| 1 |
#ifndef lint |
| 2 |
static const char RCSid[] = "$Id: ambcomp.c,v 2.95 2024/04/19 01:52:50 greg Exp $"; |
| 3 |
#endif |
| 4 |
/* |
| 5 |
* Routines to compute "ambient" values using Monte Carlo |
| 6 |
* |
| 7 |
* Hessian calculations based on "Practical Hessian-Based Error Control |
| 8 |
* for Irradiance Caching" by Schwarzhaupt, Wann Jensen, & Jarosz |
| 9 |
* from ACM SIGGRAPH Asia 2012 conference proceedings. |
| 10 |
* |
| 11 |
* Added book-keeping optimization to avoid calculations that would |
| 12 |
* cancel due to traversal both directions on edges that are adjacent |
| 13 |
* to same-valued triangles. This cuts about half of Hessian math. |
| 14 |
* |
| 15 |
* Declarations of external symbols in ambient.h |
| 16 |
*/ |
| 17 |
|
| 18 |
#include "copyright.h" |
| 19 |
|
| 20 |
#include "ray.h" |
| 21 |
#include "ambient.h" |
| 22 |
#include "random.h" |
| 23 |
|
| 24 |
#ifndef MINADIV |
| 25 |
#define MINADIV 7 /* minimum # divisions in each dimension */ |
| 26 |
#endif |
| 27 |
|
| 28 |
typedef struct { |
| 29 |
FVECT p; /* intersection point */ |
| 30 |
float d; /* reciprocal distance */ |
| 31 |
SCOLOR v; /* hemisphere sample value */ |
| 32 |
} AMBSAMP; /* sample value */ |
| 33 |
|
| 34 |
typedef struct { |
| 35 |
RAY *rp; /* originating ray sample */ |
| 36 |
int ns; /* number of samples per axis */ |
| 37 |
int sampOK; /* acquired full sample set? */ |
| 38 |
int atyp; /* RAMBIENT or TAMBIENT */ |
| 39 |
SCOLOR acoef; /* division contribution coefficient */ |
| 40 |
SCOLOR acol; /* accumulated color */ |
| 41 |
FVECT onrm; /* oriented unperturbed surface normal */ |
| 42 |
FVECT ux, uy; /* tangent axis unit vectors */ |
| 43 |
AMBSAMP sa[1]; /* sample array (extends struct) */ |
| 44 |
} AMBHEMI; /* ambient sample hemisphere */ |
| 45 |
|
| 46 |
#define AI(h,i,j) ((i)*(h)->ns + (j)) |
| 47 |
#define ambsam(h,i,j) (h)->sa[AI(h,i,j)] |
| 48 |
|
| 49 |
typedef struct { |
| 50 |
FVECT r_i, r_i1, e_i, rcp, rI2_eJ2; |
| 51 |
double I1, I2; |
| 52 |
} FFTRI; /* vectors and coefficients for Hessian calculation */ |
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|
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|
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static int |
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ambcollision( /* proposed direciton collides? */ |
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AMBHEMI *hp, |
| 58 |
int i, |
| 59 |
int j, |
| 60 |
FVECT dv |
| 61 |
) |
| 62 |
{ |
| 63 |
double cos_thresh; |
| 64 |
int ii, jj; |
| 65 |
/* min. spacing = 1/4th division */ |
| 66 |
cos_thresh = (PI/4.)/(double)hp->ns; |
| 67 |
cos_thresh = 1. - .5*cos_thresh*cos_thresh; |
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/* check existing neighbors */ |
| 69 |
for (ii = i-1; ii <= i+1; ii++) { |
| 70 |
if (ii < 0) continue; |
| 71 |
if (ii >= hp->ns) break; |
| 72 |
for (jj = j-1; jj <= j+1; jj++) { |
| 73 |
AMBSAMP *ap; |
| 74 |
FVECT avec; |
| 75 |
double dprod; |
| 76 |
if (jj < 0) continue; |
| 77 |
if (jj >= hp->ns) break; |
| 78 |
if ((ii==i) & (jj==j)) continue; |
| 79 |
ap = &ambsam(hp,ii,jj); |
| 80 |
if (ap->d <= .5/FHUGE) |
| 81 |
continue; /* no one home */ |
| 82 |
VSUB(avec, ap->p, hp->rp->rop); |
| 83 |
dprod = DOT(avec, dv); |
| 84 |
if (dprod >= cos_thresh*VLEN(avec)) |
| 85 |
return(1); /* collision */ |
| 86 |
} |
| 87 |
} |
| 88 |
return(0); /* nothing to worry about */ |
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} |
| 90 |
|
| 91 |
|
| 92 |
static int |
| 93 |
ambsample( /* initial ambient division sample */ |
| 94 |
AMBHEMI *hp, |
| 95 |
int i, |
| 96 |
int j, |
| 97 |
int n |
| 98 |
) |
| 99 |
{ |
| 100 |
AMBSAMP *ap = &ambsam(hp,i,j); |
| 101 |
RAY ar; |
| 102 |
int hlist[3], ii; |
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double ss[2]; |
| 104 |
RREAL spt[2]; |
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double zd; |
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/* generate hemispherical sample */ |
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/* ambient coefficient for weight */ |
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if (ambacc > FTINY) |
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setscolor(ar.rcoef, AVGREFL, AVGREFL, AVGREFL); |
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else |
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copyscolor(ar.rcoef, hp->acoef); |
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if (rayorigin(&ar, hp->atyp, hp->rp, ar.rcoef) < 0) |
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return(0); |
| 114 |
if (ambacc > FTINY) { |
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#ifdef SSKIPOPT |
| 116 |
ar.rsrc = -1; /* protect cache from source opt. */ |
| 117 |
ar.scorr = 1.f; |
| 118 |
#endif |
| 119 |
smultscolor(ar.rcoef, hp->acoef); |
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scalescolor(ar.rcoef, 1./AVGREFL); |
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} |
| 122 |
hlist[0] = hp->rp->rno; |
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hlist[1] = AI(hp,i,j); |
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hlist[2] = samplendx; |
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multisamp(ss, 2, urand(ilhash(hlist,3)+n)); |
| 126 |
resample: |
| 127 |
square2disk(spt, (j+ss[1])/hp->ns, (i+ss[0])/hp->ns); |
| 128 |
zd = sqrt(1. - spt[0]*spt[0] - spt[1]*spt[1]); |
| 129 |
for (ii = 3; ii--; ) |
| 130 |
ar.rdir[ii] = spt[0]*hp->ux[ii] + |
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spt[1]*hp->uy[ii] + |
| 132 |
zd*hp->onrm[ii]; |
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checknorm(ar.rdir); |
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/* avoid coincident samples */ |
| 135 |
if (!n && hp->ns >= 4 && ambcollision(hp, i, j, ar.rdir)) { |
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ss[0] = frandom(); ss[1] = frandom(); |
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goto resample; /* reject this sample */ |
| 138 |
} |
| 139 |
dimlist[ndims++] = AI(hp,i,j) + 90171; |
| 140 |
rayvalue(&ar); /* evaluate ray */ |
| 141 |
ndims--; |
| 142 |
zd = raydistance(&ar); |
| 143 |
if (zd <= FTINY) |
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return(0); /* should never happen */ |
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smultscolor(ar.rcol, ar.rcoef); /* apply coefficient */ |
| 146 |
if (zd*ap->d < 1.0) /* new/closer distance? */ |
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ap->d = 1.0/zd; |
| 148 |
if (!n) { /* record first vertex & value */ |
| 149 |
if (zd > 10.0*thescene.cusize + 1000.) |
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zd = 10.0*thescene.cusize + 1000.; |
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VSUM(ap->p, ar.rorg, ar.rdir, zd); |
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copyscolor(ap->v, ar.rcol); |
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} else { /* else update recorded value */ |
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sopscolor(hp->acol, -=, ap->v); |
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zd = 1.0/(double)(n+1); |
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scalescolor(ar.rcol, zd); |
| 157 |
zd *= (double)n; |
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scalescolor(ap->v, zd); |
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saddscolor(ap->v, ar.rcol); |
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} |
| 161 |
saddscolor(hp->acol, ap->v); /* add to our sum */ |
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return(1); |
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} |
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|
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|
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/* Estimate variance based on ambient division differences */ |
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static float * |
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getambdiffs(AMBHEMI *hp) |
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{ |
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const double normf = 1./(pbright(hp->acoef) + FTINY); |
| 171 |
float *earr = (float *)calloc(2*hp->ns*hp->ns, sizeof(float)); |
| 172 |
float *ep; |
| 173 |
AMBSAMP *ap; |
| 174 |
double b, b1, d2; |
| 175 |
int i, j; |
| 176 |
|
| 177 |
if (earr == NULL) /* out of memory? */ |
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return(NULL); |
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/* sum squared neighbor diffs */ |
| 180 |
ap = hp->sa; |
| 181 |
ep = earr + hp->ns*hp->ns; /* original estimates to scratch */ |
| 182 |
for (i = 0; i < hp->ns; i++) |
| 183 |
for (j = 0; j < hp->ns; j++, ap++, ep++) { |
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b = pbright(ap[0].v); |
| 185 |
if (i) { /* from above */ |
| 186 |
b1 = pbright(ap[-hp->ns].v); |
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d2 = b - b1; |
| 188 |
d2 *= d2*normf/(b + b1 + FTINY); |
| 189 |
ep[0] += d2; |
| 190 |
ep[-hp->ns] += d2; |
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} |
| 192 |
if (!j) continue; |
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/* from behind */ |
| 194 |
b1 = pbright(ap[-1].v); |
| 195 |
d2 = b - b1; |
| 196 |
d2 *= d2*normf/(b + b1 + FTINY); |
| 197 |
ep[0] += d2; |
| 198 |
ep[-1] += d2; |
| 199 |
if (!i) continue; |
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/* diagonal */ |
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b1 = pbright(ap[-hp->ns-1].v); |
| 202 |
d2 = b - b1; |
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d2 *= d2*normf/(b + b1 + FTINY); |
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ep[0] += d2; |
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ep[-hp->ns-1] += d2; |
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} |
| 207 |
/* correct for number of neighbors */ |
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ep = earr + hp->ns*hp->ns; |
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ep[0] *= 6./3.; |
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ep[hp->ns-1] *= 6./3.; |
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ep[(hp->ns-1)*hp->ns] *= 6./3.; |
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ep[(hp->ns-1)*hp->ns + hp->ns-1] *= 6./3.; |
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for (i = 1; i < hp->ns-1; i++) { |
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ep[i*hp->ns] *= 6./5.; |
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ep[i*hp->ns + hp->ns-1] *= 6./5.; |
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} |
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for (j = 1; j < hp->ns-1; j++) { |
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ep[j] *= 6./5.; |
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ep[(hp->ns-1)*hp->ns + j] *= 6./5.; |
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} |
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/* blur final map to reduce bias */ |
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for (i = 0; i < hp->ns-1; i++) { |
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float *ep2; |
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ep = earr + i*hp->ns; |
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ep2 = ep + hp->ns*hp->ns; |
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for (j = 0; j < hp->ns-1; j++, ep++, ep2++) { |
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ep[0] += .5*ep2[0] + .125*(ep2[1] + ep2[hp->ns]); |
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ep[1] += .125*ep2[0]; |
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ep[hp->ns] += .125*ep2[0]; |
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} |
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} |
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return(earr); |
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} |
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|
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|
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/* Perform super-sampling on hemisphere (introduces bias) */ |
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static void |
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ambsupersamp(AMBHEMI *hp, int cnt) |
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{ |
| 240 |
float *earr = getambdiffs(hp); |
| 241 |
double e2rem = 0; |
| 242 |
float *ep; |
| 243 |
int i, j, n, nss; |
| 244 |
|
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if (earr == NULL) /* just skip calc. if no memory */ |
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return; |
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/* accumulate estimated variances */ |
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for (ep = earr + hp->ns*hp->ns; ep > earr; ) |
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e2rem += *--ep; |
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ep = earr; /* perform super-sampling */ |
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for (i = 0; i < hp->ns; i++) |
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for (j = 0; j < hp->ns; j++) { |
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if (e2rem <= FTINY) |
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goto done; /* nothing left to do */ |
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nss = *ep/e2rem*cnt + frandom(); |
| 256 |
for (n = 1; n <= nss && ambsample(hp,i,j,n); n++) |
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if (!--cnt) goto done; |
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e2rem -= *ep++; /* update remainder */ |
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} |
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done: |
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free(earr); |
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} |
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|
| 264 |
|
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static AMBHEMI * |
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samp_hemi( /* sample indirect hemisphere */ |
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SCOLOR rcol, |
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RAY *r, |
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double wt |
| 270 |
) |
| 271 |
{ |
| 272 |
int backside = (wt < 0); |
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AMBHEMI *hp; |
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double d; |
| 275 |
int n, i, j; |
| 276 |
/* insignificance check */ |
| 277 |
d = sintens(rcol); |
| 278 |
if (d <= FTINY) |
| 279 |
return(NULL); |
| 280 |
/* set number of divisions */ |
| 281 |
if (backside) wt = -wt; |
| 282 |
if (ambacc <= FTINY && |
| 283 |
wt > (d *= 0.8*r->rweight/(ambdiv*minweight + 1e-20))) |
| 284 |
wt = d; /* avoid ray termination */ |
| 285 |
n = sqrt(ambdiv * wt) + 0.5; |
| 286 |
i = 1 + (MINADIV-1)*(ambacc > FTINY); |
| 287 |
if (n < i) /* use minimum number of samples? */ |
| 288 |
n = i; |
| 289 |
/* allocate sampling array */ |
| 290 |
hp = (AMBHEMI *)malloc(sizeof(AMBHEMI) + sizeof(AMBSAMP)*(n*n - 1)); |
| 291 |
if (hp == NULL) |
| 292 |
error(SYSTEM, "out of memory in samp_hemi"); |
| 293 |
|
| 294 |
if (backside) { |
| 295 |
hp->atyp = TAMBIENT; |
| 296 |
hp->onrm[0] = -r->ron[0]; |
| 297 |
hp->onrm[1] = -r->ron[1]; |
| 298 |
hp->onrm[2] = -r->ron[2]; |
| 299 |
} else { |
| 300 |
hp->atyp = RAMBIENT; |
| 301 |
VCOPY(hp->onrm, r->ron); |
| 302 |
} |
| 303 |
hp->rp = r; |
| 304 |
hp->ns = n; |
| 305 |
scolorblack(hp->acol); |
| 306 |
memset(hp->sa, 0, sizeof(AMBSAMP)*n*n); |
| 307 |
hp->sampOK = 0; |
| 308 |
/* assign coefficient */ |
| 309 |
copyscolor(hp->acoef, rcol); |
| 310 |
d = 1.0/(n*n); |
| 311 |
scalescolor(hp->acoef, d); |
| 312 |
/* make tangent plane axes */ |
| 313 |
if (!getperpendicular(hp->ux, hp->onrm, 1)) |
| 314 |
error(CONSISTENCY, "bad ray direction in samp_hemi"); |
| 315 |
VCROSS(hp->uy, hp->onrm, hp->ux); |
| 316 |
/* sample divisions */ |
| 317 |
for (i = hp->ns; i--; ) |
| 318 |
for (j = hp->ns; j--; ) |
| 319 |
hp->sampOK += ambsample(hp, i, j, 0); |
| 320 |
copyscolor(rcol, hp->acol); |
| 321 |
if (!hp->sampOK) { /* utter failure? */ |
| 322 |
free(hp); |
| 323 |
return(NULL); |
| 324 |
} |
| 325 |
if (hp->sampOK < hp->ns*hp->ns) { |
| 326 |
hp->sampOK *= -1; /* soft failure */ |
| 327 |
return(hp); |
| 328 |
} |
| 329 |
if (hp->sampOK <= MINADIV*MINADIV) |
| 330 |
return(hp); /* don't bother super-sampling */ |
| 331 |
n = ambssamp*wt + 0.5; |
| 332 |
if (n >= 4*hp->ns) { /* perform super-sampling? */ |
| 333 |
ambsupersamp(hp, n); |
| 334 |
copyscolor(rcol, hp->acol); |
| 335 |
} |
| 336 |
return(hp); /* all is well */ |
| 337 |
} |
| 338 |
|
| 339 |
|
| 340 |
/* Return brightness of farthest ambient sample */ |
| 341 |
static double |
| 342 |
back_ambval(AMBHEMI *hp, const int n1, const int n2, const int n3) |
| 343 |
{ |
| 344 |
if (hp->sa[n1].d <= hp->sa[n2].d) { |
| 345 |
if (hp->sa[n1].d <= hp->sa[n3].d) |
| 346 |
return(hp->sa[n1].v[0]); |
| 347 |
return(hp->sa[n3].v[0]); |
| 348 |
} |
| 349 |
if (hp->sa[n2].d <= hp->sa[n3].d) |
| 350 |
return(hp->sa[n2].v[0]); |
| 351 |
return(hp->sa[n3].v[0]); |
| 352 |
} |
| 353 |
|
| 354 |
|
| 355 |
/* Compute vectors and coefficients for Hessian/gradient calcs */ |
| 356 |
static void |
| 357 |
comp_fftri(FFTRI *ftp, AMBHEMI *hp, const int n0, const int n1) |
| 358 |
{ |
| 359 |
double rdot_cp, dot_e, dot_er, rdot_r, rdot_r1, J2; |
| 360 |
int ii; |
| 361 |
|
| 362 |
VSUB(ftp->r_i, hp->sa[n0].p, hp->rp->rop); |
| 363 |
VSUB(ftp->r_i1, hp->sa[n1].p, hp->rp->rop); |
| 364 |
VSUB(ftp->e_i, hp->sa[n1].p, hp->sa[n0].p); |
| 365 |
VCROSS(ftp->rcp, ftp->r_i, ftp->r_i1); |
| 366 |
rdot_cp = 1.0/DOT(ftp->rcp,ftp->rcp); |
| 367 |
dot_e = DOT(ftp->e_i,ftp->e_i); |
| 368 |
dot_er = DOT(ftp->e_i, ftp->r_i); |
| 369 |
rdot_r = 1.0/DOT(ftp->r_i,ftp->r_i); |
| 370 |
rdot_r1 = 1.0/DOT(ftp->r_i1,ftp->r_i1); |
| 371 |
ftp->I1 = acos( DOT(ftp->r_i, ftp->r_i1) * sqrt(rdot_r*rdot_r1) ) * |
| 372 |
sqrt( rdot_cp ); |
| 373 |
ftp->I2 = ( DOT(ftp->e_i, ftp->r_i1)*rdot_r1 - dot_er*rdot_r + |
| 374 |
dot_e*ftp->I1 )*0.5*rdot_cp; |
| 375 |
J2 = ( 0.5*(rdot_r - rdot_r1) - dot_er*ftp->I2 ) / dot_e; |
| 376 |
for (ii = 3; ii--; ) |
| 377 |
ftp->rI2_eJ2[ii] = ftp->I2*ftp->r_i[ii] + J2*ftp->e_i[ii]; |
| 378 |
} |
| 379 |
|
| 380 |
|
| 381 |
/* Compose 3x3 matrix from two vectors */ |
| 382 |
static void |
| 383 |
compose_matrix(FVECT mat[3], FVECT va, FVECT vb) |
| 384 |
{ |
| 385 |
mat[0][0] = 2.0*va[0]*vb[0]; |
| 386 |
mat[1][1] = 2.0*va[1]*vb[1]; |
| 387 |
mat[2][2] = 2.0*va[2]*vb[2]; |
| 388 |
mat[0][1] = mat[1][0] = va[0]*vb[1] + va[1]*vb[0]; |
| 389 |
mat[0][2] = mat[2][0] = va[0]*vb[2] + va[2]*vb[0]; |
| 390 |
mat[1][2] = mat[2][1] = va[1]*vb[2] + va[2]*vb[1]; |
| 391 |
} |
| 392 |
|
| 393 |
|
| 394 |
/* Compute partial 3x3 Hessian matrix for edge */ |
| 395 |
static void |
| 396 |
comp_hessian(FVECT hess[3], FFTRI *ftp, FVECT nrm) |
| 397 |
{ |
| 398 |
FVECT ncp; |
| 399 |
FVECT m1[3], m2[3], m3[3], m4[3]; |
| 400 |
double d1, d2, d3, d4; |
| 401 |
double I3, J3, K3; |
| 402 |
int i, j; |
| 403 |
/* compute intermediate coefficients */ |
| 404 |
d1 = 1.0/DOT(ftp->r_i,ftp->r_i); |
| 405 |
d2 = 1.0/DOT(ftp->r_i1,ftp->r_i1); |
| 406 |
d3 = 1.0/DOT(ftp->e_i,ftp->e_i); |
| 407 |
d4 = DOT(ftp->e_i, ftp->r_i); |
| 408 |
I3 = ( DOT(ftp->e_i, ftp->r_i1)*d2*d2 - d4*d1*d1 + 3.0/d3*ftp->I2 ) |
| 409 |
/ ( 4.0*DOT(ftp->rcp,ftp->rcp) ); |
| 410 |
J3 = 0.25*d3*(d1*d1 - d2*d2) - d4*d3*I3; |
| 411 |
K3 = d3*(ftp->I2 - I3/d1 - 2.0*d4*J3); |
| 412 |
/* intermediate matrices */ |
| 413 |
VCROSS(ncp, nrm, ftp->e_i); |
| 414 |
compose_matrix(m1, ncp, ftp->rI2_eJ2); |
| 415 |
compose_matrix(m2, ftp->r_i, ftp->r_i); |
| 416 |
compose_matrix(m3, ftp->e_i, ftp->e_i); |
| 417 |
compose_matrix(m4, ftp->r_i, ftp->e_i); |
| 418 |
d1 = DOT(nrm, ftp->rcp); |
| 419 |
d2 = -d1*ftp->I2; |
| 420 |
d1 *= 2.0; |
| 421 |
for (i = 3; i--; ) /* final matrix sum */ |
| 422 |
for (j = 3; j--; ) { |
| 423 |
hess[i][j] = m1[i][j] + d1*( I3*m2[i][j] + K3*m3[i][j] + |
| 424 |
2.0*J3*m4[i][j] ); |
| 425 |
hess[i][j] += d2*(i==j); |
| 426 |
hess[i][j] *= -1.0/PI; |
| 427 |
} |
| 428 |
} |
| 429 |
|
| 430 |
|
| 431 |
/* Reverse hessian calculation result for edge in other direction */ |
| 432 |
static void |
| 433 |
rev_hessian(FVECT hess[3]) |
| 434 |
{ |
| 435 |
int i; |
| 436 |
|
| 437 |
for (i = 3; i--; ) { |
| 438 |
hess[i][0] = -hess[i][0]; |
| 439 |
hess[i][1] = -hess[i][1]; |
| 440 |
hess[i][2] = -hess[i][2]; |
| 441 |
} |
| 442 |
} |
| 443 |
|
| 444 |
|
| 445 |
/* Add to radiometric Hessian from the given triangle */ |
| 446 |
static void |
| 447 |
add2hessian(FVECT hess[3], FVECT ehess1[3], |
| 448 |
FVECT ehess2[3], FVECT ehess3[3], double v) |
| 449 |
{ |
| 450 |
int i, j; |
| 451 |
|
| 452 |
for (i = 3; i--; ) |
| 453 |
for (j = 3; j--; ) |
| 454 |
hess[i][j] += v*( ehess1[i][j] + ehess2[i][j] + ehess3[i][j] ); |
| 455 |
} |
| 456 |
|
| 457 |
|
| 458 |
/* Compute partial displacement form factor gradient for edge */ |
| 459 |
static void |
| 460 |
comp_gradient(FVECT grad, FFTRI *ftp, FVECT nrm) |
| 461 |
{ |
| 462 |
FVECT ncp; |
| 463 |
double f1; |
| 464 |
int i; |
| 465 |
|
| 466 |
f1 = 2.0*DOT(nrm, ftp->rcp); |
| 467 |
VCROSS(ncp, nrm, ftp->e_i); |
| 468 |
for (i = 3; i--; ) |
| 469 |
grad[i] = (0.5/PI)*( ftp->I1*ncp[i] + f1*ftp->rI2_eJ2[i] ); |
| 470 |
} |
| 471 |
|
| 472 |
|
| 473 |
/* Reverse gradient calculation result for edge in other direction */ |
| 474 |
static void |
| 475 |
rev_gradient(FVECT grad) |
| 476 |
{ |
| 477 |
grad[0] = -grad[0]; |
| 478 |
grad[1] = -grad[1]; |
| 479 |
grad[2] = -grad[2]; |
| 480 |
} |
| 481 |
|
| 482 |
|
| 483 |
/* Add to displacement gradient from the given triangle */ |
| 484 |
static void |
| 485 |
add2gradient(FVECT grad, FVECT egrad1, FVECT egrad2, FVECT egrad3, double v) |
| 486 |
{ |
| 487 |
int i; |
| 488 |
|
| 489 |
for (i = 3; i--; ) |
| 490 |
grad[i] += v*( egrad1[i] + egrad2[i] + egrad3[i] ); |
| 491 |
} |
| 492 |
|
| 493 |
|
| 494 |
/* Compute anisotropic radii and eigenvector directions */ |
| 495 |
static void |
| 496 |
eigenvectors(FVECT uv[2], float ra[2], FVECT hessian[3]) |
| 497 |
{ |
| 498 |
double hess2[2][2]; |
| 499 |
FVECT a, b; |
| 500 |
double evalue[2], slope1, xmag1; |
| 501 |
int i; |
| 502 |
/* project Hessian to sample plane */ |
| 503 |
for (i = 3; i--; ) { |
| 504 |
a[i] = DOT(hessian[i], uv[0]); |
| 505 |
b[i] = DOT(hessian[i], uv[1]); |
| 506 |
} |
| 507 |
hess2[0][0] = DOT(uv[0], a); |
| 508 |
hess2[0][1] = DOT(uv[0], b); |
| 509 |
hess2[1][0] = DOT(uv[1], a); |
| 510 |
hess2[1][1] = DOT(uv[1], b); |
| 511 |
/* compute eigenvalue(s) */ |
| 512 |
i = quadratic(evalue, 1.0, -hess2[0][0]-hess2[1][1], |
| 513 |
hess2[0][0]*hess2[1][1]-hess2[0][1]*hess2[1][0]); |
| 514 |
if (i == 1) /* double-root (circle) */ |
| 515 |
evalue[1] = evalue[0]; |
| 516 |
if (!i || ((evalue[0] = fabs(evalue[0])) <= FTINY*FTINY) | |
| 517 |
((evalue[1] = fabs(evalue[1])) <= FTINY*FTINY) ) { |
| 518 |
ra[0] = ra[1] = maxarad; |
| 519 |
return; |
| 520 |
} |
| 521 |
if (evalue[0] > evalue[1]) { |
| 522 |
ra[0] = sqrt(sqrt(4.0/evalue[0])); |
| 523 |
ra[1] = sqrt(sqrt(4.0/evalue[1])); |
| 524 |
slope1 = evalue[1]; |
| 525 |
} else { |
| 526 |
ra[0] = sqrt(sqrt(4.0/evalue[1])); |
| 527 |
ra[1] = sqrt(sqrt(4.0/evalue[0])); |
| 528 |
slope1 = evalue[0]; |
| 529 |
} |
| 530 |
/* compute unit eigenvectors */ |
| 531 |
if (fabs(hess2[0][1]) <= FTINY) |
| 532 |
return; /* uv OK as is */ |
| 533 |
slope1 = (slope1 - hess2[0][0]) / hess2[0][1]; |
| 534 |
xmag1 = sqrt(1.0/(1.0 + slope1*slope1)); |
| 535 |
for (i = 3; i--; ) { |
| 536 |
b[i] = xmag1*uv[0][i] + slope1*xmag1*uv[1][i]; |
| 537 |
a[i] = slope1*xmag1*uv[0][i] - xmag1*uv[1][i]; |
| 538 |
} |
| 539 |
VCOPY(uv[0], a); |
| 540 |
VCOPY(uv[1], b); |
| 541 |
} |
| 542 |
|
| 543 |
|
| 544 |
static void |
| 545 |
ambHessian( /* anisotropic radii & pos. gradient */ |
| 546 |
AMBHEMI *hp, |
| 547 |
FVECT uv[2], /* returned */ |
| 548 |
float ra[2], /* returned (optional) */ |
| 549 |
float pg[2] /* returned (optional) */ |
| 550 |
) |
| 551 |
{ |
| 552 |
static char memerrmsg[] = "out of memory in ambHessian()"; |
| 553 |
FVECT (*hessrow)[3] = NULL; |
| 554 |
FVECT *gradrow = NULL; |
| 555 |
FVECT hessian[3]; |
| 556 |
FVECT gradient; |
| 557 |
FFTRI fftr; |
| 558 |
int i, j; |
| 559 |
/* be sure to assign unit vectors */ |
| 560 |
VCOPY(uv[0], hp->ux); |
| 561 |
VCOPY(uv[1], hp->uy); |
| 562 |
/* clock-wise vertex traversal from sample POV */ |
| 563 |
if (ra != NULL) { /* initialize Hessian row buffer */ |
| 564 |
hessrow = (FVECT (*)[3])malloc(sizeof(FVECT)*3*(hp->ns-1)); |
| 565 |
if (hessrow == NULL) |
| 566 |
error(SYSTEM, memerrmsg); |
| 567 |
memset(hessian, 0, sizeof(hessian)); |
| 568 |
} else if (pg == NULL) /* bogus call? */ |
| 569 |
return; |
| 570 |
if (pg != NULL) { /* initialize form factor row buffer */ |
| 571 |
gradrow = (FVECT *)malloc(sizeof(FVECT)*(hp->ns-1)); |
| 572 |
if (gradrow == NULL) |
| 573 |
error(SYSTEM, memerrmsg); |
| 574 |
memset(gradient, 0, sizeof(gradient)); |
| 575 |
} |
| 576 |
/* compute first row of edges */ |
| 577 |
for (j = 0; j < hp->ns-1; j++) { |
| 578 |
comp_fftri(&fftr, hp, AI(hp,0,j), AI(hp,0,j+1)); |
| 579 |
if (hessrow != NULL) |
| 580 |
comp_hessian(hessrow[j], &fftr, hp->onrm); |
| 581 |
if (gradrow != NULL) |
| 582 |
comp_gradient(gradrow[j], &fftr, hp->onrm); |
| 583 |
} |
| 584 |
/* sum each row of triangles */ |
| 585 |
for (i = 0; i < hp->ns-1; i++) { |
| 586 |
FVECT hesscol[3]; /* compute first vertical edge */ |
| 587 |
FVECT gradcol; |
| 588 |
comp_fftri(&fftr, hp, AI(hp,i,0), AI(hp,i+1,0)); |
| 589 |
if (hessrow != NULL) |
| 590 |
comp_hessian(hesscol, &fftr, hp->onrm); |
| 591 |
if (gradrow != NULL) |
| 592 |
comp_gradient(gradcol, &fftr, hp->onrm); |
| 593 |
for (j = 0; j < hp->ns-1; j++) { |
| 594 |
FVECT hessdia[3]; /* compute triangle contributions */ |
| 595 |
FVECT graddia; |
| 596 |
double backg; |
| 597 |
backg = back_ambval(hp, AI(hp,i,j), |
| 598 |
AI(hp,i,j+1), AI(hp,i+1,j)); |
| 599 |
/* diagonal (inner) edge */ |
| 600 |
comp_fftri(&fftr, hp, AI(hp,i,j+1), AI(hp,i+1,j)); |
| 601 |
if (hessrow != NULL) { |
| 602 |
comp_hessian(hessdia, &fftr, hp->onrm); |
| 603 |
rev_hessian(hesscol); |
| 604 |
add2hessian(hessian, hessrow[j], hessdia, hesscol, backg); |
| 605 |
} |
| 606 |
if (gradrow != NULL) { |
| 607 |
comp_gradient(graddia, &fftr, hp->onrm); |
| 608 |
rev_gradient(gradcol); |
| 609 |
add2gradient(gradient, gradrow[j], graddia, gradcol, backg); |
| 610 |
} |
| 611 |
/* initialize edge in next row */ |
| 612 |
comp_fftri(&fftr, hp, AI(hp,i+1,j+1), AI(hp,i+1,j)); |
| 613 |
if (hessrow != NULL) |
| 614 |
comp_hessian(hessrow[j], &fftr, hp->onrm); |
| 615 |
if (gradrow != NULL) |
| 616 |
comp_gradient(gradrow[j], &fftr, hp->onrm); |
| 617 |
/* new column edge & paired triangle */ |
| 618 |
backg = back_ambval(hp, AI(hp,i+1,j+1), |
| 619 |
AI(hp,i+1,j), AI(hp,i,j+1)); |
| 620 |
comp_fftri(&fftr, hp, AI(hp,i,j+1), AI(hp,i+1,j+1)); |
| 621 |
if (hessrow != NULL) { |
| 622 |
comp_hessian(hesscol, &fftr, hp->onrm); |
| 623 |
rev_hessian(hessdia); |
| 624 |
add2hessian(hessian, hessrow[j], hessdia, hesscol, backg); |
| 625 |
if (i < hp->ns-2) |
| 626 |
rev_hessian(hessrow[j]); |
| 627 |
} |
| 628 |
if (gradrow != NULL) { |
| 629 |
comp_gradient(gradcol, &fftr, hp->onrm); |
| 630 |
rev_gradient(graddia); |
| 631 |
add2gradient(gradient, gradrow[j], graddia, gradcol, backg); |
| 632 |
if (i < hp->ns-2) |
| 633 |
rev_gradient(gradrow[j]); |
| 634 |
} |
| 635 |
} |
| 636 |
} |
| 637 |
/* release row buffers */ |
| 638 |
if (hessrow != NULL) free(hessrow); |
| 639 |
if (gradrow != NULL) free(gradrow); |
| 640 |
|
| 641 |
if (ra != NULL) /* extract eigenvectors & radii */ |
| 642 |
eigenvectors(uv, ra, hessian); |
| 643 |
if (pg != NULL) { /* tangential position gradient */ |
| 644 |
pg[0] = DOT(gradient, uv[0]); |
| 645 |
pg[1] = DOT(gradient, uv[1]); |
| 646 |
} |
| 647 |
} |
| 648 |
|
| 649 |
|
| 650 |
/* Compute direction gradient from a hemispherical sampling */ |
| 651 |
static void |
| 652 |
ambdirgrad(AMBHEMI *hp, FVECT uv[2], float dg[2]) |
| 653 |
{ |
| 654 |
AMBSAMP *ap; |
| 655 |
double dgsum[2]; |
| 656 |
int n; |
| 657 |
FVECT vd; |
| 658 |
double gfact; |
| 659 |
|
| 660 |
dgsum[0] = dgsum[1] = 0.0; /* sum values times -tan(theta) */ |
| 661 |
for (ap = hp->sa, n = hp->ns*hp->ns; n--; ap++) { |
| 662 |
/* use vector for azimuth + 90deg */ |
| 663 |
VSUB(vd, ap->p, hp->rp->rop); |
| 664 |
/* brightness over cosine factor */ |
| 665 |
gfact = ap->v[0] / DOT(hp->onrm, vd); |
| 666 |
/* sine = proj_radius/vd_length */ |
| 667 |
dgsum[0] -= DOT(uv[1], vd) * gfact; |
| 668 |
dgsum[1] += DOT(uv[0], vd) * gfact; |
| 669 |
} |
| 670 |
dg[0] = dgsum[0] / (hp->ns*hp->ns); |
| 671 |
dg[1] = dgsum[1] / (hp->ns*hp->ns); |
| 672 |
} |
| 673 |
|
| 674 |
|
| 675 |
/* Compute potential light leak direction flags for cache value */ |
| 676 |
static uint32 |
| 677 |
ambcorral(AMBHEMI *hp, FVECT uv[2], const double r0, const double r1) |
| 678 |
{ |
| 679 |
const double max_d = 1.0/(minarad*ambacc + 0.001); |
| 680 |
const double ang_res = 0.5*PI/hp->ns; |
| 681 |
const double ang_step = ang_res/((int)(16/PI*ang_res) + 1.01); |
| 682 |
double avg_d = 0; |
| 683 |
uint32 flgs = 0; |
| 684 |
FVECT vec; |
| 685 |
double u, v; |
| 686 |
double ang, a1; |
| 687 |
int i, j; |
| 688 |
/* don't bother for a few samples */ |
| 689 |
if (hp->ns < 8) |
| 690 |
return(0); |
| 691 |
/* check distances overhead */ |
| 692 |
for (i = hp->ns*3/4; i-- > hp->ns>>2; ) |
| 693 |
for (j = hp->ns*3/4; j-- > hp->ns>>2; ) |
| 694 |
avg_d += ambsam(hp,i,j).d; |
| 695 |
avg_d *= 4.0/(hp->ns*hp->ns); |
| 696 |
if (avg_d*r0 >= 1.0) /* ceiling too low for corral? */ |
| 697 |
return(0); |
| 698 |
if (avg_d >= max_d) /* insurance */ |
| 699 |
return(0); |
| 700 |
/* else circle around perimeter */ |
| 701 |
for (i = 0; i < hp->ns; i++) |
| 702 |
for (j = 0; j < hp->ns; j += !i|(i==hp->ns-1) ? 1 : hp->ns-1) { |
| 703 |
AMBSAMP *ap = &ambsam(hp,i,j); |
| 704 |
if ((ap->d <= FTINY) | (ap->d >= max_d)) |
| 705 |
continue; /* too far or too near */ |
| 706 |
VSUB(vec, ap->p, hp->rp->rop); |
| 707 |
u = DOT(vec, uv[0]); |
| 708 |
v = DOT(vec, uv[1]); |
| 709 |
if ((r0*r0*u*u + r1*r1*v*v) * ap->d*ap->d <= u*u + v*v) |
| 710 |
continue; /* occluder outside ellipse */ |
| 711 |
ang = atan2a(v, u); /* else set direction flags */ |
| 712 |
for (a1 = ang-ang_res; a1 <= ang+ang_res; a1 += ang_step) |
| 713 |
flgs |= 1L<<(int)(16/PI*(a1 + 2.*PI*(a1 < 0))); |
| 714 |
} |
| 715 |
return(flgs); |
| 716 |
} |
| 717 |
|
| 718 |
|
| 719 |
int |
| 720 |
doambient( /* compute ambient component */ |
| 721 |
SCOLOR rcol, /* input/output color */ |
| 722 |
RAY *r, |
| 723 |
double wt, /* negative for back side */ |
| 724 |
FVECT uv[2], /* returned (optional) */ |
| 725 |
float ra[2], /* returned (optional) */ |
| 726 |
float pg[2], /* returned (optional) */ |
| 727 |
float dg[2], /* returned (optional) */ |
| 728 |
uint32 *crlp /* returned (optional) */ |
| 729 |
) |
| 730 |
{ |
| 731 |
AMBHEMI *hp = samp_hemi(rcol, r, wt); |
| 732 |
FVECT my_uv[2]; |
| 733 |
double d, K; |
| 734 |
AMBSAMP *ap; |
| 735 |
int i; |
| 736 |
/* clear return values */ |
| 737 |
if (uv != NULL) |
| 738 |
memset(uv, 0, sizeof(FVECT)*2); |
| 739 |
if (ra != NULL) |
| 740 |
ra[0] = ra[1] = 0.0; |
| 741 |
if (pg != NULL) |
| 742 |
pg[0] = pg[1] = 0.0; |
| 743 |
if (dg != NULL) |
| 744 |
dg[0] = dg[1] = 0.0; |
| 745 |
if (crlp != NULL) |
| 746 |
*crlp = 0; |
| 747 |
if (hp == NULL) /* sampling falure? */ |
| 748 |
return(0); |
| 749 |
|
| 750 |
if ((ra == NULL) & (pg == NULL) & (dg == NULL) || |
| 751 |
(hp->sampOK < 0) | (hp->ns < MINADIV)) { |
| 752 |
free(hp); /* Hessian not requested/possible */ |
| 753 |
return(-1); /* value-only return value */ |
| 754 |
} |
| 755 |
if ((d = scolor_mean(rcol)) > FTINY) { |
| 756 |
d = 0.99*(hp->ns*hp->ns)/d; /* normalize avg. values */ |
| 757 |
K = 0.01; |
| 758 |
} else { /* or fall back on geometric Hessian */ |
| 759 |
K = 1.0; |
| 760 |
pg = NULL; |
| 761 |
dg = NULL; |
| 762 |
crlp = NULL; |
| 763 |
} |
| 764 |
ap = hp->sa; /* single channel from here on... */ |
| 765 |
for (i = hp->ns*hp->ns; i--; ap++) |
| 766 |
ap->v[0] = scolor_mean(ap->v)*d + K; |
| 767 |
|
| 768 |
if (uv == NULL) /* make sure we have axis pointers */ |
| 769 |
uv = my_uv; |
| 770 |
/* compute radii & pos. gradient */ |
| 771 |
ambHessian(hp, uv, ra, pg); |
| 772 |
|
| 773 |
if (dg != NULL) /* compute direction gradient */ |
| 774 |
ambdirgrad(hp, uv, dg); |
| 775 |
|
| 776 |
if (ra != NULL) { /* scale/clamp radii */ |
| 777 |
if (pg != NULL) { |
| 778 |
if (ra[0]*(d = fabs(pg[0])) > 1.0) |
| 779 |
ra[0] = 1.0/d; |
| 780 |
if (ra[1]*(d = fabs(pg[1])) > 1.0) |
| 781 |
ra[1] = 1.0/d; |
| 782 |
if (ra[0] > ra[1]) |
| 783 |
ra[0] = ra[1]; |
| 784 |
} |
| 785 |
if (ra[0] < minarad) { |
| 786 |
ra[0] = minarad; |
| 787 |
if (ra[1] < minarad) |
| 788 |
ra[1] = minarad; |
| 789 |
} |
| 790 |
ra[0] *= d = 1.0/sqrt(fabs(wt)); |
| 791 |
if ((ra[1] *= d) > 2.0*ra[0]) |
| 792 |
ra[1] = 2.0*ra[0]; |
| 793 |
if (ra[1] > maxarad) { |
| 794 |
ra[1] = maxarad; |
| 795 |
if (ra[0] > maxarad) |
| 796 |
ra[0] = maxarad; |
| 797 |
} |
| 798 |
/* flag encroached directions */ |
| 799 |
if (crlp != NULL) /* XXX doesn't update with changes to ambacc */ |
| 800 |
*crlp = ambcorral(hp, uv, ra[0]*ambacc, ra[1]*ambacc); |
| 801 |
if (pg != NULL) { /* cap gradient if necessary */ |
| 802 |
d = pg[0]*pg[0]*ra[0]*ra[0] + pg[1]*pg[1]*ra[1]*ra[1]; |
| 803 |
if (d > 1.0) { |
| 804 |
d = 1.0/sqrt(d); |
| 805 |
pg[0] *= d; |
| 806 |
pg[1] *= d; |
| 807 |
} |
| 808 |
} |
| 809 |
} |
| 810 |
free(hp); /* clean up and return */ |
| 811 |
return(1); |
| 812 |
} |
