright.h"
11	greg	1.1
12			#include "ray.h"
13
14			#include "ambient.h"
15
16			#include "random.h"
17
18
19	greg	2.15	void
20	greg	2.14	inithemi( /* initialize sampling hemisphere */
21			register AMBHEMI *hp,
22	greg	2.16	COLOR ac,
23	greg	2.14	RAY *r,
24			double wt
25			)
26	greg	1.1	{
27	greg	2.16	double d;
28	greg	2.14	register int i;
29			/* set number of divisions */
30	greg	2.16	if (ambacc <= FTINY &&
31			wt > (d = 0.8bright(ac)r->rweight/(ambdiv*minweight)))
32			wt = d; /* avoid ray termination */
33			hp->nt = sqrt(ambdiv * wt / PI) + 0.5;
34	greg	2.14	i = ambacc > FTINY ? 3 : 1; /* minimum number of samples */
35			if (hp->nt < i)
36			hp->nt = i;
37			hp->np = PI * hp->nt + 0.5;
38			/* set number of super-samples */
39	greg	2.15	hp->ns = ambssamp * wt + 0.5;
40	greg	2.16	/* assign coefficient */
41	greg	2.14	copycolor(hp->acoef, ac);
42	greg	2.16	d = 1.0/(hp->nt*hp->np);
43			scalecolor(hp->acoef, d);
44	greg	2.14	/* make axes */
45			VCOPY(hp->uz, r->ron);
46			hp->uy[0] = hp->uy[1] = hp->uy[2] = 0.0;
47			for (i = 0; i < 3; i++)
48			if (hp->uz[i] < 0.6 && hp->uz[i] > -0.6)
49			break;
50			if (i >= 3)
51			error(CONSISTENCY, "bad ray direction in inithemi");
52			hp->uy[i] = 1.0;
53			fcross(hp->ux, hp->uy, hp->uz);
54			normalize(hp->ux);
55			fcross(hp->uy, hp->uz, hp->ux);
56	greg	1.1	}
57
58
59	greg	2.9	int
60	greg	2.14	divsample( /* sample a division */
61			register AMBSAMP *dp,
62			AMBHEMI *h,
63			RAY *r
64			)
65	greg	1.1	{
66			RAY ar;
67	greg	1.11	int hlist[3];
68			double spt[2];
69	greg	1.1	double xd, yd, zd;
70			double b2;
71			double phi;
72	greg	1.2	register int i;
73	greg	2.15	/* ambient coefficient for weight */
74	greg	2.16	if (ambacc > FTINY)
75			setcolor(ar.rcoef, AVGREFL, AVGREFL, AVGREFL);
76			else
77			copycolor(ar.rcoef, h->acoef);
78	greg	2.14	if (rayorigin(&ar, AMBIENT, r, ar.rcoef) < 0)
79	greg	1.4	return(-1);
80	greg	2.17	if (ambacc > FTINY) {
81			multcolor(ar.rcoef, h->acoef);
82			scalecolor(ar.rcoef, 1./AVGREFL);
83			}
84	greg	1.1	hlist[0] = r->rno;
85			hlist[1] = dp->t;
86			hlist[2] = dp->p;
87	greg	1.13	multisamp(spt, 2, urand(ilhash(hlist,3)+dp->n));
88	greg	1.11	zd = sqrt((dp->t + spt[0])/h->nt);
89			phi = 2.0PI (dp->p + spt[1])/h->np;
90	gwlarson	2.8	xd = tcos(phi) * zd;
91			yd = tsin(phi) * zd;
92	greg	1.1	zd = sqrt(1.0 - zd*zd);
93	greg	1.2	for (i = 0; i < 3; i++)
94			ar.rdir[i] = xd*h->ux[i] +
95			yd*h->uy[i] +
96			zd*h->uz[i];
97			dimlist[ndims++] = dp->t*h->np + dp->p + 90171;
98	greg	1.1	rayvalue(&ar);
99			ndims--;
100	greg	2.16	multcolor(ar.rcol, ar.rcoef); /* apply coefficient */
101	greg	1.1	addcolor(dp->v, ar.rcol);
102	greg	2.9	/* use rt to improve gradient calc */
103			if (ar.rt > FTINY && ar.rt < FHUGE)
104			dp->r += 1.0/ar.rt;
105	greg	1.1	/* (re)initialize error */
106			if (dp->n++) {
107			b2 = bright(dp->v)/dp->n - bright(ar.rcol);
108			b2 = b2b2 + dp->k((dp->n-1)*(dp->n-1));
109			dp->k = b2/(dp->n*dp->n);
110			} else
111			dp->k = 0.0;
112	greg	1.4	return(0);
113	greg	1.1	}
114
115
116	greg	2.14	static int
117			ambcmp( /* decreasing order */
118			const void *p1,
119			const void *p2
120			)
121			{
122			const AMBSAMP d1 = (const AMBSAMP )p1;
123			const AMBSAMP d2 = (const AMBSAMP )p2;
124
125			if (d1->k < d2->k)
126			return(1);
127			if (d1->k > d2->k)
128			return(-1);
129			return(0);
130			}
131
132
133			static int
134			ambnorm( /* standard order */
135			const void *p1,
136			const void *p2
137			)
138			{
139			const AMBSAMP d1 = (const AMBSAMP )p1;
140			const AMBSAMP d2 = (const AMBSAMP )p2;
141			register int c;
142
143			if ( (c = d1->t - d2->t) )
144			return(c);
145			return(d1->p - d2->p);
146			}
147
148
149	greg	1.1	double
150	greg	2.14	doambient( /* compute ambient component */
151			COLOR acol,
152			RAY *r,
153			double wt,
154			FVECT pg,
155			FVECT dg
156			)
157	greg	1.1	{
158			double b, d;
159			AMBHEMI hemi;
160			AMBSAMP *div;
161			AMBSAMP dnew;
162			register AMBSAMP *dp;
163			double arad;
164	greg	2.15	int ndivs;
165	greg	1.1	register int i, j;
166			/* initialize hemisphere */
167	greg	2.16	inithemi(&hemi, acol, r, wt);
168	greg	1.1	ndivs = hemi.nt * hemi.np;
169	greg	2.17	/* initialize */
170			if (pg != NULL)
171			pg[0] = pg[1] = pg[2] = 0.0;
172			if (dg != NULL)
173			dg[0] = dg[1] = dg[2] = 0.0;
174	greg	2.16	setcolor(acol, 0.0, 0.0, 0.0);
175	greg	1.1	if (ndivs == 0)
176			return(0.0);
177	greg	2.14	/* allocate super-samples */
178	greg	2.15	if (hemi.ns > 0 \|\| pg != NULL \|\| dg != NULL) {
179	greg	1.1	div = (AMBSAMP )malloc(ndivssizeof(AMBSAMP));
180			if (div == NULL)
181			error(SYSTEM, "out of memory in doambient");
182			} else
183			div = NULL;
184			/* sample the divisions */
185			arad = 0.0;
186			if ((dp = div) == NULL)
187			dp = &dnew;
188			for (i = 0; i < hemi.nt; i++)
189			for (j = 0; j < hemi.np; j++) {
190			dp->t = i; dp->p = j;
191			setcolor(dp->v, 0.0, 0.0, 0.0);
192	greg	1.2	dp->r = 0.0;
193	greg	1.1	dp->n = 0;
194	greg	2.16	if (divsample(dp, &hemi, r) < 0) {
195			if (div != NULL) dp++;
196	greg	2.17	hemi.ns = 0; /* incomplete sampling */
197			pg = dg = NULL;
198	greg	2.16	continue;
199			}
200	greg	2.6	arad += dp->r;
201	greg	1.1	if (div != NULL)
202			dp++;
203	greg	2.6	else
204	greg	1.1	addcolor(acol, dp->v);
205			}
206	greg	2.15	if (hemi.ns > 0 && arad > FTINY && ndivs/arad < minarad)
207			hemi.ns = 0; /* close enough */
208			else if (hemi.ns > 0) { /* else perform super-sampling */
209	greg	1.4	comperrs(div, &hemi); /* compute errors */
210	greg	1.1	qsort(div, ndivs, sizeof(AMBSAMP), ambcmp); /* sort divs */
211			/* super-sample */
212	greg	2.15	for (i = hemi.ns; i > 0; i--) {
213	schorsch	2.11	dnew = *div;
214	greg	2.16	if (divsample(&dnew, &hemi, r) < 0) {
215			dp++;
216			continue;
217			}
218			dp = div; /* reinsert */
219	greg	1.1	j = ndivs < i ? ndivs : i;
220			while (--j > 0 && dnew.k < dp[1].k) {
221	schorsch	2.11	dp = (dp+1);
222	greg	1.1	dp++;
223			}
224	schorsch	2.11	*dp = dnew;
225	greg	1.1	}
226	greg	1.2	if (pg != NULL \|\| dg != NULL) /* restore order */
227	greg	1.1	qsort(div, ndivs, sizeof(AMBSAMP), ambnorm);
228			}
229			/* compute returned values */
230	greg	1.3	if (div != NULL) {
231	greg	2.6	arad = 0.0;
232	greg	1.3	for (i = ndivs, dp = div; i-- > 0; dp++) {
233			arad += dp->r;
234			if (dp->n > 1) {
235			b = 1.0/dp->n;
236			scalecolor(dp->v, b);
237			dp->r *= b;
238			dp->n = 1;
239			}
240			addcolor(acol, dp->v);
241			}
242	greg	1.5	b = bright(acol);
243	greg	1.6	if (b > FTINY) {
244	greg	2.17	b = 1.0/b; /* compute & normalize gradient(s) */
245	greg	1.6	if (pg != NULL) {
246			posgradient(pg, div, &hemi);
247			for (i = 0; i < 3; i++)
248			pg[i] *= b;
249			}
250			if (dg != NULL) {
251			dirgradient(dg, div, &hemi);
252			for (i = 0; i < 3; i++)
253			dg[i] *= b;
254			}
255	greg	1.5	}
256	greg	2.9	free((void *)div);
257	greg	1.3	}
258	greg	1.1	if (arad <= FTINY)
259	greg	1.16	arad = maxarad;
260	greg	2.3	else
261	greg	2.15	arad = (ndivs+hemi.ns)/arad;
262	greg	1.15	if (pg != NULL) { /* reduce radius if gradient large */
263			d = DOT(pg,pg);
264			if (daradarad > 1.0)
265			arad = 1.0/sqrt(d);
266			}
267	greg	1.16	if (arad < minarad) {
268	greg	1.1	arad = minarad;
269	greg	1.16	if (pg != NULL && daradarad > 1.0) { /* cap gradient */
270			d = 1.0/arad/sqrt(d);
271			for (i = 0; i < 3; i++)
272			pg[i] *= d;
273			}
274			}
275	greg	2.3	if ((arad /= sqrt(wt)) > maxarad)
276			arad = maxarad;
277			return(arad);
278	greg	1.1	}
279
280
281	greg	2.9	void
282	greg	2.14	comperrs( /* compute initial error estimates */
283			AMBSAMP da, / assumes standard ordering */
284			register AMBHEMI *hp
285			)
286	greg	1.1	{
287			double b, b2;
288			int i, j;
289			register AMBSAMP *dp;
290			/* sum differences from neighbors */
291			dp = da;
292			for (i = 0; i < hp->nt; i++)
293			for (j = 0; j < hp->np; j++) {
294	greg	1.6	#ifdef DEBUG
295			if (dp->t != i \|\| dp->p != j)
296			error(CONSISTENCY,
297			"division order in comperrs");
298			#endif
299	greg	1.1	b = bright(dp[0].v);
300			if (i > 0) { /* from above */
301			b2 = bright(dp[-hp->np].v) - b;
302			b2 = b2 0.25;
303			dp[0].k += b2;
304			dp[-hp->np].k += b2;
305			}
306			if (j > 0) { /* from behind */
307			b2 = bright(dp[-1].v) - b;
308			b2 = b2 0.25;
309			dp[0].k += b2;
310			dp[-1].k += b2;
311	greg	1.4	} else { /* around */
312			b2 = bright(dp[hp->np-1].v) - b;
313	greg	1.1	b2 = b2 0.25;
314			dp[0].k += b2;
315	greg	1.4	dp[hp->np-1].k += b2;
316	greg	1.1	}
317			dp++;
318			}
319			/* divide by number of neighbors */
320			dp = da;
321			for (j = 0; j < hp->np; j++) /* top row */
322			(dp++)->k *= 1.0/3.0;
323			if (hp->nt < 2)
324			return;
325			for (i = 1; i < hp->nt-1; i++) /* central region */
326			for (j = 0; j < hp->np; j++)
327			(dp++)->k *= 0.25;
328			for (j = 0; j < hp->np; j++) /* bottom row */
329			(dp++)->k *= 1.0/3.0;
330			}
331
332
333	greg	2.9	void
334	greg	2.14	posgradient( /* compute position gradient */
335			FVECT gv,
336			AMBSAMP da, / assumes standard ordering */
337			register AMBHEMI *hp
338			)
339	greg	1.1	{
340	greg	1.2	register int i, j;
341	greg	2.2	double nextsine, lastsine, b, d;
342	greg	1.2	double mag0, mag1;
343			double phi, cosp, sinp, xd, yd;
344			register AMBSAMP *dp;
345
346			xd = yd = 0.0;
347			for (j = 0; j < hp->np; j++) {
348			dp = da + j;
349			mag0 = mag1 = 0.0;
350	greg	2.2	lastsine = 0.0;
351	greg	1.2	for (i = 0; i < hp->nt; i++) {
352			#ifdef DEBUG
353			if (dp->t != i \|\| dp->p != j)
354			error(CONSISTENCY,
355			"division order in posgradient");
356			#endif
357			b = bright(dp->v);
358			if (i > 0) {
359			d = dp[-hp->np].r;
360			if (dp[0].r > d) d = dp[0].r;
361	greg	2.2	/* sin(t)cos(t)^2 /
362			d = lastsine (1.0 - (double)i/hp->nt);
363	greg	1.2	mag0 += d*(b - bright(dp[-hp->np].v));
364			}
365	greg	2.2	nextsine = sqrt((double)(i+1)/hp->nt);
366	greg	1.2	if (j > 0) {
367			d = dp[-1].r;
368			if (dp[0].r > d) d = dp[0].r;
369	greg	2.2	mag1 += d * (nextsine - lastsine) *
370			(b - bright(dp[-1].v));
371	greg	1.2	} else {
372			d = dp[hp->np-1].r;
373			if (dp[0].r > d) d = dp[0].r;
374	greg	2.2	mag1 += d * (nextsine - lastsine) *
375			(b - bright(dp[hp->np-1].v));
376	greg	1.2	}
377			dp += hp->np;
378	greg	2.2	lastsine = nextsine;
379	greg	1.2	}
380	greg	2.2	mag0 = 2.0PI / hp->np;
381	greg	1.2	phi = 2.0PI (double)j/hp->np;
382	gwlarson	2.8	cosp = tcos(phi); sinp = tsin(phi);
383	greg	1.2	xd += mag0cosp - mag1sinp;
384			yd += mag0sinp + mag1cosp;
385			}
386			for (i = 0; i < 3; i++)
387	greg	2.16	gv[i] = (xdhp->ux[i] + ydhp->uy[i])(hp->nthp->np)/PI;
388	greg	1.1	}
389
390
391	greg	2.9	void
392	greg	2.14	dirgradient( /* compute direction gradient */
393			FVECT gv,
394			AMBSAMP da, / assumes standard ordering */
395			register AMBHEMI *hp
396			)
397	greg	1.1	{
398	greg	1.2	register int i, j;
399			double mag;
400			double phi, xd, yd;
401			register AMBSAMP *dp;
402
403			xd = yd = 0.0;
404			for (j = 0; j < hp->np; j++) {
405			dp = da + j;
406			mag = 0.0;
407			for (i = 0; i < hp->nt; i++) {
408			#ifdef DEBUG
409			if (dp->t != i \|\| dp->p != j)
410			error(CONSISTENCY,
411			"division order in dirgradient");
412			#endif
413	greg	2.2	/* tan(t) */
414			mag += bright(dp->v)/sqrt(hp->nt/(i+.5) - 1.0);
415	greg	1.2	dp += hp->np;
416			}
417			phi = 2.0PI (j+.5)/hp->np + PI/2.0;
418	gwlarson	2.8	xd += mag * tcos(phi);
419			yd += mag * tsin(phi);
420	greg	1.2	}
421			for (i = 0; i < 3; i++)
422	greg	2.16	gv[i] = xdhp->ux[i] + ydhp->uy[i];
423	greg	1.1	}