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);
}


double
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(0.0);
        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.rot < FHUGE)
                dp->r += 1.0/ar.rot;
                                        /* (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(ar.rot);
}


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 ((d = divsample(dp, &hemi, r)) == 0.0)
                                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 ((d = divsample(&dnew, &hemi)) == 0.0)
                                goto oopsy;
                        if (d < FHUGE)
                                arad += 1.0 / d;
                                                        /* 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);
                }
                if (pg != NULL)
                        posgradient(pg, div, &hemi);
                if (dg != NULL)
                        dirgradient(dg, div, &hemi);
                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++) {
                        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;
                        }
                        if (j == hp->np-1) {    /* 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->nt-1);
                        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])/hp->np;
}


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])/(hp->nt*hp->np);
}
Revision:	1.3
Committed:	Fri Jun 7 17:08:34 1991 UTC (32 years, 11 months ago) by greg
Content type:	text/plain
Branch:	MAIN
Changes since 1.2:	+19 -26 lines
Log Message:	bug fixes
#	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	greg	1.2	double
58	greg	1.1	divsample(dp, h, r) /* sample a division */
59			register AMBSAMP *dp;
60			AMBHEMI *h;
61			RAY *r;
62			{
63			RAY ar;
64			int hlist[4];
65			double xd, yd, zd;
66			double b2;
67			double phi;
68	greg	1.2	register int i;
69	greg	1.1
70			if (rayorigin(&ar, r, AMBIENT, 0.5) < 0)
71			return(0.0);
72			hlist[0] = r->rno;
73			hlist[1] = dp->t;
74			hlist[2] = dp->p;
75			hlist[3] = 0;
76			zd = sqrt((dp->t+urand(ilhash(hlist,4)+dp->n))/h->nt);
77			hlist[3] = 1;
78			phi = 2.0PI (dp->p+urand(ilhash(hlist,4)+dp->n))/h->np;
79			xd = cos(phi) * zd;
80			yd = sin(phi) * zd;
81			zd = sqrt(1.0 - zd*zd);
82	greg	1.2	for (i = 0; i < 3; i++)
83			ar.rdir[i] = xd*h->ux[i] +
84			yd*h->uy[i] +
85			zd*h->uz[i];
86			dimlist[ndims++] = dp->t*h->np + dp->p + 90171;
87	greg	1.1	rayvalue(&ar);
88			ndims--;
89			addcolor(dp->v, ar.rcol);
90	greg	1.2	if (ar.rot < FHUGE)
91			dp->r += 1.0/ar.rot;
92	greg	1.1	/* (re)initialize error */
93			if (dp->n++) {
94			b2 = bright(dp->v)/dp->n - bright(ar.rcol);
95			b2 = b2b2 + dp->k((dp->n-1)*(dp->n-1));
96			dp->k = b2/(dp->n*dp->n);
97			} else
98			dp->k = 0.0;
99			return(ar.rot);
100			}
101
102
103			double
104			doambient(acol, r, pg, dg) /* compute ambient component */
105			COLOR acol;
106			RAY *r;
107			FVECT pg, dg;
108			{
109			double b, d;
110			AMBHEMI hemi;
111			AMBSAMP *div;
112			AMBSAMP dnew;
113			register AMBSAMP *dp;
114			double arad;
115			int ndivs, ns;
116			register int i, j;
117			/* initialize color */
118			setcolor(acol, 0.0, 0.0, 0.0);
119			/* initialize hemisphere */
120			inithemi(&hemi, r);
121			ndivs = hemi.nt * hemi.np;
122			if (ndivs == 0)
123			return(0.0);
124			/* set number of super-samples */
125			ns = ambssamp * r->rweight + 0.5;
126			if (ns > 0 \|\| pg != NULL \|\| dg != NULL) {
127			div = (AMBSAMP )malloc(ndivssizeof(AMBSAMP));
128			if (div == NULL)
129			error(SYSTEM, "out of memory in doambient");
130			} else
131			div = NULL;
132			/* sample the divisions */
133			arad = 0.0;
134			if ((dp = div) == NULL)
135			dp = &dnew;
136			for (i = 0; i < hemi.nt; i++)
137			for (j = 0; j < hemi.np; j++) {
138			dp->t = i; dp->p = j;
139			setcolor(dp->v, 0.0, 0.0, 0.0);
140	greg	1.2	dp->r = 0.0;
141	greg	1.1	dp->n = 0;
142			if ((d = divsample(dp, &hemi, r)) == 0.0)
143			goto oopsy;
144			if (div != NULL)
145			dp++;
146	greg	1.2	else {
147	greg	1.1	addcolor(acol, dp->v);
148	greg	1.2	arad += dp->r;
149			}
150	greg	1.1	}
151			if (ns > 0) { /* perform super-sampling */
152			comperrs(div, hemi); /* compute errors */
153			qsort(div, ndivs, sizeof(AMBSAMP), ambcmp); /* sort divs */
154			/* super-sample */
155			for (i = ns; i > 0; i--) {
156			copystruct(&dnew, div);
157			if ((d = divsample(&dnew, &hemi)) == 0.0)
158			goto oopsy;
159			if (d < FHUGE)
160			arad += 1.0 / d;
161			/* reinsert */
162			dp = div;
163			j = ndivs < i ? ndivs : i;
164			while (--j > 0 && dnew.k < dp[1].k) {
165			copystruct(dp, dp+1);
166			dp++;
167			}
168			copystruct(dp, &dnew);
169			}
170	greg	1.2	if (pg != NULL \|\| dg != NULL) /* restore order */
171	greg	1.1	qsort(div, ndivs, sizeof(AMBSAMP), ambnorm);
172			}
173			/* compute returned values */
174	greg	1.3	if (div != NULL) {
175			for (i = ndivs, dp = div; i-- > 0; dp++) {
176			arad += dp->r;
177			if (dp->n > 1) {
178			b = 1.0/dp->n;
179			scalecolor(dp->v, b);
180			dp->r *= b;
181			dp->n = 1;
182			}
183			addcolor(acol, dp->v);
184			}
185			if (pg != NULL)
186			posgradient(pg, div, &hemi);
187			if (dg != NULL)
188			dirgradient(dg, div, &hemi);
189	greg	1.1	free((char *)div);
190	greg	1.3	}
191	greg	1.1	b = 1.0/ndivs;
192			scalecolor(acol, b);
193			if (arad <= FTINY)
194			arad = FHUGE;
195			else
196			arad = (ndivs+ns)/arad;
197			if (arad > maxarad)
198			arad = maxarad;
199			else if (arad < minarad)
200			arad = minarad;
201			arad /= sqrt(r->rweight);
202			return(arad);
203			oopsy:
204			if (div != NULL)
205			free((char *)div);
206			return(0.0);
207			}
208
209
210			inithemi(hp, r) /* initialize sampling hemisphere */
211			register AMBHEMI *hp;
212			RAY *r;
213			{
214	greg	1.2	register int i;
215	greg	1.1	/* set number of divisions */
216			hp->nt = sqrt(ambdiv * r->rweight * 0.5) + 0.5;
217			hp->np = 2 * hp->nt;
218			/* make axes */
219			VCOPY(hp->uz, r->ron);
220			hp->uy[0] = hp->uy[1] = hp->uy[2] = 0.0;
221	greg	1.2	for (i = 0; i < 3; i++)
222			if (hp->uz[i] < 0.6 && hp->uz[i] > -0.6)
223	greg	1.1	break;
224	greg	1.2	if (i >= 3)
225	greg	1.1	error(CONSISTENCY, "bad ray direction in inithemi");
226	greg	1.2	hp->uy[i] = 1.0;
227	greg	1.3	fcross(hp->ux, hp->uy, hp->uz);
228			normalize(hp->ux);
229			fcross(hp->uy, hp->uz, hp->ux);
230	greg	1.1	}
231
232
233			comperrs(da, hp) /* compute initial error estimates */
234	greg	1.2	AMBSAMP da; / assumes standard ordering */
235	greg	1.1	register AMBHEMI *hp;
236			{
237			double b, b2;
238			int i, j;
239			register AMBSAMP *dp;
240			/* sum differences from neighbors */
241			dp = da;
242			for (i = 0; i < hp->nt; i++)
243			for (j = 0; j < hp->np; j++) {
244			b = bright(dp[0].v);
245			if (i > 0) { /* from above */
246			b2 = bright(dp[-hp->np].v) - b;
247			b2 = b2 0.25;
248			dp[0].k += b2;
249			dp[-hp->np].k += b2;
250			}
251			if (j > 0) { /* from behind */
252			b2 = bright(dp[-1].v) - b;
253			b2 = b2 0.25;
254			dp[0].k += b2;
255			dp[-1].k += b2;
256			}
257			if (j == hp->np-1) { /* around */
258			b2 = bright(dp[-(hp->np-1)].v) - b;
259			b2 = b2 0.25;
260			dp[0].k += b2;
261			dp[-(hp->np-1)].k += b2;
262			}
263			dp++;
264			}
265			/* divide by number of neighbors */
266			dp = da;
267			for (j = 0; j < hp->np; j++) /* top row */
268			(dp++)->k *= 1.0/3.0;
269			if (hp->nt < 2)
270			return;
271			for (i = 1; i < hp->nt-1; i++) /* central region */
272			for (j = 0; j < hp->np; j++)
273			(dp++)->k *= 0.25;
274			for (j = 0; j < hp->np; j++) /* bottom row */
275			(dp++)->k *= 1.0/3.0;
276			}
277
278
279			posgradient(gv, da, hp) /* compute position gradient */
280			FVECT gv;
281	greg	1.2	AMBSAMP da; / assumes standard ordering */
282	greg	1.1	AMBHEMI *hp;
283			{
284	greg	1.2	register int i, j;
285			double b, d;
286			double mag0, mag1;
287			double phi, cosp, sinp, xd, yd;
288			register AMBSAMP *dp;
289
290			xd = yd = 0.0;
291			for (j = 0; j < hp->np; j++) {
292			dp = da + j;
293			mag0 = mag1 = 0.0;
294			for (i = 0; i < hp->nt; i++) {
295			#ifdef DEBUG
296			if (dp->t != i \|\| dp->p != j)
297			error(CONSISTENCY,
298			"division order in posgradient");
299			#endif
300			b = bright(dp->v);
301			if (i > 0) {
302			d = dp[-hp->np].r;
303			if (dp[0].r > d) d = dp[0].r;
304			d *= 1.0 - sqrt((double)i/hp->nt);
305			mag0 += d*(b - bright(dp[-hp->np].v));
306			}
307			if (j > 0) {
308			d = dp[-1].r;
309			if (dp[0].r > d) d = dp[0].r;
310			mag1 += d*(b - bright(dp[-1].v));
311			} else {
312			d = dp[hp->np-1].r;
313			if (dp[0].r > d) d = dp[0].r;
314			mag1 += d*(b - bright(dp[hp->np-1].v));
315			}
316			dp += hp->np;
317			}
318			if (hp->nt > 1) {
319			mag0 /= (double)(hp->nt-1);
320			mag1 /= (double)hp->nt;
321			}
322			phi = 2.0PI (double)j/hp->np;
323			cosp = cos(phi); sinp = sin(phi);
324			xd += mag0cosp - mag1sinp;
325			yd += mag0sinp + mag1cosp;
326			}
327			for (i = 0; i < 3; i++)
328			gv[i] = (xdhp->ux[i] + ydhp->uy[i])/hp->np;
329	greg	1.1	}
330
331
332			dirgradient(gv, da, hp) /* compute direction gradient */
333			FVECT gv;
334	greg	1.2	AMBSAMP da; / assumes standard ordering */
335	greg	1.1	AMBHEMI *hp;
336			{
337	greg	1.2	register int i, j;
338			double mag;
339			double phi, xd, yd;
340			register AMBSAMP *dp;
341
342			xd = yd = 0.0;
343			for (j = 0; j < hp->np; j++) {
344			dp = da + j;
345			mag = 0.0;
346			for (i = 0; i < hp->nt; i++) {
347			#ifdef DEBUG
348			if (dp->t != i \|\| dp->p != j)
349			error(CONSISTENCY,
350			"division order in dirgradient");
351			#endif
352			mag += sqrt((i+.5)/hp->nt)*bright(dp->v);
353			dp += hp->np;
354			}
355			phi = 2.0PI (j+.5)/hp->np + PI/2.0;
356			xd += mag * cos(phi);
357			yd += mag * sin(phi);
358			}
359			for (i = 0; i < 3; i++)
360			gv[i] = (xdhp->ux[i] + ydhp->uy[i])/(hp->nt*hp->np);
361	greg	1.1	}