| 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 |
|
* Declarations of external symbols in ambient.h |
| 12 |
|
*/ |
| 13 |
|
|
| 23 |
|
|
| 24 |
|
typedef struct { |
| 25 |
|
RAY *rp; /* originating ray sample */ |
| 26 |
< |
FVECT ux, uy; /* tangent axis directions */ |
| 26 |
> |
FVECT ux, uy; /* tangent axis unit vectors */ |
| 27 |
|
int ns; /* number of samples per axis */ |
| 28 |
|
COLOR acoef; /* division contribution coefficient */ |
| 29 |
|
struct s_ambsamp { |
| 30 |
|
COLOR v; /* hemisphere sample value */ |
| 31 |
< |
float p[3]; /* intersection point */ |
| 31 |
> |
FVECT p; /* intersection point */ |
| 32 |
|
} sa[1]; /* sample array (extends struct) */ |
| 33 |
|
} AMBHEMI; /* ambient sample hemisphere */ |
| 34 |
|
|
| 35 |
< |
#define ambsamp(h,i,j) (h)->sa[(i)*(h)->ns + (j)] |
| 35 |
> |
typedef struct s_ambsamp AMBSAMP; |
| 36 |
|
|
| 37 |
+ |
#define ambsam(h,i,j) (h)->sa[(i)*(h)->ns + (j)] |
| 38 |
|
|
| 39 |
+ |
typedef struct { |
| 40 |
+ |
FVECT r_i, r_i1, e_i, rcp, rI2_eJ2; |
| 41 |
+ |
double I1, I2; |
| 42 |
+ |
} FFTRI; /* vectors and coefficients for Hessian calculation */ |
| 43 |
+ |
|
| 44 |
+ |
|
| 45 |
|
static AMBHEMI * |
| 46 |
|
inithemi( /* initialize sampling hemisphere */ |
| 47 |
|
COLOR ac, |
| 57 |
|
wt > (d = 0.8*intens(ac)*r->rweight/(ambdiv*minweight))) |
| 58 |
|
wt = d; /* avoid ray termination */ |
| 59 |
|
n = sqrt(ambdiv * wt) + 0.5; |
| 60 |
< |
i = 1 + 4*(ambacc > FTINY); /* minimum number of samples */ |
| 60 |
> |
i = 1 + 5*(ambacc > FTINY); /* minimum number of samples */ |
| 61 |
|
if (n < i) |
| 62 |
|
n = i; |
| 63 |
|
/* allocate sampling array */ |
| 64 |
< |
hp = (AMBHEMI *)malloc(sizeof(AMBHEMI) + |
| 54 |
< |
sizeof(struct s_ambsamp)*(n*n - 1)); |
| 64 |
> |
hp = (AMBHEMI *)malloc(sizeof(AMBHEMI) + sizeof(AMBSAMP)*(n*n - 1)); |
| 65 |
|
if (hp == NULL) |
| 66 |
|
return(NULL); |
| 67 |
|
hp->rp = r; |
| 70 |
|
copycolor(hp->acoef, ac); |
| 71 |
|
d = 1.0/(n*n); |
| 72 |
|
scalecolor(hp->acoef, d); |
| 73 |
< |
/* make tangent axes */ |
| 74 |
< |
hp->uy[0] = hp->uy[1] = hp->uy[2] = 0.0; |
| 75 |
< |
for (i = 0; i < 3; i++) |
| 76 |
< |
if (r->rn[i] < 0.6 && r->rn[i] > -0.6) |
| 73 |
> |
/* make tangent plane axes */ |
| 74 |
> |
hp->uy[0] = 0.5 - frandom(); |
| 75 |
> |
hp->uy[1] = 0.5 - frandom(); |
| 76 |
> |
hp->uy[2] = 0.5 - frandom(); |
| 77 |
> |
for (i = 3; i--; ) |
| 78 |
> |
if ((-0.6 < r->ron[i]) & (r->ron[i] < 0.6)) |
| 79 |
|
break; |
| 80 |
< |
if (i >= 3) |
| 81 |
< |
error(CONSISTENCY, "bad ray direction in inithemi()"); |
| 80 |
> |
if (i < 0) |
| 81 |
> |
error(CONSISTENCY, "bad ray direction in inithemi"); |
| 82 |
|
hp->uy[i] = 1.0; |
| 83 |
< |
VCROSS(hp->ux, hp->uy, r->rn); |
| 83 |
> |
VCROSS(hp->ux, hp->uy, r->ron); |
| 84 |
|
normalize(hp->ux); |
| 85 |
< |
VCROSS(hp->uy, r->rn, hp->ux); |
| 85 |
> |
VCROSS(hp->uy, r->ron, hp->ux); |
| 86 |
|
/* we're ready to sample */ |
| 87 |
|
return(hp); |
| 88 |
|
} |
| 89 |
|
|
| 90 |
|
|
| 91 |
+ |
/* Sample ambient division and apply weighting coefficient */ |
| 92 |
|
static int |
| 93 |
< |
ambsample( /* sample an ambient direction */ |
| 81 |
< |
AMBHEMI *hp, |
| 82 |
< |
int i, |
| 83 |
< |
int j, |
| 84 |
< |
) |
| 93 |
> |
getambsamp(RAY *arp, AMBHEMI *hp, int i, int j, int n) |
| 94 |
|
{ |
| 95 |
< |
struct s_ambsamp *ap = &ambsamp(hp,i,j); |
| 96 |
< |
RAY ar; |
| 88 |
< |
int hlist[3]; |
| 89 |
< |
double spt[2], dz; |
| 90 |
< |
int ii; |
| 95 |
> |
int hlist[3], ii; |
| 96 |
> |
double spt[2], zd; |
| 97 |
|
/* ambient coefficient for weight */ |
| 98 |
|
if (ambacc > FTINY) |
| 99 |
< |
setcolor(ar.rcoef, AVGREFL, AVGREFL, AVGREFL); |
| 99 |
> |
setcolor(arp->rcoef, AVGREFL, AVGREFL, AVGREFL); |
| 100 |
|
else |
| 101 |
< |
copycolor(ar.rcoef, hp->acoef); |
| 102 |
< |
if (rayorigin(&ar, AMBIENT, hp->rp, ar.rcoef) < 0) { |
| 103 |
< |
setcolor(ap->v, 0., 0., 0.); |
| 98 |
< |
ap->r = 0.; |
| 99 |
< |
return(0); /* no sample taken */ |
| 100 |
< |
} |
| 101 |
> |
copycolor(arp->rcoef, hp->acoef); |
| 102 |
> |
if (rayorigin(arp, AMBIENT, hp->rp, arp->rcoef) < 0) |
| 103 |
> |
return(0); |
| 104 |
|
if (ambacc > FTINY) { |
| 105 |
< |
multcolor(ar.rcoef, hp->acoef); |
| 106 |
< |
scalecolor(ar.rcoef, 1./AVGREFL); |
| 105 |
> |
multcolor(arp->rcoef, hp->acoef); |
| 106 |
> |
scalecolor(arp->rcoef, 1./AVGREFL); |
| 107 |
|
} |
| 108 |
< |
/* generate hemispherical sample */ |
| 109 |
< |
SDsquare2disk(spt, (i+frandom())/hp->ns, (j+frandom())/hp->ns); |
| 108 |
> |
hlist[0] = hp->rp->rno; |
| 109 |
> |
hlist[1] = i; |
| 110 |
> |
hlist[2] = j; |
| 111 |
> |
multisamp(spt, 2, urand(ilhash(hlist,3)+n)); |
| 112 |
> |
if (!n) { /* avoid border samples for n==0 */ |
| 113 |
> |
if ((spt[0] < 0.1) | (spt[0] > 0.9)) |
| 114 |
> |
spt[0] = 0.1 + 0.8*frandom(); |
| 115 |
> |
if ((spt[1] < 0.1) | (spt[1] > 0.9)) |
| 116 |
> |
spt[1] = 0.1 + 0.8*frandom(); |
| 117 |
> |
} |
| 118 |
> |
SDsquare2disk(spt, (i+spt[0])/hp->ns, (j+spt[1])/hp->ns); |
| 119 |
|
zd = sqrt(1. - spt[0]*spt[0] - spt[1]*spt[1]); |
| 120 |
|
for (ii = 3; ii--; ) |
| 121 |
< |
ar.rdir[ii] = spt[0]*hp->ux[ii] + |
| 121 |
> |
arp->rdir[ii] = spt[0]*hp->ux[ii] + |
| 122 |
|
spt[1]*hp->uy[ii] + |
| 123 |
|
zd*hp->rp->ron[ii]; |
| 124 |
< |
checknorm(ar.rdir); |
| 124 |
> |
checknorm(arp->rdir); |
| 125 |
|
dimlist[ndims++] = i*hp->ns + j + 90171; |
| 126 |
< |
rayvalue(&ar); /* evaluate ray */ |
| 127 |
< |
ndims--; |
| 128 |
< |
multcolor(ar.rcol, ar.rcoef); /* apply coefficient */ |
| 117 |
< |
copycolor(ap->v, ar.rcol); |
| 118 |
< |
if (ar.rt > 20.0*maxarad) /* limit vertex distance */ |
| 119 |
< |
ar.rt = 20.0*maxarad; |
| 120 |
< |
VSUM(ap->p, ar.rorg, ar.rdir, ar.rt); |
| 126 |
> |
rayvalue(arp); /* evaluate ray */ |
| 127 |
> |
ndims--; /* apply coefficient */ |
| 128 |
> |
multcolor(arp->rcol, arp->rcoef); |
| 129 |
|
return(1); |
| 130 |
|
} |
| 131 |
|
|
| 132 |
|
|
| 133 |
+ |
static AMBSAMP * |
| 134 |
+ |
ambsample( /* initial ambient division sample */ |
| 135 |
+ |
AMBHEMI *hp, |
| 136 |
+ |
int i, |
| 137 |
+ |
int j |
| 138 |
+ |
) |
| 139 |
+ |
{ |
| 140 |
+ |
AMBSAMP *ap = &ambsam(hp,i,j); |
| 141 |
+ |
RAY ar; |
| 142 |
+ |
/* generate hemispherical sample */ |
| 143 |
+ |
if (!getambsamp(&ar, hp, i, j, 0)) |
| 144 |
+ |
goto badsample; |
| 145 |
+ |
/* limit vertex distance */ |
| 146 |
+ |
if (ar.rt > 10.0*thescene.cusize) |
| 147 |
+ |
ar.rt = 10.0*thescene.cusize; |
| 148 |
+ |
else if (ar.rt <= FTINY) /* should never happen! */ |
| 149 |
+ |
goto badsample; |
| 150 |
+ |
VSUM(ap->p, ar.rorg, ar.rdir, ar.rt); |
| 151 |
+ |
copycolor(ap->v, ar.rcol); |
| 152 |
+ |
return(ap); |
| 153 |
+ |
badsample: |
| 154 |
+ |
setcolor(ap->v, 0., 0., 0.); |
| 155 |
+ |
VCOPY(ap->p, hp->rp->rop); |
| 156 |
+ |
return(NULL); |
| 157 |
+ |
} |
| 158 |
+ |
|
| 159 |
+ |
|
| 160 |
+ |
/* Estimate errors based on ambient division differences */ |
| 161 |
+ |
static float * |
| 162 |
+ |
getambdiffs(AMBHEMI *hp) |
| 163 |
+ |
{ |
| 164 |
+ |
float *earr = calloc(hp->ns*hp->ns, sizeof(float)); |
| 165 |
+ |
float *ep; |
| 166 |
+ |
AMBSAMP *ap; |
| 167 |
+ |
double b, d2; |
| 168 |
+ |
int i, j; |
| 169 |
+ |
|
| 170 |
+ |
if (earr == NULL) /* out of memory? */ |
| 171 |
+ |
return(NULL); |
| 172 |
+ |
/* compute squared neighbor diffs */ |
| 173 |
+ |
for (ap = hp->sa, ep = earr, i = 0; i < hp->ns; i++) |
| 174 |
+ |
for (j = 0; j < hp->ns; j++, ap++, ep++) { |
| 175 |
+ |
b = bright(ap[0].v); |
| 176 |
+ |
if (i) { /* from above */ |
| 177 |
+ |
d2 = b - bright(ap[-hp->ns].v); |
| 178 |
+ |
d2 *= d2; |
| 179 |
+ |
ep[0] += d2; |
| 180 |
+ |
ep[-hp->ns] += d2; |
| 181 |
+ |
} |
| 182 |
+ |
if (j) { /* from behind */ |
| 183 |
+ |
d2 = b - bright(ap[-1].v); |
| 184 |
+ |
d2 *= d2; |
| 185 |
+ |
ep[0] += d2; |
| 186 |
+ |
ep[-1] += d2; |
| 187 |
+ |
} |
| 188 |
+ |
} |
| 189 |
+ |
/* correct for number of neighbors */ |
| 190 |
+ |
earr[0] *= 2.f; |
| 191 |
+ |
earr[hp->ns-1] *= 2.f; |
| 192 |
+ |
earr[(hp->ns-1)*hp->ns] *= 2.f; |
| 193 |
+ |
earr[(hp->ns-1)*hp->ns + hp->ns-1] *= 2.f; |
| 194 |
+ |
for (i = 1; i < hp->ns-1; i++) { |
| 195 |
+ |
earr[i*hp->ns] *= 4./3.; |
| 196 |
+ |
earr[i*hp->ns + hp->ns-1] *= 4./3.; |
| 197 |
+ |
} |
| 198 |
+ |
for (j = 1; j < hp->ns-1; j++) { |
| 199 |
+ |
earr[j] *= 4./3.; |
| 200 |
+ |
earr[(hp->ns-1)*hp->ns + j] *= 4./3.; |
| 201 |
+ |
} |
| 202 |
+ |
return(earr); |
| 203 |
+ |
} |
| 204 |
+ |
|
| 205 |
+ |
|
| 206 |
+ |
/* Perform super-sampling on hemisphere (introduces bias) */ |
| 207 |
|
static void |
| 208 |
+ |
ambsupersamp(double acol[3], AMBHEMI *hp, int cnt) |
| 209 |
+ |
{ |
| 210 |
+ |
float *earr = getambdiffs(hp); |
| 211 |
+ |
double e2sum = 0; |
| 212 |
+ |
AMBSAMP *ap; |
| 213 |
+ |
RAY ar; |
| 214 |
+ |
COLOR asum; |
| 215 |
+ |
float *ep; |
| 216 |
+ |
int i, j, n; |
| 217 |
+ |
|
| 218 |
+ |
if (earr == NULL) /* just skip calc. if no memory */ |
| 219 |
+ |
return; |
| 220 |
+ |
/* add up estimated variances */ |
| 221 |
+ |
for (ep = earr + hp->ns*hp->ns; ep-- > earr; ) |
| 222 |
+ |
e2sum += *ep; |
| 223 |
+ |
ep = earr; /* perform super-sampling */ |
| 224 |
+ |
for (ap = hp->sa, i = 0; i < hp->ns; i++) |
| 225 |
+ |
for (j = 0; j < hp->ns; j++, ap++) { |
| 226 |
+ |
int nss = *ep/e2sum*cnt + frandom(); |
| 227 |
+ |
setcolor(asum, 0., 0., 0.); |
| 228 |
+ |
for (n = 1; n <= nss; n++) { |
| 229 |
+ |
if (!getambsamp(&ar, hp, i, j, n)) { |
| 230 |
+ |
nss = n-1; |
| 231 |
+ |
break; |
| 232 |
+ |
} |
| 233 |
+ |
addcolor(asum, ar.rcol); |
| 234 |
+ |
} |
| 235 |
+ |
if (nss) { /* update returned ambient value */ |
| 236 |
+ |
const double ssf = 1./(nss + 1); |
| 237 |
+ |
for (n = 3; n--; ) |
| 238 |
+ |
acol[n] += ssf*colval(asum,n) + |
| 239 |
+ |
(ssf - 1.)*colval(ap->v,n); |
| 240 |
+ |
} |
| 241 |
+ |
e2sum -= *ep++; /* update remainders */ |
| 242 |
+ |
cnt -= nss; |
| 243 |
+ |
} |
| 244 |
+ |
free(earr); |
| 245 |
+ |
} |
| 246 |
+ |
|
| 247 |
+ |
|
| 248 |
+ |
/* Compute vectors and coefficients for Hessian/gradient calcs */ |
| 249 |
+ |
static void |
| 250 |
+ |
comp_fftri(FFTRI *ftp, FVECT ap0, FVECT ap1, FVECT rop) |
| 251 |
+ |
{ |
| 252 |
+ |
double rdot_cp, dot_e, dot_er, rdot_r, rdot_r1, J2; |
| 253 |
+ |
int i; |
| 254 |
+ |
|
| 255 |
+ |
VSUB(ftp->r_i, ap0, rop); |
| 256 |
+ |
VSUB(ftp->r_i1, ap1, rop); |
| 257 |
+ |
VSUB(ftp->e_i, ap1, ap0); |
| 258 |
+ |
VCROSS(ftp->rcp, ftp->r_i, ftp->r_i1); |
| 259 |
+ |
rdot_cp = 1.0/DOT(ftp->rcp,ftp->rcp); |
| 260 |
+ |
dot_e = DOT(ftp->e_i,ftp->e_i); |
| 261 |
+ |
dot_er = DOT(ftp->e_i, ftp->r_i); |
| 262 |
+ |
rdot_r = 1.0/DOT(ftp->r_i,ftp->r_i); |
| 263 |
+ |
rdot_r1 = 1.0/DOT(ftp->r_i1,ftp->r_i1); |
| 264 |
+ |
ftp->I1 = acos( DOT(ftp->r_i, ftp->r_i1) * sqrt(rdot_r*rdot_r1) ) * |
| 265 |
+ |
sqrt( rdot_cp ); |
| 266 |
+ |
ftp->I2 = ( DOT(ftp->e_i, ftp->r_i1)*rdot_r1 - dot_er*rdot_r + |
| 267 |
+ |
dot_e*ftp->I1 )*0.5*rdot_cp; |
| 268 |
+ |
J2 = ( 0.5*(rdot_r - rdot_r1) - dot_er*ftp->I2 ) / dot_e; |
| 269 |
+ |
for (i = 3; i--; ) |
| 270 |
+ |
ftp->rI2_eJ2[i] = ftp->I2*ftp->r_i[i] + J2*ftp->e_i[i]; |
| 271 |
+ |
} |
| 272 |
+ |
|
| 273 |
+ |
|
| 274 |
+ |
/* Compose 3x3 matrix from two vectors */ |
| 275 |
+ |
static void |
| 276 |
+ |
compose_matrix(FVECT mat[3], FVECT va, FVECT vb) |
| 277 |
+ |
{ |
| 278 |
+ |
mat[0][0] = 2.0*va[0]*vb[0]; |
| 279 |
+ |
mat[1][1] = 2.0*va[1]*vb[1]; |
| 280 |
+ |
mat[2][2] = 2.0*va[2]*vb[2]; |
| 281 |
+ |
mat[0][1] = mat[1][0] = va[0]*vb[1] + va[1]*vb[0]; |
| 282 |
+ |
mat[0][2] = mat[2][0] = va[0]*vb[2] + va[2]*vb[0]; |
| 283 |
+ |
mat[1][2] = mat[2][1] = va[1]*vb[2] + va[2]*vb[1]; |
| 284 |
+ |
} |
| 285 |
+ |
|
| 286 |
+ |
|
| 287 |
+ |
/* Compute partial 3x3 Hessian matrix for edge */ |
| 288 |
+ |
static void |
| 289 |
+ |
comp_hessian(FVECT hess[3], FFTRI *ftp, FVECT nrm) |
| 290 |
+ |
{ |
| 291 |
+ |
FVECT ncp; |
| 292 |
+ |
FVECT m1[3], m2[3], m3[3], m4[3]; |
| 293 |
+ |
double d1, d2, d3, d4; |
| 294 |
+ |
double I3, J3, K3; |
| 295 |
+ |
int i, j; |
| 296 |
+ |
/* compute intermediate coefficients */ |
| 297 |
+ |
d1 = 1.0/DOT(ftp->r_i,ftp->r_i); |
| 298 |
+ |
d2 = 1.0/DOT(ftp->r_i1,ftp->r_i1); |
| 299 |
+ |
d3 = 1.0/DOT(ftp->e_i,ftp->e_i); |
| 300 |
+ |
d4 = DOT(ftp->e_i, ftp->r_i); |
| 301 |
+ |
I3 = ( DOT(ftp->e_i, ftp->r_i1)*d2*d2 - d4*d1*d1 + 3.0/d3*ftp->I2 ) |
| 302 |
+ |
/ ( 4.0*DOT(ftp->rcp,ftp->rcp) ); |
| 303 |
+ |
J3 = 0.25*d3*(d1*d1 - d2*d2) - d4*d3*I3; |
| 304 |
+ |
K3 = d3*(ftp->I2 - I3/d1 - 2.0*d4*J3); |
| 305 |
+ |
/* intermediate matrices */ |
| 306 |
+ |
VCROSS(ncp, nrm, ftp->e_i); |
| 307 |
+ |
compose_matrix(m1, ncp, ftp->rI2_eJ2); |
| 308 |
+ |
compose_matrix(m2, ftp->r_i, ftp->r_i); |
| 309 |
+ |
compose_matrix(m3, ftp->e_i, ftp->e_i); |
| 310 |
+ |
compose_matrix(m4, ftp->r_i, ftp->e_i); |
| 311 |
+ |
d1 = DOT(nrm, ftp->rcp); |
| 312 |
+ |
d2 = -d1*ftp->I2; |
| 313 |
+ |
d1 *= 2.0; |
| 314 |
+ |
for (i = 3; i--; ) /* final matrix sum */ |
| 315 |
+ |
for (j = 3; j--; ) { |
| 316 |
+ |
hess[i][j] = m1[i][j] + d1*( I3*m2[i][j] + K3*m3[i][j] + |
| 317 |
+ |
2.0*J3*m4[i][j] ); |
| 318 |
+ |
hess[i][j] += d2*(i==j); |
| 319 |
+ |
hess[i][j] *= 1.0/PI; |
| 320 |
+ |
} |
| 321 |
+ |
} |
| 322 |
+ |
|
| 323 |
+ |
|
| 324 |
+ |
/* Reverse hessian calculation result for edge in other direction */ |
| 325 |
+ |
static void |
| 326 |
+ |
rev_hessian(FVECT hess[3]) |
| 327 |
+ |
{ |
| 328 |
+ |
int i; |
| 329 |
+ |
|
| 330 |
+ |
for (i = 3; i--; ) { |
| 331 |
+ |
hess[i][0] = -hess[i][0]; |
| 332 |
+ |
hess[i][1] = -hess[i][1]; |
| 333 |
+ |
hess[i][2] = -hess[i][2]; |
| 334 |
+ |
} |
| 335 |
+ |
} |
| 336 |
+ |
|
| 337 |
+ |
|
| 338 |
+ |
/* Add to radiometric Hessian from the given triangle */ |
| 339 |
+ |
static void |
| 340 |
+ |
add2hessian(FVECT hess[3], FVECT ehess1[3], |
| 341 |
+ |
FVECT ehess2[3], FVECT ehess3[3], COLORV v) |
| 342 |
+ |
{ |
| 343 |
+ |
int i, j; |
| 344 |
+ |
|
| 345 |
+ |
for (i = 3; i--; ) |
| 346 |
+ |
for (j = 3; j--; ) |
| 347 |
+ |
hess[i][j] += v*( ehess1[i][j] + ehess2[i][j] + ehess3[i][j] ); |
| 348 |
+ |
} |
| 349 |
+ |
|
| 350 |
+ |
|
| 351 |
+ |
/* Compute partial displacement form factor gradient for edge */ |
| 352 |
+ |
static void |
| 353 |
+ |
comp_gradient(FVECT grad, FFTRI *ftp, FVECT nrm) |
| 354 |
+ |
{ |
| 355 |
+ |
FVECT ncp; |
| 356 |
+ |
double f1; |
| 357 |
+ |
int i; |
| 358 |
+ |
|
| 359 |
+ |
f1 = 2.0*DOT(nrm, ftp->rcp); |
| 360 |
+ |
VCROSS(ncp, nrm, ftp->e_i); |
| 361 |
+ |
for (i = 3; i--; ) |
| 362 |
+ |
grad[i] = (-0.5/PI)*( ftp->I1*ncp[i] + f1*ftp->rI2_eJ2[i] ); |
| 363 |
+ |
} |
| 364 |
+ |
|
| 365 |
+ |
|
| 366 |
+ |
/* Reverse gradient calculation result for edge in other direction */ |
| 367 |
+ |
static void |
| 368 |
+ |
rev_gradient(FVECT grad) |
| 369 |
+ |
{ |
| 370 |
+ |
grad[0] = -grad[0]; |
| 371 |
+ |
grad[1] = -grad[1]; |
| 372 |
+ |
grad[2] = -grad[2]; |
| 373 |
+ |
} |
| 374 |
+ |
|
| 375 |
+ |
|
| 376 |
+ |
/* Add to displacement gradient from the given triangle */ |
| 377 |
+ |
static void |
| 378 |
+ |
add2gradient(FVECT grad, FVECT egrad1, FVECT egrad2, FVECT egrad3, COLORV v) |
| 379 |
+ |
{ |
| 380 |
+ |
int i; |
| 381 |
+ |
|
| 382 |
+ |
for (i = 3; i--; ) |
| 383 |
+ |
grad[i] += v*( egrad1[i] + egrad2[i] + egrad3[i] ); |
| 384 |
+ |
} |
| 385 |
+ |
|
| 386 |
+ |
|
| 387 |
+ |
/* Return brightness of furthest ambient sample */ |
| 388 |
+ |
static COLORV |
| 389 |
+ |
back_ambval(AMBSAMP *ap1, AMBSAMP *ap2, AMBSAMP *ap3, FVECT orig) |
| 390 |
+ |
{ |
| 391 |
+ |
COLORV vback; |
| 392 |
+ |
FVECT vec; |
| 393 |
+ |
double d2, d2best; |
| 394 |
+ |
|
| 395 |
+ |
VSUB(vec, ap1->p, orig); |
| 396 |
+ |
d2best = DOT(vec,vec); |
| 397 |
+ |
vback = colval(ap1->v,CIEY); |
| 398 |
+ |
VSUB(vec, ap2->p, orig); |
| 399 |
+ |
d2 = DOT(vec,vec); |
| 400 |
+ |
if (d2 > d2best) { |
| 401 |
+ |
d2best = d2; |
| 402 |
+ |
vback = colval(ap2->v,CIEY); |
| 403 |
+ |
} |
| 404 |
+ |
VSUB(vec, ap3->p, orig); |
| 405 |
+ |
d2 = DOT(vec,vec); |
| 406 |
+ |
if (d2 > d2best) |
| 407 |
+ |
return(colval(ap3->v,CIEY)); |
| 408 |
+ |
return(vback); |
| 409 |
+ |
} |
| 410 |
+ |
|
| 411 |
+ |
|
| 412 |
+ |
/* Compute anisotropic radii and eigenvector directions */ |
| 413 |
+ |
static int |
| 414 |
+ |
eigenvectors(FVECT uv[2], float ra[2], FVECT hessian[3]) |
| 415 |
+ |
{ |
| 416 |
+ |
double hess2[2][2]; |
| 417 |
+ |
FVECT a, b; |
| 418 |
+ |
double evalue[2], slope1, xmag1; |
| 419 |
+ |
int i; |
| 420 |
+ |
/* project Hessian to sample plane */ |
| 421 |
+ |
for (i = 3; i--; ) { |
| 422 |
+ |
a[i] = DOT(hessian[i], uv[0]); |
| 423 |
+ |
b[i] = DOT(hessian[i], uv[1]); |
| 424 |
+ |
} |
| 425 |
+ |
hess2[0][0] = DOT(uv[0], a); |
| 426 |
+ |
hess2[0][1] = DOT(uv[0], b); |
| 427 |
+ |
hess2[1][0] = DOT(uv[1], a); |
| 428 |
+ |
hess2[1][1] = DOT(uv[1], b); |
| 429 |
+ |
/* compute eigenvalue(s) */ |
| 430 |
+ |
i = quadratic(evalue, 1.0, -hess2[0][0]-hess2[1][1], |
| 431 |
+ |
hess2[0][0]*hess2[1][1]-hess2[0][1]*hess2[1][0]); |
| 432 |
+ |
if (i == 1) /* double-root (circle) */ |
| 433 |
+ |
evalue[1] = evalue[0]; |
| 434 |
+ |
if (!i || ((evalue[0] = fabs(evalue[0])) <= FTINY*FTINY) | |
| 435 |
+ |
((evalue[1] = fabs(evalue[1])) <= FTINY*FTINY) ) |
| 436 |
+ |
error(INTERNAL, "bad eigenvalue calculation"); |
| 437 |
+ |
|
| 438 |
+ |
if (evalue[0] > evalue[1]) { |
| 439 |
+ |
ra[0] = sqrt(sqrt(4.0/evalue[0])); |
| 440 |
+ |
ra[1] = sqrt(sqrt(4.0/evalue[1])); |
| 441 |
+ |
slope1 = evalue[1]; |
| 442 |
+ |
} else { |
| 443 |
+ |
ra[0] = sqrt(sqrt(4.0/evalue[1])); |
| 444 |
+ |
ra[1] = sqrt(sqrt(4.0/evalue[0])); |
| 445 |
+ |
slope1 = evalue[0]; |
| 446 |
+ |
} |
| 447 |
+ |
/* compute unit eigenvectors */ |
| 448 |
+ |
if (fabs(hess2[0][1]) <= FTINY) |
| 449 |
+ |
return; /* uv OK as is */ |
| 450 |
+ |
slope1 = (slope1 - hess2[0][0]) / hess2[0][1]; |
| 451 |
+ |
xmag1 = sqrt(1.0/(1.0 + slope1*slope1)); |
| 452 |
+ |
for (i = 3; i--; ) { |
| 453 |
+ |
b[i] = xmag1*uv[0][i] + slope1*xmag1*uv[1][i]; |
| 454 |
+ |
a[i] = slope1*xmag1*uv[0][i] - xmag1*uv[1][i]; |
| 455 |
+ |
} |
| 456 |
+ |
VCOPY(uv[0], a); |
| 457 |
+ |
VCOPY(uv[1], b); |
| 458 |
+ |
} |
| 459 |
+ |
|
| 460 |
+ |
|
| 461 |
+ |
static void |
| 462 |
|
ambHessian( /* anisotropic radii & pos. gradient */ |
| 463 |
|
AMBHEMI *hp, |
| 464 |
|
FVECT uv[2], /* returned */ |
| 465 |
< |
float ra[2], /* returned */ |
| 466 |
< |
float pg[2] /* returned */ |
| 465 |
> |
float ra[2], /* returned (optional) */ |
| 466 |
> |
float pg[2] /* returned (optional) */ |
| 467 |
|
) |
| 468 |
|
{ |
| 469 |
< |
if (ra != NULL) { /* compute Hessian-derived radii */ |
| 470 |
< |
} else { /* else copy original tangent axes */ |
| 471 |
< |
VCOPY(uv[0], hp->ux); |
| 472 |
< |
VCOPY(uv[1], hp->uy); |
| 473 |
< |
} |
| 474 |
< |
if (pg == NULL) /* no position gradient requested? */ |
| 469 |
> |
static char memerrmsg[] = "out of memory in ambHessian()"; |
| 470 |
> |
FVECT (*hessrow)[3] = NULL; |
| 471 |
> |
FVECT *gradrow = NULL; |
| 472 |
> |
FVECT hessian[3]; |
| 473 |
> |
FVECT gradient; |
| 474 |
> |
FFTRI fftr; |
| 475 |
> |
int i, j; |
| 476 |
> |
/* be sure to assign unit vectors */ |
| 477 |
> |
VCOPY(uv[0], hp->ux); |
| 478 |
> |
VCOPY(uv[1], hp->uy); |
| 479 |
> |
/* clock-wise vertex traversal from sample POV */ |
| 480 |
> |
if (ra != NULL) { /* initialize Hessian row buffer */ |
| 481 |
> |
hessrow = (FVECT (*)[3])malloc(sizeof(FVECT)*3*(hp->ns-1)); |
| 482 |
> |
if (hessrow == NULL) |
| 483 |
> |
error(SYSTEM, memerrmsg); |
| 484 |
> |
memset(hessian, 0, sizeof(hessian)); |
| 485 |
> |
} else if (pg == NULL) /* bogus call? */ |
| 486 |
|
return; |
| 487 |
+ |
if (pg != NULL) { /* initialize form factor row buffer */ |
| 488 |
+ |
gradrow = (FVECT *)malloc(sizeof(FVECT)*(hp->ns-1)); |
| 489 |
+ |
if (gradrow == NULL) |
| 490 |
+ |
error(SYSTEM, memerrmsg); |
| 491 |
+ |
memset(gradient, 0, sizeof(gradient)); |
| 492 |
+ |
} |
| 493 |
+ |
/* compute first row of edges */ |
| 494 |
+ |
for (j = 0; j < hp->ns-1; j++) { |
| 495 |
+ |
comp_fftri(&fftr, ambsam(hp,0,j).p, |
| 496 |
+ |
ambsam(hp,0,j+1).p, hp->rp->rop); |
| 497 |
+ |
if (hessrow != NULL) |
| 498 |
+ |
comp_hessian(hessrow[j], &fftr, hp->rp->ron); |
| 499 |
+ |
if (gradrow != NULL) |
| 500 |
+ |
comp_gradient(gradrow[j], &fftr, hp->rp->ron); |
| 501 |
+ |
} |
| 502 |
+ |
/* sum each row of triangles */ |
| 503 |
+ |
for (i = 0; i < hp->ns-1; i++) { |
| 504 |
+ |
FVECT hesscol[3]; /* compute first vertical edge */ |
| 505 |
+ |
FVECT gradcol; |
| 506 |
+ |
comp_fftri(&fftr, ambsam(hp,i,0).p, |
| 507 |
+ |
ambsam(hp,i+1,0).p, hp->rp->rop); |
| 508 |
+ |
if (hessrow != NULL) |
| 509 |
+ |
comp_hessian(hesscol, &fftr, hp->rp->ron); |
| 510 |
+ |
if (gradrow != NULL) |
| 511 |
+ |
comp_gradient(gradcol, &fftr, hp->rp->ron); |
| 512 |
+ |
for (j = 0; j < hp->ns-1; j++) { |
| 513 |
+ |
FVECT hessdia[3]; /* compute triangle contributions */ |
| 514 |
+ |
FVECT graddia; |
| 515 |
+ |
COLORV backg; |
| 516 |
+ |
backg = back_ambval(&ambsam(hp,i,j), &ambsam(hp,i,j+1), |
| 517 |
+ |
&ambsam(hp,i+1,j), hp->rp->rop); |
| 518 |
+ |
/* diagonal (inner) edge */ |
| 519 |
+ |
comp_fftri(&fftr, ambsam(hp,i,j+1).p, |
| 520 |
+ |
ambsam(hp,i+1,j).p, hp->rp->rop); |
| 521 |
+ |
if (hessrow != NULL) { |
| 522 |
+ |
comp_hessian(hessdia, &fftr, hp->rp->ron); |
| 523 |
+ |
rev_hessian(hesscol); |
| 524 |
+ |
add2hessian(hessian, hessrow[j], hessdia, hesscol, backg); |
| 525 |
+ |
} |
| 526 |
+ |
if (gradrow != NULL) { |
| 527 |
+ |
comp_gradient(graddia, &fftr, hp->rp->ron); |
| 528 |
+ |
rev_gradient(gradcol); |
| 529 |
+ |
add2gradient(gradient, gradrow[j], graddia, gradcol, backg); |
| 530 |
+ |
} |
| 531 |
+ |
/* initialize edge in next row */ |
| 532 |
+ |
comp_fftri(&fftr, ambsam(hp,i+1,j+1).p, |
| 533 |
+ |
ambsam(hp,i+1,j).p, hp->rp->rop); |
| 534 |
+ |
if (hessrow != NULL) |
| 535 |
+ |
comp_hessian(hessrow[j], &fftr, hp->rp->ron); |
| 536 |
+ |
if (gradrow != NULL) |
| 537 |
+ |
comp_gradient(gradrow[j], &fftr, hp->rp->ron); |
| 538 |
+ |
/* new column edge & paired triangle */ |
| 539 |
+ |
backg = back_ambval(&ambsam(hp,i,j+1), &ambsam(hp,i+1,j+1), |
| 540 |
+ |
&ambsam(hp,i+1,j), hp->rp->rop); |
| 541 |
+ |
comp_fftri(&fftr, ambsam(hp,i,j+1).p, ambsam(hp,i+1,j+1).p, |
| 542 |
+ |
hp->rp->rop); |
| 543 |
+ |
if (hessrow != NULL) { |
| 544 |
+ |
comp_hessian(hesscol, &fftr, hp->rp->ron); |
| 545 |
+ |
rev_hessian(hessdia); |
| 546 |
+ |
add2hessian(hessian, hessrow[j], hessdia, hesscol, backg); |
| 547 |
+ |
if (i < hp->ns-2) |
| 548 |
+ |
rev_hessian(hessrow[j]); |
| 549 |
+ |
} |
| 550 |
+ |
if (gradrow != NULL) { |
| 551 |
+ |
comp_gradient(gradcol, &fftr, hp->rp->ron); |
| 552 |
+ |
rev_gradient(graddia); |
| 553 |
+ |
add2gradient(gradient, gradrow[j], graddia, gradcol, backg); |
| 554 |
+ |
if (i < hp->ns-2) |
| 555 |
+ |
rev_gradient(gradrow[j]); |
| 556 |
+ |
} |
| 557 |
+ |
} |
| 558 |
+ |
} |
| 559 |
+ |
/* release row buffers */ |
| 560 |
+ |
if (hessrow != NULL) free(hessrow); |
| 561 |
+ |
if (gradrow != NULL) free(gradrow); |
| 562 |
+ |
|
| 563 |
+ |
if (ra != NULL) /* extract eigenvectors & radii */ |
| 564 |
+ |
eigenvectors(uv, ra, hessian); |
| 565 |
+ |
if (pg != NULL) { /* tangential position gradient */ |
| 566 |
+ |
pg[0] = DOT(gradient, uv[0]); |
| 567 |
+ |
pg[1] = DOT(gradient, uv[1]); |
| 568 |
+ |
} |
| 569 |
|
} |
| 570 |
|
|
| 571 |
+ |
|
| 572 |
+ |
/* Compute direction gradient from a hemispherical sampling */ |
| 573 |
+ |
static void |
| 574 |
+ |
ambdirgrad(AMBHEMI *hp, FVECT uv[2], float dg[2]) |
| 575 |
+ |
{ |
| 576 |
+ |
AMBSAMP *ap; |
| 577 |
+ |
double dgsum[2]; |
| 578 |
+ |
int n; |
| 579 |
+ |
FVECT vd; |
| 580 |
+ |
double gfact; |
| 581 |
+ |
|
| 582 |
+ |
dgsum[0] = dgsum[1] = 0.0; /* sum values times -tan(theta) */ |
| 583 |
+ |
for (ap = hp->sa, n = hp->ns*hp->ns; n--; ap++) { |
| 584 |
+ |
/* use vector for azimuth + 90deg */ |
| 585 |
+ |
VSUB(vd, ap->p, hp->rp->rop); |
| 586 |
+ |
/* brightness over cosine factor */ |
| 587 |
+ |
gfact = colval(ap->v,CIEY) / DOT(hp->rp->ron, vd); |
| 588 |
+ |
/* sine = proj_radius/vd_length */ |
| 589 |
+ |
dgsum[0] -= DOT(uv[1], vd) * gfact; |
| 590 |
+ |
dgsum[1] += DOT(uv[0], vd) * gfact; |
| 591 |
+ |
} |
| 592 |
+ |
dg[0] = dgsum[0] / (hp->ns*hp->ns); |
| 593 |
+ |
dg[1] = dgsum[1] / (hp->ns*hp->ns); |
| 594 |
+ |
} |
| 595 |
+ |
|
| 596 |
+ |
|
| 597 |
|
int |
| 598 |
|
doambient( /* compute ambient component */ |
| 599 |
|
COLOR rcol, /* input/output color */ |
| 600 |
|
RAY *r, |
| 601 |
|
double wt, |
| 602 |
< |
FVECT uv[2], /* returned */ |
| 603 |
< |
float ra[2], /* returned */ |
| 604 |
< |
float pg[2], /* returned */ |
| 605 |
< |
float dg[2] /* returned */ |
| 602 |
> |
FVECT uv[2], /* returned (optional) */ |
| 603 |
> |
float ra[2], /* returned (optional) */ |
| 604 |
> |
float pg[2], /* returned (optional) */ |
| 605 |
> |
float dg[2] /* returned (optional) */ |
| 606 |
|
) |
| 607 |
|
{ |
| 608 |
< |
int cnt = 0; |
| 609 |
< |
FVECT my_uv[2]; |
| 610 |
< |
AMBHEMI *hp; |
| 611 |
< |
double d, acol[3]; |
| 612 |
< |
struct s_ambsamp *ap; |
| 613 |
< |
int i, j; |
| 614 |
< |
/* initialize */ |
| 615 |
< |
if ((hp = inithemi(rcol, r, wt)) == NULL) |
| 608 |
> |
AMBHEMI *hp = inithemi(rcol, r, wt); |
| 609 |
> |
int cnt = 0; |
| 610 |
> |
FVECT my_uv[2]; |
| 611 |
> |
double d, K, acol[3]; |
| 612 |
> |
AMBSAMP *ap; |
| 613 |
> |
int i, j; |
| 614 |
> |
/* check/initialize */ |
| 615 |
> |
if (hp == NULL) |
| 616 |
|
return(0); |
| 617 |
|
if (uv != NULL) |
| 618 |
|
memset(uv, 0, sizeof(FVECT)*2); |
| 624 |
|
dg[0] = dg[1] = 0.0; |
| 625 |
|
/* sample the hemisphere */ |
| 626 |
|
acol[0] = acol[1] = acol[2] = 0.0; |
| 627 |
< |
for (i = hemi.ns; i--; ) |
| 628 |
< |
for (j = hemi.ns; j--; ) |
| 629 |
< |
if (ambsample(hp, i, j)) { |
| 175 |
< |
ap = &ambsamp(hp,i,j); |
| 627 |
> |
for (i = hp->ns; i--; ) |
| 628 |
> |
for (j = hp->ns; j--; ) |
| 629 |
> |
if ((ap = ambsample(hp, i, j)) != NULL) { |
| 630 |
|
addcolor(acol, ap->v); |
| 631 |
|
++cnt; |
| 632 |
|
} |
| 635 |
|
free(hp); |
| 636 |
|
return(0); /* no valid samples */ |
| 637 |
|
} |
| 638 |
< |
d = 1.0 / cnt; /* final indirect irradiance/PI */ |
| 639 |
< |
acol[0] *= d; acol[1] *= d; acol[2] *= d; |
| 186 |
< |
copycolor(rcol, acol); |
| 187 |
< |
if (cnt < hp->ns*hp->ns || /* incomplete sampling? */ |
| 188 |
< |
(ra == NULL) & (pg == NULL) & (dg == NULL)) { |
| 638 |
> |
if (cnt < hp->ns*hp->ns) { /* incomplete sampling? */ |
| 639 |
> |
copycolor(rcol, acol); |
| 640 |
|
free(hp); |
| 641 |
+ |
return(-1); /* return value w/o Hessian */ |
| 642 |
+ |
} |
| 643 |
+ |
cnt = ambssamp*wt + 0.5; /* perform super-sampling? */ |
| 644 |
+ |
if (cnt > 0) |
| 645 |
+ |
ambsupersamp(acol, hp, cnt); |
| 646 |
+ |
copycolor(rcol, acol); /* final indirect irradiance/PI */ |
| 647 |
+ |
if ((ra == NULL) & (pg == NULL) & (dg == NULL)) { |
| 648 |
+ |
free(hp); |
| 649 |
|
return(-1); /* no radius or gradient calc. */ |
| 650 |
|
} |
| 651 |
< |
d = 0.01 * bright(rcol); /* add in 1% before Hessian comp. */ |
| 652 |
< |
if (d < FTINY) d = FTINY; |
| 653 |
< |
ap = hp->sa; /* using Y channel from here on... */ |
| 651 |
> |
if (bright(acol) > FTINY) { /* normalize Y values */ |
| 652 |
> |
d = 0.99*cnt/bright(acol); |
| 653 |
> |
K = 0.01; |
| 654 |
> |
} else { /* geometric Hessian fall-back */ |
| 655 |
> |
d = 0.0; |
| 656 |
> |
K = 1.0; |
| 657 |
> |
pg = NULL; |
| 658 |
> |
dg = NULL; |
| 659 |
> |
} |
| 660 |
> |
ap = hp->sa; /* relative Y channel from here on... */ |
| 661 |
|
for (i = hp->ns*hp->ns; i--; ap++) |
| 662 |
< |
colval(ap->v,CIEY) = bright(ap->v) + d; |
| 662 |
> |
colval(ap->v,CIEY) = bright(ap->v)*d + K; |
| 663 |
|
|
| 664 |
|
if (uv == NULL) /* make sure we have axis pointers */ |
| 665 |
|
uv = my_uv; |
| 666 |
|
/* compute radii & pos. gradient */ |
| 667 |
|
ambHessian(hp, uv, ra, pg); |
| 668 |
+ |
|
| 669 |
|
if (dg != NULL) /* compute direction gradient */ |
| 670 |
|
ambdirgrad(hp, uv, dg); |
| 671 |
< |
if (ra != NULL) { /* adjust/clamp radii */ |
| 672 |
< |
d = pow(wt, -0.25); |
| 673 |
< |
if ((ra[0] *= d) > maxarad) |
| 674 |
< |
ra[0] = maxarad; |
| 671 |
> |
|
| 672 |
> |
if (ra != NULL) { /* scale/clamp radii */ |
| 673 |
> |
if (pg != NULL) { |
| 674 |
> |
if (ra[0]*(d = fabs(pg[0])) > 1.0) |
| 675 |
> |
ra[0] = 1.0/d; |
| 676 |
> |
if (ra[1]*(d = fabs(pg[1])) > 1.0) |
| 677 |
> |
ra[1] = 1.0/d; |
| 678 |
> |
if (ra[0] > ra[1]) |
| 679 |
> |
ra[0] = ra[1]; |
| 680 |
> |
} |
| 681 |
> |
if (ra[0] < minarad) { |
| 682 |
> |
ra[0] = minarad; |
| 683 |
> |
if (ra[1] < minarad) |
| 684 |
> |
ra[1] = minarad; |
| 685 |
> |
} |
| 686 |
> |
ra[0] *= d = 1.0/sqrt(sqrt(wt)); |
| 687 |
|
if ((ra[1] *= d) > 2.0*ra[0]) |
| 688 |
|
ra[1] = 2.0*ra[0]; |
| 689 |
+ |
if (ra[1] > maxarad) { |
| 690 |
+ |
ra[1] = maxarad; |
| 691 |
+ |
if (ra[0] > maxarad) |
| 692 |
+ |
ra[0] = maxarad; |
| 693 |
+ |
} |
| 694 |
+ |
if (pg != NULL) { /* cap gradient if necessary */ |
| 695 |
+ |
d = pg[0]*pg[0]*ra[0]*ra[0] + pg[1]*pg[1]*ra[1]*ra[1]; |
| 696 |
+ |
if (d > 1.0) { |
| 697 |
+ |
d = 1.0/sqrt(d); |
| 698 |
+ |
pg[0] *= d; |
| 699 |
+ |
pg[1] *= d; |
| 700 |
+ |
} |
| 701 |
+ |
} |
| 702 |
|
} |
| 703 |
|
free(hp); /* clean up and return */ |
| 704 |
|
return(1); |
