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Sat, May 11, 23:49

ambcomp.c
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#ifndef lint
static const char RCSid[] = "$Id: ambcomp.c,v 2.86 2021/02/17 01:29:22 greg Exp $";
#endif
/*
* Routines to compute "ambient" values using Monte Carlo
*
* Hessian calculations based on "Practical Hessian-Based Error Control
* for Irradiance Caching" by Schwarzhaupt, Wann Jensen, & Jarosz
* from ACM SIGGRAPH Asia 2012 conference proceedings.
*
* Added book-keeping optimization to avoid calculations that would
* cancel due to traversal both directions on edges that are adjacent
* to same-valued triangles. This cuts about half of Hessian math.
*
* Declarations of external symbols in ambient.h
*/
#include "copyright.h"
#include "ray.h"
#include "ambient.h"
#include "random.h"
#ifndef MINADIV
#define MINADIV 7 /* minimum # divisions in each dimension */
#endif
extern void SDsquare2disk(double ds[2], double seedx, double seedy);
typedef struct {
COLOR v; /* hemisphere sample value */
float d; /* reciprocal distance */
FVECT p; /* intersection point */
} AMBSAMP; /* sample value */
typedef struct {
RAY *rp; /* originating ray sample */
int ns; /* number of samples per axis */
int sampOK; /* acquired full sample set? */
COLOR acoef; /* division contribution coefficient */
double acol[3]; /* accumulated color */
FVECT ux, uy; /* tangent axis unit vectors */
AMBSAMP sa[1]; /* sample array (extends struct) */
} AMBHEMI; /* ambient sample hemisphere */
#define AI(h,i,j) ((i)*(h)->ns + (j))
#define ambsam(h,i,j) (h)->sa[AI(h,i,j)]
typedef struct {
FVECT r_i, r_i1, e_i, rcp, rI2_eJ2;
double I1, I2;
} FFTRI; /* vectors and coefficients for Hessian calculation */
static int
ambcollision( /* proposed direciton collides? */
AMBHEMI *hp,
int i,
int j,
FVECT dv
)
{
double cos_thresh;
int ii, jj;
/* min. spacing = 1/4th division */
cos_thresh = (PI/4.)/(double)hp->ns;
cos_thresh = 1. - .5*cos_thresh*cos_thresh;
/* check existing neighbors */
for (ii = i-1; ii <= i+1; ii++) {
if (ii < 0) continue;
if (ii >= hp->ns) break;
for (jj = j-1; jj <= j+1; jj++) {
AMBSAMP *ap;
FVECT avec;
double dprod;
if (jj < 0) continue;
if (jj >= hp->ns) break;
if ((ii==i) & (jj==j)) continue;
ap = &ambsam(hp,ii,jj);
if (ap->d <= .5/FHUGE)
continue; /* no one home */
VSUB(avec, ap->p, hp->rp->rop);
dprod = DOT(avec, dv);
if (dprod >= cos_thresh*VLEN(avec))
return(1); /* collision */
}
}
return(0); /* nothing to worry about */
}
static int
ambsample( /* initial ambient division sample */
AMBHEMI *hp,
int i,
int j,
int n
)
{
AMBSAMP *ap = &ambsam(hp,i,j);
RAY ar;
int hlist[3], ii;
double spt[2], zd;
/* generate hemispherical sample */
/* ambient coefficient for weight */
if (ambacc > FTINY)
setcolor(ar.rcoef, AVGREFL, AVGREFL, AVGREFL);
else
copycolor(ar.rcoef, hp->acoef);
if (rayorigin(&ar, AMBIENT, hp->rp, ar.rcoef) < 0)
return(0);
if (ambacc > FTINY) {
multcolor(ar.rcoef, hp->acoef);
scalecolor(ar.rcoef, 1./AVGREFL);
}
hlist[0] = hp->rp->rno;
hlist[1] = j;
hlist[2] = i;
multisamp(spt, 2, urand(ilhash(hlist,3)+n));
resample:
SDsquare2disk(spt, (j+spt[1])/hp->ns, (i+spt[0])/hp->ns);
zd = sqrt(1. - spt[0]*spt[0] - spt[1]*spt[1]);
for (ii = 3; ii--; )
ar.rdir[ii] = spt[0]*hp->ux[ii] +
spt[1]*hp->uy[ii] +
zd*hp->rp->ron[ii];
checknorm(ar.rdir);
/* avoid coincident samples */
if (!n && ambcollision(hp, i, j, ar.rdir)) {
spt[0] = frandom(); spt[1] = frandom();
goto resample; /* reject this sample */
}
dimlist[ndims++] = AI(hp,i,j) + 90171;
rayvalue(&ar); /* evaluate ray */
ndims--;
zd = raydistance(&ar);
if (zd <= FTINY)
return(0); /* should never happen */
multcolor(ar.rcol, ar.rcoef); /* apply coefficient */
if (zd*ap->d < 1.0) /* new/closer distance? */
ap->d = 1.0/zd;
if (!n) { /* record first vertex & value */
if (zd > 10.0*thescene.cusize + 1000.)
zd = 10.0*thescene.cusize + 1000.;
VSUM(ap->p, ar.rorg, ar.rdir, zd);
copycolor(ap->v, ar.rcol);
} else { /* else update recorded value */
hp->acol[RED] -= colval(ap->v,RED);
hp->acol[GRN] -= colval(ap->v,GRN);
hp->acol[BLU] -= colval(ap->v,BLU);
zd = 1.0/(double)(n+1);
scalecolor(ar.rcol, zd);
zd *= (double)n;
scalecolor(ap->v, zd);
addcolor(ap->v, ar.rcol);
}
addcolor(hp->acol, ap->v); /* add to our sum */
return(1);
}
/* Estimate variance based on ambient division differences */
static float *
getambdiffs(AMBHEMI *hp)
{
const double normf = 1./bright(hp->acoef);
float *earr = (float *)calloc(hp->ns*hp->ns, sizeof(float));
float *ep;
AMBSAMP *ap;
double b, b1, d2;
int i, j;
if (earr == NULL) /* out of memory? */
return(NULL);
/* sum squared neighbor diffs */
for (ap = hp->sa, ep = earr, i = 0; i < hp->ns; i++)
for (j = 0; j < hp->ns; j++, ap++, ep++) {
b = bright(ap[0].v);
if (i) { /* from above */
b1 = bright(ap[-hp->ns].v);
d2 = b - b1;
d2 *= d2*normf/(b + b1);
ep[0] += d2;
ep[-hp->ns] += d2;
}
if (!j) continue;
/* from behind */
b1 = bright(ap[-1].v);
d2 = b - b1;
d2 *= d2*normf/(b + b1);
ep[0] += d2;
ep[-1] += d2;
if (!i) continue;
/* diagonal */
b1 = bright(ap[-hp->ns-1].v);
d2 = b - b1;
d2 *= d2*normf/(b + b1);
ep[0] += d2;
ep[-hp->ns-1] += d2;
}
/* correct for number of neighbors */
earr[0] *= 8./3.;
earr[hp->ns-1] *= 8./3.;
earr[(hp->ns-1)*hp->ns] *= 8./3.;
earr[(hp->ns-1)*hp->ns + hp->ns-1] *= 8./3.;
for (i = 1; i < hp->ns-1; i++) {
earr[i*hp->ns] *= 8./5.;
earr[i*hp->ns + hp->ns-1] *= 8./5.;
}
for (j = 1; j < hp->ns-1; j++) {
earr[j] *= 8./5.;
earr[(hp->ns-1)*hp->ns + j] *= 8./5.;
}
return(earr);
}
/* Perform super-sampling on hemisphere (introduces bias) */
static void
ambsupersamp(AMBHEMI *hp, int cnt)
{
float *earr = getambdiffs(hp);
double e2rem = 0;
float *ep;
int i, j, n, nss;
if (earr == NULL) /* just skip calc. if no memory */
return;
/* accumulate estimated variances */
for (ep = earr + hp->ns*hp->ns; ep > earr; )
e2rem += *--ep;
ep = earr; /* perform super-sampling */
for (i = 0; i < hp->ns; i++)
for (j = 0; j < hp->ns; j++) {
if (e2rem <= FTINY)
goto done; /* nothing left to do */
nss = *ep/e2rem*cnt + frandom();
for (n = 1; n <= nss && ambsample(hp,i,j,n); n++)
if (!--cnt) goto done;
e2rem -= *ep++; /* update remainder */
}
done:
free(earr);
}
static AMBHEMI *
samp_hemi( /* sample indirect hemisphere */
COLOR rcol,
RAY *r,
double wt
)
{
AMBHEMI *hp;
double d;
int n, i, j;
/* insignificance check */
if (bright(rcol) <= FTINY)
return(NULL);
/* set number of divisions */
if (ambacc <= FTINY &&
wt > (d = 0.8*intens(rcol)*r->rweight/(ambdiv*minweight)))
wt = d; /* avoid ray termination */
n = sqrt(ambdiv * wt) + 0.5;
i = 1 + (MINADIV-1)*(ambacc > FTINY);
if (n < i) /* use minimum number of samples? */
n = i;
/* allocate sampling array */
hp = (AMBHEMI *)malloc(sizeof(AMBHEMI) + sizeof(AMBSAMP)*(n*n - 1));
if (hp == NULL)
error(SYSTEM, "out of memory in samp_hemi");
hp->rp = r;
hp->ns = n;
hp->acol[RED] = hp->acol[GRN] = hp->acol[BLU] = 0.0;
memset(hp->sa, 0, sizeof(AMBSAMP)*n*n);
hp->sampOK = 0;
/* assign coefficient */
copycolor(hp->acoef, rcol);
d = 1.0/(n*n);
scalecolor(hp->acoef, d);
/* make tangent plane axes */
if (!getperpendicular(hp->ux, r->ron, 1))
error(CONSISTENCY, "bad ray direction in samp_hemi");
VCROSS(hp->uy, r->ron, hp->ux);
/* sample divisions */
for (i = hp->ns; i--; )
for (j = hp->ns; j--; )
hp->sampOK += ambsample(hp, i, j, 0);
copycolor(rcol, hp->acol);
if (!hp->sampOK) { /* utter failure? */
free(hp);
return(NULL);
}
if (hp->sampOK < hp->ns*hp->ns) {
hp->sampOK *= -1; /* soft failure */
return(hp);
}
if (hp->sampOK <= MINADIV*MINADIV)
return(hp); /* don't bother super-sampling */
n = ambssamp*wt + 0.5;
if (n > 8) { /* perform super-sampling? */
ambsupersamp(hp, n);
copycolor(rcol, hp->acol);
}
return(hp); /* all is well */
}
/* Return brightness of farthest ambient sample */
static double
back_ambval(AMBHEMI *hp, const int n1, const int n2, const int n3)
{
if (hp->sa[n1].d <= hp->sa[n2].d) {
if (hp->sa[n1].d <= hp->sa[n3].d)
return(colval(hp->sa[n1].v,CIEY));
return(colval(hp->sa[n3].v,CIEY));
}
if (hp->sa[n2].d <= hp->sa[n3].d)
return(colval(hp->sa[n2].v,CIEY));
return(colval(hp->sa[n3].v,CIEY));
}
/* Compute vectors and coefficients for Hessian/gradient calcs */
static void
comp_fftri(FFTRI *ftp, AMBHEMI *hp, const int n0, const int n1)
{
double rdot_cp, dot_e, dot_er, rdot_r, rdot_r1, J2;
int ii;
VSUB(ftp->r_i, hp->sa[n0].p, hp->rp->rop);
VSUB(ftp->r_i1, hp->sa[n1].p, hp->rp->rop);
VSUB(ftp->e_i, hp->sa[n1].p, hp->sa[n0].p);
VCROSS(ftp->rcp, ftp->r_i, ftp->r_i1);
rdot_cp = 1.0/DOT(ftp->rcp,ftp->rcp);
dot_e = DOT(ftp->e_i,ftp->e_i);
dot_er = DOT(ftp->e_i, ftp->r_i);
rdot_r = 1.0/DOT(ftp->r_i,ftp->r_i);
rdot_r1 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
ftp->I1 = acos( DOT(ftp->r_i, ftp->r_i1) * sqrt(rdot_r*rdot_r1) ) *
sqrt( rdot_cp );
ftp->I2 = ( DOT(ftp->e_i, ftp->r_i1)*rdot_r1 - dot_er*rdot_r +
dot_e*ftp->I1 )*0.5*rdot_cp;
J2 = ( 0.5*(rdot_r - rdot_r1) - dot_er*ftp->I2 ) / dot_e;
for (ii = 3; ii--; )
ftp->rI2_eJ2[ii] = ftp->I2*ftp->r_i[ii] + J2*ftp->e_i[ii];
}
/* Compose 3x3 matrix from two vectors */
static void
compose_matrix(FVECT mat[3], FVECT va, FVECT vb)
{
mat[0][0] = 2.0*va[0]*vb[0];
mat[1][1] = 2.0*va[1]*vb[1];
mat[2][2] = 2.0*va[2]*vb[2];
mat[0][1] = mat[1][0] = va[0]*vb[1] + va[1]*vb[0];
mat[0][2] = mat[2][0] = va[0]*vb[2] + va[2]*vb[0];
mat[1][2] = mat[2][1] = va[1]*vb[2] + va[2]*vb[1];
}
/* Compute partial 3x3 Hessian matrix for edge */
static void
comp_hessian(FVECT hess[3], FFTRI *ftp, FVECT nrm)
{
FVECT ncp;
FVECT m1[3], m2[3], m3[3], m4[3];
double d1, d2, d3, d4;
double I3, J3, K3;
int i, j;
/* compute intermediate coefficients */
d1 = 1.0/DOT(ftp->r_i,ftp->r_i);
d2 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
d3 = 1.0/DOT(ftp->e_i,ftp->e_i);
d4 = DOT(ftp->e_i, ftp->r_i);
I3 = ( DOT(ftp->e_i, ftp->r_i1)*d2*d2 - d4*d1*d1 + 3.0/d3*ftp->I2 )
/ ( 4.0*DOT(ftp->rcp,ftp->rcp) );
J3 = 0.25*d3*(d1*d1 - d2*d2) - d4*d3*I3;
K3 = d3*(ftp->I2 - I3/d1 - 2.0*d4*J3);
/* intermediate matrices */
VCROSS(ncp, nrm, ftp->e_i);
compose_matrix(m1, ncp, ftp->rI2_eJ2);
compose_matrix(m2, ftp->r_i, ftp->r_i);
compose_matrix(m3, ftp->e_i, ftp->e_i);
compose_matrix(m4, ftp->r_i, ftp->e_i);
d1 = DOT(nrm, ftp->rcp);
d2 = -d1*ftp->I2;
d1 *= 2.0;
for (i = 3; i--; ) /* final matrix sum */
for (j = 3; j--; ) {
hess[i][j] = m1[i][j] + d1*( I3*m2[i][j] + K3*m3[i][j] +
2.0*J3*m4[i][j] );
hess[i][j] += d2*(i==j);
hess[i][j] *= -1.0/PI;
}
}
/* Reverse hessian calculation result for edge in other direction */
static void
rev_hessian(FVECT hess[3])
{
int i;
for (i = 3; i--; ) {
hess[i][0] = -hess[i][0];
hess[i][1] = -hess[i][1];
hess[i][2] = -hess[i][2];
}
}
/* Add to radiometric Hessian from the given triangle */
static void
add2hessian(FVECT hess[3], FVECT ehess1[3],
FVECT ehess2[3], FVECT ehess3[3], double v)
{
int i, j;
for (i = 3; i--; )
for (j = 3; j--; )
hess[i][j] += v*( ehess1[i][j] + ehess2[i][j] + ehess3[i][j] );
}
/* Compute partial displacement form factor gradient for edge */
static void
comp_gradient(FVECT grad, FFTRI *ftp, FVECT nrm)
{
FVECT ncp;
double f1;
int i;
f1 = 2.0*DOT(nrm, ftp->rcp);
VCROSS(ncp, nrm, ftp->e_i);
for (i = 3; i--; )
grad[i] = (0.5/PI)*( ftp->I1*ncp[i] + f1*ftp->rI2_eJ2[i] );
}
/* Reverse gradient calculation result for edge in other direction */
static void
rev_gradient(FVECT grad)
{
grad[0] = -grad[0];
grad[1] = -grad[1];
grad[2] = -grad[2];
}
/* Add to displacement gradient from the given triangle */
static void
add2gradient(FVECT grad, FVECT egrad1, FVECT egrad2, FVECT egrad3, double v)
{
int i;
for (i = 3; i--; )
grad[i] += v*( egrad1[i] + egrad2[i] + egrad3[i] );
}
/* Compute anisotropic radii and eigenvector directions */
static void
eigenvectors(FVECT uv[2], float ra[2], FVECT hessian[3])
{
double hess2[2][2];
FVECT a, b;
double evalue[2], slope1, xmag1;
int i;
/* project Hessian to sample plane */
for (i = 3; i--; ) {
a[i] = DOT(hessian[i], uv[0]);
b[i] = DOT(hessian[i], uv[1]);
}
hess2[0][0] = DOT(uv[0], a);
hess2[0][1] = DOT(uv[0], b);
hess2[1][0] = DOT(uv[1], a);
hess2[1][1] = DOT(uv[1], b);
/* compute eigenvalue(s) */
i = quadratic(evalue, 1.0, -hess2[0][0]-hess2[1][1],
hess2[0][0]*hess2[1][1]-hess2[0][1]*hess2[1][0]);
if (i == 1) /* double-root (circle) */
evalue[1] = evalue[0];
if (!i || ((evalue[0] = fabs(evalue[0])) <= FTINY*FTINY) |
((evalue[1] = fabs(evalue[1])) <= FTINY*FTINY) ) {
ra[0] = ra[1] = maxarad;
return;
}
if (evalue[0] > evalue[1]) {
ra[0] = sqrt(sqrt(4.0/evalue[0]));
ra[1] = sqrt(sqrt(4.0/evalue[1]));
slope1 = evalue[1];
} else {
ra[0] = sqrt(sqrt(4.0/evalue[1]));
ra[1] = sqrt(sqrt(4.0/evalue[0]));
slope1 = evalue[0];
}
/* compute unit eigenvectors */
if (fabs(hess2[0][1]) <= FTINY)
return; /* uv OK as is */
slope1 = (slope1 - hess2[0][0]) / hess2[0][1];
xmag1 = sqrt(1.0/(1.0 + slope1*slope1));
for (i = 3; i--; ) {
b[i] = xmag1*uv[0][i] + slope1*xmag1*uv[1][i];
a[i] = slope1*xmag1*uv[0][i] - xmag1*uv[1][i];
}
VCOPY(uv[0], a);
VCOPY(uv[1], b);
}
static void
ambHessian( /* anisotropic radii & pos. gradient */
AMBHEMI *hp,
FVECT uv[2], /* returned */
float ra[2], /* returned (optional) */
float pg[2] /* returned (optional) */
)
{
static char memerrmsg[] = "out of memory in ambHessian()";
FVECT (*hessrow)[3] = NULL;
FVECT *gradrow = NULL;
FVECT hessian[3];
FVECT gradient;
FFTRI fftr;
int i, j;
/* be sure to assign unit vectors */
VCOPY(uv[0], hp->ux);
VCOPY(uv[1], hp->uy);
/* clock-wise vertex traversal from sample POV */
if (ra != NULL) { /* initialize Hessian row buffer */
hessrow = (FVECT (*)[3])malloc(sizeof(FVECT)*3*(hp->ns-1));
if (hessrow == NULL)
error(SYSTEM, memerrmsg);
memset(hessian, 0, sizeof(hessian));
} else if (pg == NULL) /* bogus call? */
return;
if (pg != NULL) { /* initialize form factor row buffer */
gradrow = (FVECT *)malloc(sizeof(FVECT)*(hp->ns-1));
if (gradrow == NULL)
error(SYSTEM, memerrmsg);
memset(gradient, 0, sizeof(gradient));
}
/* compute first row of edges */
for (j = 0; j < hp->ns-1; j++) {
comp_fftri(&fftr, hp, AI(hp,0,j), AI(hp,0,j+1));
if (hessrow != NULL)
comp_hessian(hessrow[j], &fftr, hp->rp->ron);
if (gradrow != NULL)
comp_gradient(gradrow[j], &fftr, hp->rp->ron);
}
/* sum each row of triangles */
for (i = 0; i < hp->ns-1; i++) {
FVECT hesscol[3]; /* compute first vertical edge */
FVECT gradcol;
comp_fftri(&fftr, hp, AI(hp,i,0), AI(hp,i+1,0));
if (hessrow != NULL)
comp_hessian(hesscol, &fftr, hp->rp->ron);
if (gradrow != NULL)
comp_gradient(gradcol, &fftr, hp->rp->ron);
for (j = 0; j < hp->ns-1; j++) {
FVECT hessdia[3]; /* compute triangle contributions */
FVECT graddia;
double backg;
backg = back_ambval(hp, AI(hp,i,j),
AI(hp,i,j+1), AI(hp,i+1,j));
/* diagonal (inner) edge */
comp_fftri(&fftr, hp, AI(hp,i,j+1), AI(hp,i+1,j));
if (hessrow != NULL) {
comp_hessian(hessdia, &fftr, hp->rp->ron);
rev_hessian(hesscol);
add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
}
if (gradrow != NULL) {
comp_gradient(graddia, &fftr, hp->rp->ron);
rev_gradient(gradcol);
add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
}
/* initialize edge in next row */
comp_fftri(&fftr, hp, AI(hp,i+1,j+1), AI(hp,i+1,j));
if (hessrow != NULL)
comp_hessian(hessrow[j], &fftr, hp->rp->ron);
if (gradrow != NULL)
comp_gradient(gradrow[j], &fftr, hp->rp->ron);
/* new column edge & paired triangle */
backg = back_ambval(hp, AI(hp,i+1,j+1),
AI(hp,i+1,j), AI(hp,i,j+1));
comp_fftri(&fftr, hp, AI(hp,i,j+1), AI(hp,i+1,j+1));
if (hessrow != NULL) {
comp_hessian(hesscol, &fftr, hp->rp->ron);
rev_hessian(hessdia);
add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
if (i < hp->ns-2)
rev_hessian(hessrow[j]);
}
if (gradrow != NULL) {
comp_gradient(gradcol, &fftr, hp->rp->ron);
rev_gradient(graddia);
add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
if (i < hp->ns-2)
rev_gradient(gradrow[j]);
}
}
}
/* release row buffers */
if (hessrow != NULL) free(hessrow);
if (gradrow != NULL) free(gradrow);
if (ra != NULL) /* extract eigenvectors & radii */
eigenvectors(uv, ra, hessian);
if (pg != NULL) { /* tangential position gradient */
pg[0] = DOT(gradient, uv[0]);
pg[1] = DOT(gradient, uv[1]);
}
}
/* Compute direction gradient from a hemispherical sampling */
static void
ambdirgrad(AMBHEMI *hp, FVECT uv[2], float dg[2])
{
AMBSAMP *ap;
double dgsum[2];
int n;
FVECT vd;
double gfact;
dgsum[0] = dgsum[1] = 0.0; /* sum values times -tan(theta) */
for (ap = hp->sa, n = hp->ns*hp->ns; n--; ap++) {
/* use vector for azimuth + 90deg */
VSUB(vd, ap->p, hp->rp->rop);
/* brightness over cosine factor */
gfact = colval(ap->v,CIEY) / DOT(hp->rp->ron, vd);
/* sine = proj_radius/vd_length */
dgsum[0] -= DOT(uv[1], vd) * gfact;
dgsum[1] += DOT(uv[0], vd) * gfact;
}
dg[0] = dgsum[0] / (hp->ns*hp->ns);
dg[1] = dgsum[1] / (hp->ns*hp->ns);
}
/* Compute potential light leak direction flags for cache value */
static uint32
ambcorral(AMBHEMI *hp, FVECT uv[2], const double r0, const double r1)
{
const double max_d = 1.0/(minarad*ambacc + 0.001);
const double ang_res = 0.5*PI/hp->ns;
const double ang_step = ang_res/((int)(16/PI*ang_res) + 1.01);
double avg_d = 0;
uint32 flgs = 0;
FVECT vec;
double u, v;
double ang, a1;
int i, j;
/* don't bother for a few samples */
if (hp->ns < 8)
return(0);
/* check distances overhead */
for (i = hp->ns*3/4; i-- > hp->ns>>2; )
for (j = hp->ns*3/4; j-- > hp->ns>>2; )
avg_d += ambsam(hp,i,j).d;
avg_d *= 4.0/(hp->ns*hp->ns);
if (avg_d*r0 >= 1.0) /* ceiling too low for corral? */
return(0);
if (avg_d >= max_d) /* insurance */
return(0);
/* else circle around perimeter */
for (i = 0; i < hp->ns; i++)
for (j = 0; j < hp->ns; j += !i|(i==hp->ns-1) ? 1 : hp->ns-1) {
AMBSAMP *ap = &ambsam(hp,i,j);
if ((ap->d <= FTINY) | (ap->d >= max_d))
continue; /* too far or too near */
VSUB(vec, ap->p, hp->rp->rop);
u = DOT(vec, uv[0]);
v = DOT(vec, uv[1]);
if ((r0*r0*u*u + r1*r1*v*v) * ap->d*ap->d <= u*u + v*v)
continue; /* occluder outside ellipse */
ang = atan2a(v, u); /* else set direction flags */
for (a1 = ang-ang_res; a1 <= ang+ang_res; a1 += ang_step)
flgs |= 1L<<(int)(16/PI*(a1 + 2.*PI*(a1 < 0)));
}
return(flgs);
}
int
doambient( /* compute ambient component */
COLOR rcol, /* input/output color */
RAY *r,
double wt,
FVECT uv[2], /* returned (optional) */
float ra[2], /* returned (optional) */
float pg[2], /* returned (optional) */
float dg[2], /* returned (optional) */
uint32 *crlp /* returned (optional) */
)
{
AMBHEMI *hp = samp_hemi(rcol, r, wt);
FVECT my_uv[2];
double d, K;
AMBSAMP *ap;
int i;
/* clear return values */
if (uv != NULL)
memset(uv, 0, sizeof(FVECT)*2);
if (ra != NULL)
ra[0] = ra[1] = 0.0;
if (pg != NULL)
pg[0] = pg[1] = 0.0;
if (dg != NULL)
dg[0] = dg[1] = 0.0;
if (crlp != NULL)
*crlp = 0;
if (hp == NULL) /* sampling falure? */
return(0);
if ((ra == NULL) & (pg == NULL) & (dg == NULL) ||
(hp->sampOK < 0) | (hp->ns < MINADIV)) {
free(hp); /* Hessian not requested/possible */
return(-1); /* value-only return value */
}
if ((d = bright(rcol)) > FTINY) { /* normalize Y values */
d = 0.99*(hp->ns*hp->ns)/d;
K = 0.01;
} else { /* or fall back on geometric Hessian */
K = 1.0;
pg = NULL;
dg = NULL;
crlp = NULL;
}
ap = hp->sa; /* relative Y channel from here on... */
for (i = hp->ns*hp->ns; i--; ap++)
colval(ap->v,CIEY) = bright(ap->v)*d + K;
if (uv == NULL) /* make sure we have axis pointers */
uv = my_uv;
/* compute radii & pos. gradient */
ambHessian(hp, uv, ra, pg);
if (dg != NULL) /* compute direction gradient */
ambdirgrad(hp, uv, dg);
if (ra != NULL) { /* scale/clamp radii */
if (pg != NULL) {
if (ra[0]*(d = fabs(pg[0])) > 1.0)
ra[0] = 1.0/d;
if (ra[1]*(d = fabs(pg[1])) > 1.0)
ra[1] = 1.0/d;
if (ra[0] > ra[1])
ra[0] = ra[1];
}
if (ra[0] < minarad) {
ra[0] = minarad;
if (ra[1] < minarad)
ra[1] = minarad;
}
ra[0] *= d = 1.0/sqrt(wt);
if ((ra[1] *= d) > 2.0*ra[0])
ra[1] = 2.0*ra[0];
if (ra[1] > maxarad) {
ra[1] = maxarad;
if (ra[0] > maxarad)
ra[0] = maxarad;
}
/* flag encroached directions */
if (crlp != NULL)
*crlp = ambcorral(hp, uv, ra[0]*ambacc, ra[1]*ambacc);
if (pg != NULL) { /* cap gradient if necessary */
d = pg[0]*pg[0]*ra[0]*ra[0] + pg[1]*pg[1]*ra[1]*ra[1];
if (d > 1.0) {
d = 1.0/sqrt(d);
pg[0] *= d;
pg[1] *= d;
}
}
}
free(hp); /* clean up and return */
return(1);
}

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