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#ifndef lint |
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static const char RCSid[] = "$Id: ambcomp.c,v 2.50 2014/05/07 16:02:26 greg Exp $"; |
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#endif |
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/* |
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* Routines to compute "ambient" values using Monte Carlo |
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* |
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* Hessian calculations based on "Practical Hessian-Based Error Control |
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* for Irradiance Caching" by Schwarzhaupt, Wann Jensen, & Jarosz |
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* from ACM SIGGRAPH Asia 2012 conference proceedings. |
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* |
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* Added book-keeping optimization to avoid calculations that would |
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* cancel due to traversal both directions on edges that are adjacent |
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* to same-valued triangles. This cuts about half of Hessian math. |
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* |
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* Declarations of external symbols in ambient.h |
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*/ |
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|
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#include "copyright.h" |
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|
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#include "ray.h" |
21 |
#include "ambient.h" |
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#include "random.h" |
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|
24 |
#ifdef NEWAMB |
25 |
|
26 |
extern void SDsquare2disk(double ds[2], double seedx, double seedy); |
27 |
|
28 |
/* vertex direction bit positions */ |
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#define VDB_xy 0 |
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#define VDB_y 01 |
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#define VDB_x 02 |
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#define VDB_Xy 03 |
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#define VDB_xY 04 |
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#define VDB_X 05 |
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#define VDB_Y 06 |
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#define VDB_XY 07 |
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/* get opposite vertex direction bit */ |
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#define VDB_OPP(f) (~(f) & 07) |
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/* adjacent triangle vertex flags */ |
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static const int adjacent_trifl[8] = { |
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0, /* forbidden diagonal */ |
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1<<VDB_x|1<<VDB_y|1<<VDB_Xy, |
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1<<VDB_y|1<<VDB_x|1<<VDB_xY, |
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1<<VDB_y|1<<VDB_Xy|1<<VDB_X, |
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1<<VDB_x|1<<VDB_xY|1<<VDB_Y, |
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1<<VDB_Xy|1<<VDB_X|1<<VDB_Y, |
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1<<VDB_xY|1<<VDB_Y|1<<VDB_X, |
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0, /* forbidden diagonal */ |
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}; |
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|
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typedef struct { |
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COLOR v; /* hemisphere sample value */ |
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float d; /* reciprocal distance (1/rt) */ |
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FVECT p; /* intersection point */ |
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} AMBSAMP; /* sample value */ |
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|
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typedef struct { |
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RAY *rp; /* originating ray sample */ |
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FVECT ux, uy; /* tangent axis unit vectors */ |
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int ns; /* number of samples per axis */ |
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COLOR acoef; /* division contribution coefficient */ |
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AMBSAMP sa[1]; /* sample array (extends struct) */ |
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} AMBHEMI; /* ambient sample hemisphere */ |
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|
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#define ambndx(h,i,j) ((i)*(h)->ns + (j)) |
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#define ambsam(h,i,j) (h)->sa[ambndx(h,i,j)] |
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|
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typedef struct { |
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FVECT r_i, r_i1, e_i, rcp, rI2_eJ2; |
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double I1, I2; |
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int valid; |
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} FFTRI; /* vectors and coefficients for Hessian calculation */ |
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|
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|
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/* Get index for adjacent vertex */ |
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static int |
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adjacent_verti(AMBHEMI *hp, int i, int j, int dbit) |
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{ |
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int i0 = i*hp->ns + j; |
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|
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switch (dbit) { |
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case VDB_y: return(i0 - hp->ns); |
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case VDB_x: return(i0 - 1); |
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case VDB_Xy: return(i0 - hp->ns + 1); |
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case VDB_xY: return(i0 + hp->ns - 1); |
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case VDB_X: return(i0 + 1); |
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case VDB_Y: return(i0 + hp->ns); |
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/* the following should never occur */ |
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case VDB_xy: return(i0 - hp->ns - 1); |
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case VDB_XY: return(i0 + hp->ns + 1); |
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} |
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return(-1); |
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} |
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|
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|
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/* Get vertex direction bit for the opposite edge to complete triangle */ |
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static int |
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vdb_edge(int db1, int db2) |
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{ |
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switch (db1) { |
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case VDB_x: return(db2==VDB_y ? VDB_Xy : VDB_Y); |
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case VDB_y: return(db2==VDB_x ? VDB_xY : VDB_X); |
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case VDB_X: return(db2==VDB_Xy ? VDB_y : VDB_xY); |
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case VDB_Y: return(db2==VDB_xY ? VDB_x : VDB_Xy); |
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case VDB_xY: return(db2==VDB_x ? VDB_y : VDB_X); |
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case VDB_Xy: return(db2==VDB_y ? VDB_x : VDB_Y); |
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} |
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error(INTERNAL, "forbidden diagonal in vdb_edge()"); |
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return(-1); |
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} |
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|
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|
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static AMBHEMI * |
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inithemi( /* initialize sampling hemisphere */ |
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COLOR ac, |
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RAY *r, |
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double wt |
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) |
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{ |
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AMBHEMI *hp; |
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double d; |
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int n, i; |
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/* set number of divisions */ |
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if (ambacc <= FTINY && |
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wt > (d = 0.8*intens(ac)*r->rweight/(ambdiv*minweight))) |
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wt = d; /* avoid ray termination */ |
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n = sqrt(ambdiv * wt) + 0.5; |
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i = 1 + 5*(ambacc > FTINY); /* minimum number of samples */ |
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if (n < i) |
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n = i; |
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/* allocate sampling array */ |
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hp = (AMBHEMI *)malloc(sizeof(AMBHEMI) + sizeof(AMBSAMP)*(n*n - 1)); |
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if (hp == NULL) |
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return(NULL); |
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hp->rp = r; |
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hp->ns = n; |
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/* assign coefficient */ |
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copycolor(hp->acoef, ac); |
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d = 1.0/(n*n); |
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scalecolor(hp->acoef, d); |
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/* make tangent plane axes */ |
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hp->uy[0] = 0.5 - frandom(); |
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hp->uy[1] = 0.5 - frandom(); |
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hp->uy[2] = 0.5 - frandom(); |
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for (i = 3; i--; ) |
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if ((-0.6 < r->ron[i]) & (r->ron[i] < 0.6)) |
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break; |
148 |
if (i < 0) |
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error(CONSISTENCY, "bad ray direction in inithemi"); |
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hp->uy[i] = 1.0; |
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VCROSS(hp->ux, hp->uy, r->ron); |
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normalize(hp->ux); |
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VCROSS(hp->uy, r->ron, hp->ux); |
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/* we're ready to sample */ |
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return(hp); |
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} |
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|
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|
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/* Sample ambient division and apply weighting coefficient */ |
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static int |
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getambsamp(RAY *arp, AMBHEMI *hp, int i, int j, int n) |
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{ |
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int hlist[3], ii; |
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double spt[2], zd; |
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/* ambient coefficient for weight */ |
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if (ambacc > FTINY) |
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setcolor(arp->rcoef, AVGREFL, AVGREFL, AVGREFL); |
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else |
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copycolor(arp->rcoef, hp->acoef); |
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if (rayorigin(arp, AMBIENT, hp->rp, arp->rcoef) < 0) |
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return(0); |
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if (ambacc > FTINY) { |
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multcolor(arp->rcoef, hp->acoef); |
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scalecolor(arp->rcoef, 1./AVGREFL); |
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} |
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hlist[0] = hp->rp->rno; |
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hlist[1] = j; |
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hlist[2] = i; |
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multisamp(spt, 2, urand(ilhash(hlist,3)+n)); |
180 |
if (!n) { /* avoid border samples for n==0 */ |
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if ((spt[0] < 0.1) | (spt[0] >= 0.9)) |
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spt[0] = 0.1 + 0.8*frandom(); |
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if ((spt[1] < 0.1) | (spt[1] >= 0.9)) |
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spt[1] = 0.1 + 0.8*frandom(); |
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} |
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SDsquare2disk(spt, (j+spt[1])/hp->ns, (i+spt[0])/hp->ns); |
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zd = sqrt(1. - spt[0]*spt[0] - spt[1]*spt[1]); |
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for (ii = 3; ii--; ) |
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arp->rdir[ii] = spt[0]*hp->ux[ii] + |
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spt[1]*hp->uy[ii] + |
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zd*hp->rp->ron[ii]; |
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checknorm(arp->rdir); |
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dimlist[ndims++] = ambndx(hp,i,j) + 90171; |
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rayvalue(arp); /* evaluate ray */ |
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ndims--; /* apply coefficient */ |
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multcolor(arp->rcol, arp->rcoef); |
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return(1); |
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} |
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|
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|
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static AMBSAMP * |
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ambsample( /* initial ambient division sample */ |
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AMBHEMI *hp, |
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int i, |
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int j |
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) |
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{ |
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AMBSAMP *ap = &ambsam(hp,i,j); |
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RAY ar; |
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/* generate hemispherical sample */ |
211 |
if (!getambsamp(&ar, hp, i, j, 0) || ar.rt <= FTINY) { |
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memset(ap, 0, sizeof(AMBSAMP)); |
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return(NULL); |
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} |
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ap->d = 1.0/ar.rt; /* limit vertex distance */ |
216 |
if (ar.rt > 10.0*thescene.cusize) |
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ar.rt = 10.0*thescene.cusize; |
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VSUM(ap->p, ar.rorg, ar.rdir, ar.rt); |
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copycolor(ap->v, ar.rcol); |
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return(ap); |
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} |
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|
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|
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/* Estimate errors 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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float *earr = (float *)calloc(hp->ns*hp->ns, sizeof(float)); |
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float *ep; |
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AMBSAMP *ap; |
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double b, d2; |
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int i, j; |
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|
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if (earr == NULL) /* out of memory? */ |
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return(NULL); |
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/* compute squared neighbor diffs */ |
237 |
for (ap = hp->sa, ep = earr, i = 0; i < hp->ns; i++) |
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for (j = 0; j < hp->ns; j++, ap++, ep++) { |
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b = bright(ap[0].v); |
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if (i) { /* from above */ |
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d2 = b - bright(ap[-hp->ns].v); |
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d2 *= d2; |
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ep[0] += d2; |
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ep[-hp->ns] += d2; |
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} |
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if (j) { /* from behind */ |
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d2 = b - bright(ap[-1].v); |
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d2 *= d2; |
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ep[0] += d2; |
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ep[-1] += d2; |
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} |
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} |
253 |
/* correct for number of neighbors */ |
254 |
earr[0] *= 2.f; |
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earr[hp->ns-1] *= 2.f; |
256 |
earr[(hp->ns-1)*hp->ns] *= 2.f; |
257 |
earr[(hp->ns-1)*hp->ns + hp->ns-1] *= 2.f; |
258 |
for (i = 1; i < hp->ns-1; i++) { |
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earr[i*hp->ns] *= 4./3.; |
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earr[i*hp->ns + hp->ns-1] *= 4./3.; |
261 |
} |
262 |
for (j = 1; j < hp->ns-1; j++) { |
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earr[j] *= 4./3.; |
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earr[(hp->ns-1)*hp->ns + j] *= 4./3.; |
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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) */ |
271 |
static void |
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ambsupersamp(double acol[3], AMBHEMI *hp, int cnt) |
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{ |
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float *earr = getambdiffs(hp); |
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double e2sum = 0.0; |
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AMBSAMP *ap; |
277 |
RAY ar; |
278 |
double asum[3]; |
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float *ep; |
280 |
int i, j, n; |
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|
282 |
if (earr == NULL) /* just skip calc. if no memory */ |
283 |
return; |
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/* add up estimated variances */ |
285 |
for (ep = earr + hp->ns*hp->ns; ep-- > earr; ) |
286 |
e2sum += *ep; |
287 |
ep = earr; /* perform super-sampling */ |
288 |
for (ap = hp->sa, i = 0; i < hp->ns; i++) |
289 |
for (j = 0; j < hp->ns; j++, ap++) { |
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int nss = *ep/e2sum*cnt + frandom(); |
291 |
asum[0] = asum[1] = asum[2] = 0.0; |
292 |
for (n = 1; n <= nss; n++) { |
293 |
if (!getambsamp(&ar, hp, i, j, n)) { |
294 |
nss = n-1; |
295 |
break; |
296 |
} |
297 |
addcolor(asum, ar.rcol); |
298 |
} |
299 |
if (nss) { /* update returned ambient value */ |
300 |
const double ssf = 1./(nss + 1); |
301 |
for (n = 3; n--; ) |
302 |
acol[n] += ssf*asum[n] + |
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(ssf - 1.)*colval(ap->v,n); |
304 |
} |
305 |
e2sum -= *ep++; /* update remainders */ |
306 |
cnt -= nss; |
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} |
308 |
free(earr); |
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} |
310 |
|
311 |
|
312 |
/* Compute vertex flags, indicating farthest in each direction */ |
313 |
static uby8 * |
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vertex_flags(AMBHEMI *hp) |
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{ |
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uby8 *vflags = (uby8 *)calloc(hp->ns*hp->ns, sizeof(uby8)); |
317 |
uby8 *vf; |
318 |
AMBSAMP *ap; |
319 |
int i, j; |
320 |
|
321 |
if (vflags == NULL) |
322 |
error(SYSTEM, "out of memory in vertex_flags()"); |
323 |
vf = vflags; |
324 |
ap = hp->sa; /* compute farthest along first row */ |
325 |
for (j = 0; j < hp->ns-1; j++, vf++, ap++) |
326 |
if (ap[0].d <= ap[1].d) |
327 |
vf[0] |= 1<<VDB_X; |
328 |
else |
329 |
vf[1] |= 1<<VDB_x; |
330 |
++vf; ++ap; |
331 |
/* flag subsequent rows */ |
332 |
for (i = 1; i < hp->ns; i++) { |
333 |
for (j = 0; j < hp->ns-1; j++, vf++, ap++) { |
334 |
if (ap[0].d <= ap[-hp->ns].d) /* row before */ |
335 |
vf[0] |= 1<<VDB_y; |
336 |
else |
337 |
vf[-hp->ns] |= 1<<VDB_Y; |
338 |
if (ap[0].d <= ap[1-hp->ns].d) /* diagonal we care about */ |
339 |
vf[0] |= 1<<VDB_Xy; |
340 |
else |
341 |
vf[1-hp->ns] |= 1<<VDB_xY; |
342 |
if (ap[0].d <= ap[1].d) /* column after */ |
343 |
vf[0] |= 1<<VDB_X; |
344 |
else |
345 |
vf[1] |= 1<<VDB_x; |
346 |
} |
347 |
if (ap[0].d <= ap[-hp->ns].d) /* final column edge */ |
348 |
vf[0] |= 1<<VDB_y; |
349 |
else |
350 |
vf[-hp->ns] |= 1<<VDB_Y; |
351 |
++vf; ++ap; |
352 |
} |
353 |
return(vflags); |
354 |
} |
355 |
|
356 |
|
357 |
/* Return brightness of farthest ambient sample */ |
358 |
static double |
359 |
back_ambval(AMBHEMI *hp, int i, int j, int dbit1, int dbit2, const uby8 *vflags) |
360 |
{ |
361 |
const int v0 = ambndx(hp,i,j); |
362 |
const int tflags = (1<<dbit1 | 1<<dbit2); |
363 |
int v1, v2; |
364 |
|
365 |
if ((vflags[v0] & tflags) == tflags) /* is v0 the farthest? */ |
366 |
return(colval(hp->sa[v0].v,CIEY)); |
367 |
v1 = adjacent_verti(hp, i, j, dbit1); |
368 |
if (vflags[v0] & 1<<dbit2) /* v1 farthest if v0>v2 */ |
369 |
return(colval(hp->sa[v1].v,CIEY)); |
370 |
v2 = adjacent_verti(hp, i, j, dbit2); |
371 |
if (vflags[v0] & 1<<dbit1) /* v2 farthest if v0>v1 */ |
372 |
return(colval(hp->sa[v2].v,CIEY)); |
373 |
/* else check if v1>v2 */ |
374 |
if (vflags[v1] & 1<<vdb_edge(dbit1,dbit2)) |
375 |
return(colval(hp->sa[v1].v,CIEY)); |
376 |
return(colval(hp->sa[v2].v,CIEY)); |
377 |
} |
378 |
|
379 |
|
380 |
/* Compute vectors and coefficients for Hessian/gradient calcs */ |
381 |
static void |
382 |
comp_fftri(FFTRI *ftp, AMBHEMI *hp, int i, int j, int dbit, const uby8 *vflags) |
383 |
{ |
384 |
const int i0 = ambndx(hp,i,j); |
385 |
double rdot_cp, dot_e, dot_er, rdot_r, rdot_r1, J2; |
386 |
int i1, ii; |
387 |
|
388 |
ftp->valid = 0; /* check if we can skip this edge */ |
389 |
ii = adjacent_trifl[dbit]; |
390 |
if ((vflags[i0] & ii) == ii) /* cancels if vertex used as value */ |
391 |
return; |
392 |
i1 = adjacent_verti(hp, i, j, dbit); |
393 |
ii = adjacent_trifl[VDB_OPP(dbit)]; |
394 |
if ((vflags[i1] & ii) == ii) /* on either end (for both triangles) */ |
395 |
return; |
396 |
/* else go ahead with calculation */ |
397 |
VSUB(ftp->r_i, hp->sa[i0].p, hp->rp->rop); |
398 |
VSUB(ftp->r_i1, hp->sa[i1].p, hp->rp->rop); |
399 |
VSUB(ftp->e_i, hp->sa[i1].p, hp->sa[i0].p); |
400 |
VCROSS(ftp->rcp, ftp->r_i, ftp->r_i1); |
401 |
rdot_cp = 1.0/DOT(ftp->rcp,ftp->rcp); |
402 |
dot_e = DOT(ftp->e_i,ftp->e_i); |
403 |
dot_er = DOT(ftp->e_i, ftp->r_i); |
404 |
rdot_r = 1.0/DOT(ftp->r_i,ftp->r_i); |
405 |
rdot_r1 = 1.0/DOT(ftp->r_i1,ftp->r_i1); |
406 |
ftp->I1 = acos( DOT(ftp->r_i, ftp->r_i1) * sqrt(rdot_r*rdot_r1) ) * |
407 |
sqrt( rdot_cp ); |
408 |
ftp->I2 = ( DOT(ftp->e_i, ftp->r_i1)*rdot_r1 - dot_er*rdot_r + |
409 |
dot_e*ftp->I1 )*0.5*rdot_cp; |
410 |
J2 = ( 0.5*(rdot_r - rdot_r1) - dot_er*ftp->I2 ) / dot_e; |
411 |
for (ii = 3; ii--; ) |
412 |
ftp->rI2_eJ2[ii] = ftp->I2*ftp->r_i[ii] + J2*ftp->e_i[ii]; |
413 |
ftp->valid++; |
414 |
} |
415 |
|
416 |
|
417 |
/* Compose 3x3 matrix from two vectors */ |
418 |
static void |
419 |
compose_matrix(FVECT mat[3], FVECT va, FVECT vb) |
420 |
{ |
421 |
mat[0][0] = 2.0*va[0]*vb[0]; |
422 |
mat[1][1] = 2.0*va[1]*vb[1]; |
423 |
mat[2][2] = 2.0*va[2]*vb[2]; |
424 |
mat[0][1] = mat[1][0] = va[0]*vb[1] + va[1]*vb[0]; |
425 |
mat[0][2] = mat[2][0] = va[0]*vb[2] + va[2]*vb[0]; |
426 |
mat[1][2] = mat[2][1] = va[1]*vb[2] + va[2]*vb[1]; |
427 |
} |
428 |
|
429 |
|
430 |
/* Compute partial 3x3 Hessian matrix for edge */ |
431 |
static void |
432 |
comp_hessian(FVECT hess[3], FFTRI *ftp, FVECT nrm) |
433 |
{ |
434 |
FVECT ncp; |
435 |
FVECT m1[3], m2[3], m3[3], m4[3]; |
436 |
double d1, d2, d3, d4; |
437 |
double I3, J3, K3; |
438 |
int i, j; |
439 |
|
440 |
if (!ftp->valid) { /* preemptive test */ |
441 |
memset(hess, 0, sizeof(FVECT)*3); |
442 |
return; |
443 |
} |
444 |
/* compute intermediate coefficients */ |
445 |
d1 = 1.0/DOT(ftp->r_i,ftp->r_i); |
446 |
d2 = 1.0/DOT(ftp->r_i1,ftp->r_i1); |
447 |
d3 = 1.0/DOT(ftp->e_i,ftp->e_i); |
448 |
d4 = DOT(ftp->e_i, ftp->r_i); |
449 |
I3 = ( DOT(ftp->e_i, ftp->r_i1)*d2*d2 - d4*d1*d1 + 3.0/d3*ftp->I2 ) |
450 |
/ ( 4.0*DOT(ftp->rcp,ftp->rcp) ); |
451 |
J3 = 0.25*d3*(d1*d1 - d2*d2) - d4*d3*I3; |
452 |
K3 = d3*(ftp->I2 - I3/d1 - 2.0*d4*J3); |
453 |
/* intermediate matrices */ |
454 |
VCROSS(ncp, nrm, ftp->e_i); |
455 |
compose_matrix(m1, ncp, ftp->rI2_eJ2); |
456 |
compose_matrix(m2, ftp->r_i, ftp->r_i); |
457 |
compose_matrix(m3, ftp->e_i, ftp->e_i); |
458 |
compose_matrix(m4, ftp->r_i, ftp->e_i); |
459 |
d1 = DOT(nrm, ftp->rcp); |
460 |
d2 = -d1*ftp->I2; |
461 |
d1 *= 2.0; |
462 |
for (i = 3; i--; ) /* final matrix sum */ |
463 |
for (j = 3; j--; ) { |
464 |
hess[i][j] = m1[i][j] + d1*( I3*m2[i][j] + K3*m3[i][j] + |
465 |
2.0*J3*m4[i][j] ); |
466 |
hess[i][j] += d2*(i==j); |
467 |
hess[i][j] *= -1.0/PI; |
468 |
} |
469 |
} |
470 |
|
471 |
|
472 |
/* Reverse hessian calculation result for edge in other direction */ |
473 |
static void |
474 |
rev_hessian(FVECT hess[3]) |
475 |
{ |
476 |
int i; |
477 |
|
478 |
for (i = 3; i--; ) { |
479 |
hess[i][0] = -hess[i][0]; |
480 |
hess[i][1] = -hess[i][1]; |
481 |
hess[i][2] = -hess[i][2]; |
482 |
} |
483 |
} |
484 |
|
485 |
|
486 |
/* Add to radiometric Hessian from the given triangle */ |
487 |
static void |
488 |
add2hessian(FVECT hess[3], FVECT ehess1[3], |
489 |
FVECT ehess2[3], FVECT ehess3[3], double v) |
490 |
{ |
491 |
int i, j; |
492 |
|
493 |
for (i = 3; i--; ) |
494 |
for (j = 3; j--; ) |
495 |
hess[i][j] += v*( ehess1[i][j] + ehess2[i][j] + ehess3[i][j] ); |
496 |
} |
497 |
|
498 |
|
499 |
/* Compute partial displacement form factor gradient for edge */ |
500 |
static void |
501 |
comp_gradient(FVECT grad, FFTRI *ftp, FVECT nrm) |
502 |
{ |
503 |
FVECT ncp; |
504 |
double f1; |
505 |
int i; |
506 |
|
507 |
if (!ftp->valid) { /* preemptive test */ |
508 |
memset(grad, 0, sizeof(FVECT)); |
509 |
return; |
510 |
} |
511 |
f1 = 2.0*DOT(nrm, ftp->rcp); |
512 |
VCROSS(ncp, nrm, ftp->e_i); |
513 |
for (i = 3; i--; ) |
514 |
grad[i] = (0.5/PI)*( ftp->I1*ncp[i] + f1*ftp->rI2_eJ2[i] ); |
515 |
} |
516 |
|
517 |
|
518 |
/* Reverse gradient calculation result for edge in other direction */ |
519 |
static void |
520 |
rev_gradient(FVECT grad) |
521 |
{ |
522 |
grad[0] = -grad[0]; |
523 |
grad[1] = -grad[1]; |
524 |
grad[2] = -grad[2]; |
525 |
} |
526 |
|
527 |
|
528 |
/* Add to displacement gradient from the given triangle */ |
529 |
static void |
530 |
add2gradient(FVECT grad, FVECT egrad1, FVECT egrad2, FVECT egrad3, double v) |
531 |
{ |
532 |
int i; |
533 |
|
534 |
for (i = 3; i--; ) |
535 |
grad[i] += v*( egrad1[i] + egrad2[i] + egrad3[i] ); |
536 |
} |
537 |
|
538 |
|
539 |
/* Compute anisotropic radii and eigenvector directions */ |
540 |
static int |
541 |
eigenvectors(FVECT uv[2], float ra[2], FVECT hessian[3]) |
542 |
{ |
543 |
double hess2[2][2]; |
544 |
FVECT a, b; |
545 |
double evalue[2], slope1, xmag1; |
546 |
int i; |
547 |
/* project Hessian to sample plane */ |
548 |
for (i = 3; i--; ) { |
549 |
a[i] = DOT(hessian[i], uv[0]); |
550 |
b[i] = DOT(hessian[i], uv[1]); |
551 |
} |
552 |
hess2[0][0] = DOT(uv[0], a); |
553 |
hess2[0][1] = DOT(uv[0], b); |
554 |
hess2[1][0] = DOT(uv[1], a); |
555 |
hess2[1][1] = DOT(uv[1], b); |
556 |
/* compute eigenvalue(s) */ |
557 |
i = quadratic(evalue, 1.0, -hess2[0][0]-hess2[1][1], |
558 |
hess2[0][0]*hess2[1][1]-hess2[0][1]*hess2[1][0]); |
559 |
if (i == 1) /* double-root (circle) */ |
560 |
evalue[1] = evalue[0]; |
561 |
if (!i || ((evalue[0] = fabs(evalue[0])) <= FTINY*FTINY) | |
562 |
((evalue[1] = fabs(evalue[1])) <= FTINY*FTINY) ) |
563 |
error(INTERNAL, "bad eigenvalue calculation"); |
564 |
|
565 |
if (evalue[0] > evalue[1]) { |
566 |
ra[0] = sqrt(sqrt(4.0/evalue[0])); |
567 |
ra[1] = sqrt(sqrt(4.0/evalue[1])); |
568 |
slope1 = evalue[1]; |
569 |
} else { |
570 |
ra[0] = sqrt(sqrt(4.0/evalue[1])); |
571 |
ra[1] = sqrt(sqrt(4.0/evalue[0])); |
572 |
slope1 = evalue[0]; |
573 |
} |
574 |
/* compute unit eigenvectors */ |
575 |
if (fabs(hess2[0][1]) <= FTINY) |
576 |
return; /* uv OK as is */ |
577 |
slope1 = (slope1 - hess2[0][0]) / hess2[0][1]; |
578 |
xmag1 = sqrt(1.0/(1.0 + slope1*slope1)); |
579 |
for (i = 3; i--; ) { |
580 |
b[i] = xmag1*uv[0][i] + slope1*xmag1*uv[1][i]; |
581 |
a[i] = slope1*xmag1*uv[0][i] - xmag1*uv[1][i]; |
582 |
} |
583 |
VCOPY(uv[0], a); |
584 |
VCOPY(uv[1], b); |
585 |
} |
586 |
|
587 |
|
588 |
static void |
589 |
ambHessian( /* anisotropic radii & pos. gradient */ |
590 |
AMBHEMI *hp, |
591 |
FVECT uv[2], /* returned */ |
592 |
float ra[2], /* returned (optional) */ |
593 |
float pg[2] /* returned (optional) */ |
594 |
) |
595 |
{ |
596 |
static char memerrmsg[] = "out of memory in ambHessian()"; |
597 |
FVECT (*hessrow)[3] = NULL; |
598 |
FVECT *gradrow = NULL; |
599 |
uby8 *vflags; |
600 |
FVECT hessian[3]; |
601 |
FVECT gradient; |
602 |
FFTRI fftr; |
603 |
int i, j; |
604 |
/* be sure to assign unit vectors */ |
605 |
VCOPY(uv[0], hp->ux); |
606 |
VCOPY(uv[1], hp->uy); |
607 |
/* clock-wise vertex traversal from sample POV */ |
608 |
if (ra != NULL) { /* initialize Hessian row buffer */ |
609 |
hessrow = (FVECT (*)[3])malloc(sizeof(FVECT)*3*(hp->ns-1)); |
610 |
if (hessrow == NULL) |
611 |
error(SYSTEM, memerrmsg); |
612 |
memset(hessian, 0, sizeof(hessian)); |
613 |
} else if (pg == NULL) /* bogus call? */ |
614 |
return; |
615 |
if (pg != NULL) { /* initialize form factor row buffer */ |
616 |
gradrow = (FVECT *)malloc(sizeof(FVECT)*(hp->ns-1)); |
617 |
if (gradrow == NULL) |
618 |
error(SYSTEM, memerrmsg); |
619 |
memset(gradient, 0, sizeof(gradient)); |
620 |
} |
621 |
/* get vertex position flags */ |
622 |
vflags = vertex_flags(hp); |
623 |
/* compute first row of edges */ |
624 |
for (j = 0; j < hp->ns-1; j++) { |
625 |
comp_fftri(&fftr, hp, 0, j, VDB_X, vflags); |
626 |
if (hessrow != NULL) |
627 |
comp_hessian(hessrow[j], &fftr, hp->rp->ron); |
628 |
if (gradrow != NULL) |
629 |
comp_gradient(gradrow[j], &fftr, hp->rp->ron); |
630 |
} |
631 |
/* sum each row of triangles */ |
632 |
for (i = 0; i < hp->ns-1; i++) { |
633 |
FVECT hesscol[3]; /* compute first vertical edge */ |
634 |
FVECT gradcol; |
635 |
comp_fftri(&fftr, hp, i, 0, VDB_Y, vflags); |
636 |
if (hessrow != NULL) |
637 |
comp_hessian(hesscol, &fftr, hp->rp->ron); |
638 |
if (gradrow != NULL) |
639 |
comp_gradient(gradcol, &fftr, hp->rp->ron); |
640 |
for (j = 0; j < hp->ns-1; j++) { |
641 |
FVECT hessdia[3]; /* compute triangle contributions */ |
642 |
FVECT graddia; |
643 |
double backg; |
644 |
backg = back_ambval(hp, i, j, VDB_X, VDB_Y, vflags); |
645 |
/* diagonal (inner) edge */ |
646 |
comp_fftri(&fftr, hp, i, j+1, VDB_xY, vflags); |
647 |
if (hessrow != NULL) { |
648 |
comp_hessian(hessdia, &fftr, hp->rp->ron); |
649 |
rev_hessian(hesscol); |
650 |
add2hessian(hessian, hessrow[j], hessdia, hesscol, backg); |
651 |
} |
652 |
if (gradrow != NULL) { |
653 |
comp_gradient(graddia, &fftr, hp->rp->ron); |
654 |
rev_gradient(gradcol); |
655 |
add2gradient(gradient, gradrow[j], graddia, gradcol, backg); |
656 |
} |
657 |
/* initialize edge in next row */ |
658 |
comp_fftri(&fftr, hp, i+1, j+1, VDB_x, vflags); |
659 |
if (hessrow != NULL) |
660 |
comp_hessian(hessrow[j], &fftr, hp->rp->ron); |
661 |
if (gradrow != NULL) |
662 |
comp_gradient(gradrow[j], &fftr, hp->rp->ron); |
663 |
/* new column edge & paired triangle */ |
664 |
backg = back_ambval(hp, i+1, j+1, VDB_x, VDB_y, vflags); |
665 |
comp_fftri(&fftr, hp, i, j+1, VDB_Y, vflags); |
666 |
if (hessrow != NULL) { |
667 |
comp_hessian(hesscol, &fftr, hp->rp->ron); |
668 |
rev_hessian(hessdia); |
669 |
add2hessian(hessian, hessrow[j], hessdia, hesscol, backg); |
670 |
if (i < hp->ns-2) |
671 |
rev_hessian(hessrow[j]); |
672 |
} |
673 |
if (gradrow != NULL) { |
674 |
comp_gradient(gradcol, &fftr, hp->rp->ron); |
675 |
rev_gradient(graddia); |
676 |
add2gradient(gradient, gradrow[j], graddia, gradcol, backg); |
677 |
if (i < hp->ns-2) |
678 |
rev_gradient(gradrow[j]); |
679 |
} |
680 |
} |
681 |
} |
682 |
/* release row buffers */ |
683 |
if (hessrow != NULL) free(hessrow); |
684 |
if (gradrow != NULL) free(gradrow); |
685 |
free(vflags); |
686 |
|
687 |
if (ra != NULL) /* extract eigenvectors & radii */ |
688 |
eigenvectors(uv, ra, hessian); |
689 |
if (pg != NULL) { /* tangential position gradient */ |
690 |
pg[0] = DOT(gradient, uv[0]); |
691 |
pg[1] = DOT(gradient, uv[1]); |
692 |
} |
693 |
} |
694 |
|
695 |
|
696 |
/* Compute direction gradient from a hemispherical sampling */ |
697 |
static void |
698 |
ambdirgrad(AMBHEMI *hp, FVECT uv[2], float dg[2]) |
699 |
{ |
700 |
AMBSAMP *ap; |
701 |
double dgsum[2]; |
702 |
int n; |
703 |
FVECT vd; |
704 |
double gfact; |
705 |
|
706 |
dgsum[0] = dgsum[1] = 0.0; /* sum values times -tan(theta) */ |
707 |
for (ap = hp->sa, n = hp->ns*hp->ns; n--; ap++) { |
708 |
/* use vector for azimuth + 90deg */ |
709 |
VSUB(vd, ap->p, hp->rp->rop); |
710 |
/* brightness over cosine factor */ |
711 |
gfact = colval(ap->v,CIEY) / DOT(hp->rp->ron, vd); |
712 |
/* sine = proj_radius/vd_length */ |
713 |
dgsum[0] -= DOT(uv[1], vd) * gfact; |
714 |
dgsum[1] += DOT(uv[0], vd) * gfact; |
715 |
} |
716 |
dg[0] = dgsum[0] / (hp->ns*hp->ns); |
717 |
dg[1] = dgsum[1] / (hp->ns*hp->ns); |
718 |
} |
719 |
|
720 |
|
721 |
/* Compute potential light leak direction flags for cache value */ |
722 |
static uint32 |
723 |
ambcorral(AMBHEMI *hp, FVECT uv[2], const double r0, const double r1) |
724 |
{ |
725 |
const double max_d = 1.0/(minarad*ambacc + 0.001); |
726 |
const double ang_res = 0.5*PI/(hp->ns-1); |
727 |
const double ang_step = ang_res/((int)(16/PI*ang_res) + (1+FTINY)); |
728 |
double avg_d = 0; |
729 |
uint32 flgs = 0; |
730 |
int i, j; |
731 |
/* check distances above us */ |
732 |
for (i = hp->ns*3/4; i-- > hp->ns>>2; ) |
733 |
for (j = hp->ns*3/4; j-- > hp->ns>>2; ) |
734 |
avg_d += ambsam(hp,i,j).d; |
735 |
avg_d *= 4.0/(hp->ns*hp->ns); |
736 |
if (avg_d >= max_d) /* too close to corral? */ |
737 |
return(0); |
738 |
/* else circle around perimeter */ |
739 |
for (i = 0; i < hp->ns; i++) |
740 |
for (j = 0; j < hp->ns; j += !i|(i==hp->ns-1) ? 1 : hp->ns-1) { |
741 |
AMBSAMP *ap = &ambsam(hp,i,j); |
742 |
FVECT vec; |
743 |
double u, v; |
744 |
double ang, a1; |
745 |
int abp; |
746 |
if ((ap->d <= FTINY) | (ap->d >= max_d)) |
747 |
continue; /* too far or too near */ |
748 |
VSUB(vec, ap->p, hp->rp->rop); |
749 |
u = DOT(vec, uv[0]) * ap->d; |
750 |
v = DOT(vec, uv[1]) * ap->d; |
751 |
if ((r0*r0*u*u + r1*r1*v*v) * ap->d*ap->d <= 1.0) |
752 |
continue; /* occluder outside ellipse */ |
753 |
ang = atan2a(v, u); /* else set direction flags */ |
754 |
for (a1 = ang-.5*ang_res; a1 <= ang+.5*ang_res; a1 += ang_step) |
755 |
flgs |= 1L<<(int)(16/PI*(a1 + 2.*PI*(a1 < 0))); |
756 |
} |
757 |
return(flgs); |
758 |
} |
759 |
|
760 |
|
761 |
int |
762 |
doambient( /* compute ambient component */ |
763 |
COLOR rcol, /* input/output color */ |
764 |
RAY *r, |
765 |
double wt, |
766 |
FVECT uv[2], /* returned (optional) */ |
767 |
float ra[2], /* returned (optional) */ |
768 |
float pg[2], /* returned (optional) */ |
769 |
float dg[2], /* returned (optional) */ |
770 |
uint32 *crlp /* returned (optional) */ |
771 |
) |
772 |
{ |
773 |
AMBHEMI *hp = inithemi(rcol, r, wt); |
774 |
int cnt; |
775 |
FVECT my_uv[2]; |
776 |
double d, K, acol[3]; |
777 |
AMBSAMP *ap; |
778 |
int i, j; |
779 |
/* check/initialize */ |
780 |
if (hp == NULL) |
781 |
return(0); |
782 |
if (uv != NULL) |
783 |
memset(uv, 0, sizeof(FVECT)*2); |
784 |
if (ra != NULL) |
785 |
ra[0] = ra[1] = 0.0; |
786 |
if (pg != NULL) |
787 |
pg[0] = pg[1] = 0.0; |
788 |
if (dg != NULL) |
789 |
dg[0] = dg[1] = 0.0; |
790 |
if (crlp != NULL) |
791 |
*crlp = 0; |
792 |
/* sample the hemisphere */ |
793 |
acol[0] = acol[1] = acol[2] = 0.0; |
794 |
cnt = 0; |
795 |
for (i = hp->ns; i--; ) |
796 |
for (j = hp->ns; j--; ) |
797 |
if ((ap = ambsample(hp, i, j)) != NULL) { |
798 |
addcolor(acol, ap->v); |
799 |
++cnt; |
800 |
} |
801 |
if (!cnt) { |
802 |
setcolor(rcol, 0.0, 0.0, 0.0); |
803 |
free(hp); |
804 |
return(0); /* no valid samples */ |
805 |
} |
806 |
if (cnt < hp->ns*hp->ns) { /* incomplete sampling? */ |
807 |
copycolor(rcol, acol); |
808 |
free(hp); |
809 |
return(-1); /* return value w/o Hessian */ |
810 |
} |
811 |
cnt = ambssamp*wt + 0.5; /* perform super-sampling? */ |
812 |
if (cnt > 8) |
813 |
ambsupersamp(acol, hp, cnt); |
814 |
copycolor(rcol, acol); /* final indirect irradiance/PI */ |
815 |
if ((ra == NULL) & (pg == NULL) & (dg == NULL)) { |
816 |
free(hp); |
817 |
return(-1); /* no radius or gradient calc. */ |
818 |
} |
819 |
if ((d = bright(acol)) > FTINY) { /* normalize Y values */ |
820 |
d = 0.99*(hp->ns*hp->ns)/d; |
821 |
K = 0.01; |
822 |
} else { /* or fall back on geometric Hessian */ |
823 |
K = 1.0; |
824 |
pg = NULL; |
825 |
dg = NULL; |
826 |
} |
827 |
ap = hp->sa; /* relative Y channel from here on... */ |
828 |
for (i = hp->ns*hp->ns; i--; ap++) |
829 |
colval(ap->v,CIEY) = bright(ap->v)*d + K; |
830 |
|
831 |
if (uv == NULL) /* make sure we have axis pointers */ |
832 |
uv = my_uv; |
833 |
/* compute radii & pos. gradient */ |
834 |
ambHessian(hp, uv, ra, pg); |
835 |
|
836 |
if (dg != NULL) /* compute direction gradient */ |
837 |
ambdirgrad(hp, uv, dg); |
838 |
|
839 |
if (ra != NULL) { /* scale/clamp radii */ |
840 |
if (pg != NULL) { |
841 |
if (ra[0]*(d = fabs(pg[0])) > 1.0) |
842 |
ra[0] = 1.0/d; |
843 |
if (ra[1]*(d = fabs(pg[1])) > 1.0) |
844 |
ra[1] = 1.0/d; |
845 |
if (ra[0] > ra[1]) |
846 |
ra[0] = ra[1]; |
847 |
} |
848 |
if (ra[0] < minarad) { |
849 |
ra[0] = minarad; |
850 |
if (ra[1] < minarad) |
851 |
ra[1] = minarad; |
852 |
} |
853 |
ra[0] *= d = 1.0/sqrt(sqrt(wt)); |
854 |
if ((ra[1] *= d) > 2.0*ra[0]) |
855 |
ra[1] = 2.0*ra[0]; |
856 |
if (ra[1] > maxarad) { |
857 |
ra[1] = maxarad; |
858 |
if (ra[0] > maxarad) |
859 |
ra[0] = maxarad; |
860 |
} |
861 |
if (crlp != NULL) /* flag encroached directions */ |
862 |
*crlp = ambcorral(hp, uv, ra[0]*ambacc, ra[1]*ambacc); |
863 |
if (pg != NULL) { /* cap gradient if necessary */ |
864 |
d = pg[0]*pg[0]*ra[0]*ra[0] + pg[1]*pg[1]*ra[1]*ra[1]; |
865 |
if (d > 1.0) { |
866 |
d = 1.0/sqrt(d); |
867 |
pg[0] *= d; |
868 |
pg[1] *= d; |
869 |
} |
870 |
} |
871 |
} |
872 |
free(hp); /* clean up and return */ |
873 |
return(1); |
874 |
} |
875 |
|
876 |
|
877 |
#else /* ! NEWAMB */ |
878 |
|
879 |
|
880 |
void |
881 |
inithemi( /* initialize sampling hemisphere */ |
882 |
AMBHEMI *hp, |
883 |
COLOR ac, |
884 |
RAY *r, |
885 |
double wt |
886 |
) |
887 |
{ |
888 |
double d; |
889 |
int i; |
890 |
/* set number of divisions */ |
891 |
if (ambacc <= FTINY && |
892 |
wt > (d = 0.8*intens(ac)*r->rweight/(ambdiv*minweight))) |
893 |
wt = d; /* avoid ray termination */ |
894 |
hp->nt = sqrt(ambdiv * wt / PI) + 0.5; |
895 |
i = ambacc > FTINY ? 3 : 1; /* minimum number of samples */ |
896 |
if (hp->nt < i) |
897 |
hp->nt = i; |
898 |
hp->np = PI * hp->nt + 0.5; |
899 |
/* set number of super-samples */ |
900 |
hp->ns = ambssamp * wt + 0.5; |
901 |
/* assign coefficient */ |
902 |
copycolor(hp->acoef, ac); |
903 |
d = 1.0/(hp->nt*hp->np); |
904 |
scalecolor(hp->acoef, d); |
905 |
/* make axes */ |
906 |
VCOPY(hp->uz, r->ron); |
907 |
hp->uy[0] = hp->uy[1] = hp->uy[2] = 0.0; |
908 |
for (i = 0; i < 3; i++) |
909 |
if (hp->uz[i] < 0.6 && hp->uz[i] > -0.6) |
910 |
break; |
911 |
if (i >= 3) |
912 |
error(CONSISTENCY, "bad ray direction in inithemi"); |
913 |
hp->uy[i] = 1.0; |
914 |
fcross(hp->ux, hp->uy, hp->uz); |
915 |
normalize(hp->ux); |
916 |
fcross(hp->uy, hp->uz, hp->ux); |
917 |
} |
918 |
|
919 |
|
920 |
int |
921 |
divsample( /* sample a division */ |
922 |
AMBSAMP *dp, |
923 |
AMBHEMI *h, |
924 |
RAY *r |
925 |
) |
926 |
{ |
927 |
RAY ar; |
928 |
int hlist[3]; |
929 |
double spt[2]; |
930 |
double xd, yd, zd; |
931 |
double b2; |
932 |
double phi; |
933 |
int i; |
934 |
/* ambient coefficient for weight */ |
935 |
if (ambacc > FTINY) |
936 |
setcolor(ar.rcoef, AVGREFL, AVGREFL, AVGREFL); |
937 |
else |
938 |
copycolor(ar.rcoef, h->acoef); |
939 |
if (rayorigin(&ar, AMBIENT, r, ar.rcoef) < 0) |
940 |
return(-1); |
941 |
if (ambacc > FTINY) { |
942 |
multcolor(ar.rcoef, h->acoef); |
943 |
scalecolor(ar.rcoef, 1./AVGREFL); |
944 |
} |
945 |
hlist[0] = r->rno; |
946 |
hlist[1] = dp->t; |
947 |
hlist[2] = dp->p; |
948 |
multisamp(spt, 2, urand(ilhash(hlist,3)+dp->n)); |
949 |
zd = sqrt((dp->t + spt[0])/h->nt); |
950 |
phi = 2.0*PI * (dp->p + spt[1])/h->np; |
951 |
xd = tcos(phi) * zd; |
952 |
yd = tsin(phi) * zd; |
953 |
zd = sqrt(1.0 - zd*zd); |
954 |
for (i = 0; i < 3; i++) |
955 |
ar.rdir[i] = xd*h->ux[i] + |
956 |
yd*h->uy[i] + |
957 |
zd*h->uz[i]; |
958 |
checknorm(ar.rdir); |
959 |
dimlist[ndims++] = dp->t*h->np + dp->p + 90171; |
960 |
rayvalue(&ar); |
961 |
ndims--; |
962 |
multcolor(ar.rcol, ar.rcoef); /* apply coefficient */ |
963 |
addcolor(dp->v, ar.rcol); |
964 |
/* use rt to improve gradient calc */ |
965 |
if (ar.rt > FTINY && ar.rt < FHUGE) |
966 |
dp->r += 1.0/ar.rt; |
967 |
/* (re)initialize error */ |
968 |
if (dp->n++) { |
969 |
b2 = bright(dp->v)/dp->n - bright(ar.rcol); |
970 |
b2 = b2*b2 + dp->k*((dp->n-1)*(dp->n-1)); |
971 |
dp->k = b2/(dp->n*dp->n); |
972 |
} else |
973 |
dp->k = 0.0; |
974 |
return(0); |
975 |
} |
976 |
|
977 |
|
978 |
static int |
979 |
ambcmp( /* decreasing order */ |
980 |
const void *p1, |
981 |
const void *p2 |
982 |
) |
983 |
{ |
984 |
const AMBSAMP *d1 = (const AMBSAMP *)p1; |
985 |
const AMBSAMP *d2 = (const AMBSAMP *)p2; |
986 |
|
987 |
if (d1->k < d2->k) |
988 |
return(1); |
989 |
if (d1->k > d2->k) |
990 |
return(-1); |
991 |
return(0); |
992 |
} |
993 |
|
994 |
|
995 |
static int |
996 |
ambnorm( /* standard order */ |
997 |
const void *p1, |
998 |
const void *p2 |
999 |
) |
1000 |
{ |
1001 |
const AMBSAMP *d1 = (const AMBSAMP *)p1; |
1002 |
const AMBSAMP *d2 = (const AMBSAMP *)p2; |
1003 |
int c; |
1004 |
|
1005 |
if ( (c = d1->t - d2->t) ) |
1006 |
return(c); |
1007 |
return(d1->p - d2->p); |
1008 |
} |
1009 |
|
1010 |
|
1011 |
double |
1012 |
doambient( /* compute ambient component */ |
1013 |
COLOR rcol, |
1014 |
RAY *r, |
1015 |
double wt, |
1016 |
FVECT pg, |
1017 |
FVECT dg |
1018 |
) |
1019 |
{ |
1020 |
double b, d=0; |
1021 |
AMBHEMI hemi; |
1022 |
AMBSAMP *div; |
1023 |
AMBSAMP dnew; |
1024 |
double acol[3]; |
1025 |
AMBSAMP *dp; |
1026 |
double arad; |
1027 |
int divcnt; |
1028 |
int i, j; |
1029 |
/* initialize hemisphere */ |
1030 |
inithemi(&hemi, rcol, r, wt); |
1031 |
divcnt = hemi.nt * hemi.np; |
1032 |
/* initialize */ |
1033 |
if (pg != NULL) |
1034 |
pg[0] = pg[1] = pg[2] = 0.0; |
1035 |
if (dg != NULL) |
1036 |
dg[0] = dg[1] = dg[2] = 0.0; |
1037 |
setcolor(rcol, 0.0, 0.0, 0.0); |
1038 |
if (divcnt == 0) |
1039 |
return(0.0); |
1040 |
/* allocate super-samples */ |
1041 |
if (hemi.ns > 0 || pg != NULL || dg != NULL) { |
1042 |
div = (AMBSAMP *)malloc(divcnt*sizeof(AMBSAMP)); |
1043 |
if (div == NULL) |
1044 |
error(SYSTEM, "out of memory in doambient"); |
1045 |
} else |
1046 |
div = NULL; |
1047 |
/* sample the divisions */ |
1048 |
arad = 0.0; |
1049 |
acol[0] = acol[1] = acol[2] = 0.0; |
1050 |
if ((dp = div) == NULL) |
1051 |
dp = &dnew; |
1052 |
divcnt = 0; |
1053 |
for (i = 0; i < hemi.nt; i++) |
1054 |
for (j = 0; j < hemi.np; j++) { |
1055 |
dp->t = i; dp->p = j; |
1056 |
setcolor(dp->v, 0.0, 0.0, 0.0); |
1057 |
dp->r = 0.0; |
1058 |
dp->n = 0; |
1059 |
if (divsample(dp, &hemi, r) < 0) { |
1060 |
if (div != NULL) |
1061 |
dp++; |
1062 |
continue; |
1063 |
} |
1064 |
arad += dp->r; |
1065 |
divcnt++; |
1066 |
if (div != NULL) |
1067 |
dp++; |
1068 |
else |
1069 |
addcolor(acol, dp->v); |
1070 |
} |
1071 |
if (!divcnt) { |
1072 |
if (div != NULL) |
1073 |
free((void *)div); |
1074 |
return(0.0); /* no samples taken */ |
1075 |
} |
1076 |
if (divcnt < hemi.nt*hemi.np) { |
1077 |
pg = dg = NULL; /* incomplete sampling */ |
1078 |
hemi.ns = 0; |
1079 |
} else if (arad > FTINY && divcnt/arad < minarad) { |
1080 |
hemi.ns = 0; /* close enough */ |
1081 |
} else if (hemi.ns > 0) { /* else perform super-sampling? */ |
1082 |
comperrs(div, &hemi); /* compute errors */ |
1083 |
qsort(div, divcnt, sizeof(AMBSAMP), ambcmp); /* sort divs */ |
1084 |
/* super-sample */ |
1085 |
for (i = hemi.ns; i > 0; i--) { |
1086 |
dnew = *div; |
1087 |
if (divsample(&dnew, &hemi, r) < 0) { |
1088 |
dp++; |
1089 |
continue; |
1090 |
} |
1091 |
dp = div; /* reinsert */ |
1092 |
j = divcnt < i ? divcnt : i; |
1093 |
while (--j > 0 && dnew.k < dp[1].k) { |
1094 |
*dp = *(dp+1); |
1095 |
dp++; |
1096 |
} |
1097 |
*dp = dnew; |
1098 |
} |
1099 |
if (pg != NULL || dg != NULL) /* restore order */ |
1100 |
qsort(div, divcnt, sizeof(AMBSAMP), ambnorm); |
1101 |
} |
1102 |
/* compute returned values */ |
1103 |
if (div != NULL) { |
1104 |
arad = 0.0; /* note: divcnt may be < nt*np */ |
1105 |
for (i = hemi.nt*hemi.np, dp = div; i-- > 0; dp++) { |
1106 |
arad += dp->r; |
1107 |
if (dp->n > 1) { |
1108 |
b = 1.0/dp->n; |
1109 |
scalecolor(dp->v, b); |
1110 |
dp->r *= b; |
1111 |
dp->n = 1; |
1112 |
} |
1113 |
addcolor(acol, dp->v); |
1114 |
} |
1115 |
b = bright(acol); |
1116 |
if (b > FTINY) { |
1117 |
b = 1.0/b; /* compute & normalize gradient(s) */ |
1118 |
if (pg != NULL) { |
1119 |
posgradient(pg, div, &hemi); |
1120 |
for (i = 0; i < 3; i++) |
1121 |
pg[i] *= b; |
1122 |
} |
1123 |
if (dg != NULL) { |
1124 |
dirgradient(dg, div, &hemi); |
1125 |
for (i = 0; i < 3; i++) |
1126 |
dg[i] *= b; |
1127 |
} |
1128 |
} |
1129 |
free((void *)div); |
1130 |
} |
1131 |
copycolor(rcol, acol); |
1132 |
if (arad <= FTINY) |
1133 |
arad = maxarad; |
1134 |
else |
1135 |
arad = (divcnt+hemi.ns)/arad; |
1136 |
if (pg != NULL) { /* reduce radius if gradient large */ |
1137 |
d = DOT(pg,pg); |
1138 |
if (d*arad*arad > 1.0) |
1139 |
arad = 1.0/sqrt(d); |
1140 |
} |
1141 |
if (arad < minarad) { |
1142 |
arad = minarad; |
1143 |
if (pg != NULL && d*arad*arad > 1.0) { /* cap gradient */ |
1144 |
d = 1.0/arad/sqrt(d); |
1145 |
for (i = 0; i < 3; i++) |
1146 |
pg[i] *= d; |
1147 |
} |
1148 |
} |
1149 |
if ((arad /= sqrt(wt)) > maxarad) |
1150 |
arad = maxarad; |
1151 |
return(arad); |
1152 |
} |
1153 |
|
1154 |
|
1155 |
void |
1156 |
comperrs( /* compute initial error estimates */ |
1157 |
AMBSAMP *da, /* assumes standard ordering */ |
1158 |
AMBHEMI *hp |
1159 |
) |
1160 |
{ |
1161 |
double b, b2; |
1162 |
int i, j; |
1163 |
AMBSAMP *dp; |
1164 |
/* sum differences from neighbors */ |
1165 |
dp = da; |
1166 |
for (i = 0; i < hp->nt; i++) |
1167 |
for (j = 0; j < hp->np; j++) { |
1168 |
#ifdef DEBUG |
1169 |
if (dp->t != i || dp->p != j) |
1170 |
error(CONSISTENCY, |
1171 |
"division order in comperrs"); |
1172 |
#endif |
1173 |
b = bright(dp[0].v); |
1174 |
if (i > 0) { /* from above */ |
1175 |
b2 = bright(dp[-hp->np].v) - b; |
1176 |
b2 *= b2 * 0.25; |
1177 |
dp[0].k += b2; |
1178 |
dp[-hp->np].k += b2; |
1179 |
} |
1180 |
if (j > 0) { /* from behind */ |
1181 |
b2 = bright(dp[-1].v) - b; |
1182 |
b2 *= b2 * 0.25; |
1183 |
dp[0].k += b2; |
1184 |
dp[-1].k += b2; |
1185 |
} else { /* around */ |
1186 |
b2 = bright(dp[hp->np-1].v) - b; |
1187 |
b2 *= b2 * 0.25; |
1188 |
dp[0].k += b2; |
1189 |
dp[hp->np-1].k += b2; |
1190 |
} |
1191 |
dp++; |
1192 |
} |
1193 |
/* divide by number of neighbors */ |
1194 |
dp = da; |
1195 |
for (j = 0; j < hp->np; j++) /* top row */ |
1196 |
(dp++)->k *= 1.0/3.0; |
1197 |
if (hp->nt < 2) |
1198 |
return; |
1199 |
for (i = 1; i < hp->nt-1; i++) /* central region */ |
1200 |
for (j = 0; j < hp->np; j++) |
1201 |
(dp++)->k *= 0.25; |
1202 |
for (j = 0; j < hp->np; j++) /* bottom row */ |
1203 |
(dp++)->k *= 1.0/3.0; |
1204 |
} |
1205 |
|
1206 |
|
1207 |
void |
1208 |
posgradient( /* compute position gradient */ |
1209 |
FVECT gv, |
1210 |
AMBSAMP *da, /* assumes standard ordering */ |
1211 |
AMBHEMI *hp |
1212 |
) |
1213 |
{ |
1214 |
int i, j; |
1215 |
double nextsine, lastsine, b, d; |
1216 |
double mag0, mag1; |
1217 |
double phi, cosp, sinp, xd, yd; |
1218 |
AMBSAMP *dp; |
1219 |
|
1220 |
xd = yd = 0.0; |
1221 |
for (j = 0; j < hp->np; j++) { |
1222 |
dp = da + j; |
1223 |
mag0 = mag1 = 0.0; |
1224 |
lastsine = 0.0; |
1225 |
for (i = 0; i < hp->nt; i++) { |
1226 |
#ifdef DEBUG |
1227 |
if (dp->t != i || dp->p != j) |
1228 |
error(CONSISTENCY, |
1229 |
"division order in posgradient"); |
1230 |
#endif |
1231 |
b = bright(dp->v); |
1232 |
if (i > 0) { |
1233 |
d = dp[-hp->np].r; |
1234 |
if (dp[0].r > d) d = dp[0].r; |
1235 |
/* sin(t)*cos(t)^2 */ |
1236 |
d *= lastsine * (1.0 - (double)i/hp->nt); |
1237 |
mag0 += d*(b - bright(dp[-hp->np].v)); |
1238 |
} |
1239 |
nextsine = sqrt((double)(i+1)/hp->nt); |
1240 |
if (j > 0) { |
1241 |
d = dp[-1].r; |
1242 |
if (dp[0].r > d) d = dp[0].r; |
1243 |
mag1 += d * (nextsine - lastsine) * |
1244 |
(b - bright(dp[-1].v)); |
1245 |
} else { |
1246 |
d = dp[hp->np-1].r; |
1247 |
if (dp[0].r > d) d = dp[0].r; |
1248 |
mag1 += d * (nextsine - lastsine) * |
1249 |
(b - bright(dp[hp->np-1].v)); |
1250 |
} |
1251 |
dp += hp->np; |
1252 |
lastsine = nextsine; |
1253 |
} |
1254 |
mag0 *= 2.0*PI / hp->np; |
1255 |
phi = 2.0*PI * (double)j/hp->np; |
1256 |
cosp = tcos(phi); sinp = tsin(phi); |
1257 |
xd += mag0*cosp - mag1*sinp; |
1258 |
yd += mag0*sinp + mag1*cosp; |
1259 |
} |
1260 |
for (i = 0; i < 3; i++) |
1261 |
gv[i] = (xd*hp->ux[i] + yd*hp->uy[i])*(hp->nt*hp->np)/PI; |
1262 |
} |
1263 |
|
1264 |
|
1265 |
void |
1266 |
dirgradient( /* compute direction gradient */ |
1267 |
FVECT gv, |
1268 |
AMBSAMP *da, /* assumes standard ordering */ |
1269 |
AMBHEMI *hp |
1270 |
) |
1271 |
{ |
1272 |
int i, j; |
1273 |
double mag; |
1274 |
double phi, xd, yd; |
1275 |
AMBSAMP *dp; |
1276 |
|
1277 |
xd = yd = 0.0; |
1278 |
for (j = 0; j < hp->np; j++) { |
1279 |
dp = da + j; |
1280 |
mag = 0.0; |
1281 |
for (i = 0; i < hp->nt; i++) { |
1282 |
#ifdef DEBUG |
1283 |
if (dp->t != i || dp->p != j) |
1284 |
error(CONSISTENCY, |
1285 |
"division order in dirgradient"); |
1286 |
#endif |
1287 |
/* tan(t) */ |
1288 |
mag += bright(dp->v)/sqrt(hp->nt/(i+.5) - 1.0); |
1289 |
dp += hp->np; |
1290 |
} |
1291 |
phi = 2.0*PI * (j+.5)/hp->np + PI/2.0; |
1292 |
xd += mag * tcos(phi); |
1293 |
yd += mag * tsin(phi); |
1294 |
} |
1295 |
for (i = 0; i < 3; i++) |
1296 |
gv[i] = xd*hp->ux[i] + yd*hp->uy[i]; |
1297 |
} |
1298 |
|
1299 |
#endif /* ! NEWAMB */ |