35 |
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#define ambsamp(h,i,j) (h)->sa[(i)*(h)->ns + (j)] |
36 |
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|
37 |
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typedef struct { |
38 |
< |
FVECT r_i, r_i1, e_i, rI2_eJ2; |
39 |
< |
double nf, I1, I2; |
38 |
> |
FVECT r_i, r_i1, e_i, rcp, rI2_eJ2; |
39 |
> |
double I1, I2; |
40 |
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} FFTRI; /* vectors and coefficients for Hessian calculation */ |
41 |
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|
42 |
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70 |
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d = 1.0/(n*n); |
71 |
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scalecolor(hp->acoef, d); |
72 |
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/* make tangent plane axes */ |
73 |
< |
hp->uy[0] = 0.1 - 0.2*frandom(); |
74 |
< |
hp->uy[1] = 0.1 - 0.2*frandom(); |
75 |
< |
hp->uy[2] = 0.1 - 0.2*frandom(); |
76 |
< |
for (i = 0; i < 3; i++) |
77 |
< |
if (r->ron[i] < 0.6 && r->ron[i] > -0.6) |
73 |
> |
hp->uy[0] = hp->uy[1] = hp->uy[2] = 0.0; |
74 |
> |
for (i = 3; i--; ) |
75 |
> |
if ((-0.6 < r->ron[i]) & (r->ron[i] < 0.6)) |
76 |
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break; |
77 |
< |
if (i >= 3) |
78 |
< |
error(CONSISTENCY, "bad ray direction in inithemi()"); |
77 |
> |
if (i < 0) |
78 |
> |
error(CONSISTENCY, "bad ray direction in inithemi"); |
79 |
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hp->uy[i] = 1.0; |
80 |
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VCROSS(hp->ux, hp->uy, r->ron); |
81 |
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normalize(hp->ux); |
139 |
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static void |
140 |
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comp_fftri(FFTRI *ftp, FVECT ap0, FVECT ap1, FVECT rop) |
141 |
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{ |
142 |
< |
FVECT vcp; |
145 |
< |
double dot_e, dot_er, rdot_r, rdot_r1, J2; |
142 |
> |
double rdot_cp, dot_e, dot_er, rdot_r, rdot_r1, J2; |
143 |
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int i; |
144 |
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145 |
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VSUB(ftp->r_i, ap0, rop); |
146 |
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VSUB(ftp->r_i1, ap1, rop); |
147 |
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VSUB(ftp->e_i, ap1, ap0); |
148 |
< |
VCROSS(vcp, ftp->e_i, ftp->r_i); |
149 |
< |
ftp->nf = 1.0/DOT(vcp,vcp); |
148 |
> |
VCROSS(ftp->rcp, ftp->r_i, ftp->r_i1); |
149 |
> |
rdot_cp = 1.0/DOT(ftp->rcp,ftp->rcp); |
150 |
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dot_e = DOT(ftp->e_i,ftp->e_i); |
151 |
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dot_er = DOT(ftp->e_i, ftp->r_i); |
152 |
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rdot_r = 1.0/DOT(ftp->r_i,ftp->r_i); |
153 |
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rdot_r1 = 1.0/DOT(ftp->r_i1,ftp->r_i1); |
154 |
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ftp->I1 = acos( DOT(ftp->r_i, ftp->r_i1) * sqrt(rdot_r*rdot_r1) ) * |
155 |
< |
sqrt( ftp->nf ); |
155 |
> |
sqrt( rdot_cp ); |
156 |
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ftp->I2 = ( DOT(ftp->e_i, ftp->r_i1)*rdot_r1 - dot_er*rdot_r + |
157 |
< |
dot_e*ftp->I1 )*0.5*ftp->nf; |
157 |
> |
dot_e*ftp->I1 )*0.5*rdot_cp; |
158 |
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J2 = ( 0.5*(rdot_r - rdot_r1) - dot_er*ftp->I2 ) / dot_e; |
159 |
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for (i = 3; i--; ) |
160 |
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ftp->rI2_eJ2[i] = ftp->I2*ftp->r_i[i] + J2*ftp->e_i[i]; |
178 |
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static void |
179 |
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comp_hessian(FVECT hess[3], FFTRI *ftp, FVECT nrm) |
180 |
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{ |
181 |
< |
FVECT vcp; |
181 |
> |
FVECT ncp; |
182 |
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FVECT m1[3], m2[3], m3[3], m4[3]; |
183 |
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double d1, d2, d3, d4; |
184 |
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double I3, J3, K3; |
188 |
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d2 = 1.0/DOT(ftp->r_i1,ftp->r_i1); |
189 |
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d3 = 1.0/DOT(ftp->e_i,ftp->e_i); |
190 |
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d4 = DOT(ftp->e_i, ftp->r_i); |
191 |
< |
I3 = 0.25*ftp->nf*( DOT(ftp->e_i, ftp->r_i1)*d2*d2 - d4*d1*d1 + |
192 |
< |
3.0/d3*ftp->I2 ); |
191 |
> |
I3 = ( DOT(ftp->e_i, ftp->r_i1)*d2*d2 - d4*d1*d1 + 3.0/d3*ftp->I2 ) |
192 |
> |
/ ( 4.0*DOT(ftp->rcp,ftp->rcp) ); |
193 |
|
J3 = 0.25*d3*(d1*d1 - d2*d2) - d4*d3*I3; |
194 |
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K3 = d3*(ftp->I2 - I3/d1 - 2.0*d4*J3); |
195 |
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/* intermediate matrices */ |
196 |
< |
VCROSS(vcp, nrm, ftp->e_i); |
197 |
< |
compose_matrix(m1, vcp, ftp->rI2_eJ2); |
196 |
> |
VCROSS(ncp, nrm, ftp->e_i); |
197 |
> |
compose_matrix(m1, ncp, ftp->rI2_eJ2); |
198 |
|
compose_matrix(m2, ftp->r_i, ftp->r_i); |
199 |
|
compose_matrix(m3, ftp->e_i, ftp->e_i); |
200 |
|
compose_matrix(m4, ftp->r_i, ftp->e_i); |
201 |
< |
VCROSS(vcp, ftp->r_i, ftp->e_i); |
205 |
< |
d1 = DOT(nrm, vcp); |
201 |
> |
d1 = DOT(nrm, ftp->rcp); |
202 |
|
d2 = -d1*ftp->I2; |
203 |
|
d1 *= 2.0; |
204 |
|
for (i = 3; i--; ) /* final matrix sum */ |
242 |
|
static void |
243 |
|
comp_gradient(FVECT grad, FFTRI *ftp, FVECT nrm) |
244 |
|
{ |
245 |
< |
FVECT vcp; |
245 |
> |
FVECT ncp; |
246 |
|
double f1; |
247 |
|
int i; |
248 |
|
|
249 |
< |
VCROSS(vcp, ftp->r_i, ftp->r_i1); |
250 |
< |
f1 = 2.0*DOT(nrm, vcp); |
255 |
< |
VCROSS(vcp, nrm, ftp->e_i); |
249 |
> |
f1 = 2.0*DOT(nrm, ftp->rcp); |
250 |
> |
VCROSS(ncp, nrm, ftp->e_i); |
251 |
|
for (i = 3; i--; ) |
252 |
< |
grad[i] = (-0.5/PI)*( ftp->I1*vcp[i] + f1*ftp->rI2_eJ2[i] ); |
252 |
> |
grad[i] = (-0.5/PI)*( ftp->I1*ncp[i] + f1*ftp->rI2_eJ2[i] ); |
253 |
|
} |
254 |
|
|
255 |
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|
320 |
|
/* compute eigenvalues */ |
321 |
|
if ( quadratic(evalue, 1.0, -hess2[0][0]-hess2[1][1], |
322 |
|
hess2[0][0]*hess2[1][1]-hess2[0][1]*hess2[1][0]) != 2 || |
323 |
< |
(evalue[0] = fabs(evalue[0])) <= FTINY*FTINY || |
324 |
< |
(evalue[1] = fabs(evalue[1])) <= FTINY*FTINY ) |
323 |
> |
((evalue[0] = fabs(evalue[0])) <= FTINY*FTINY) | |
324 |
> |
((evalue[1] = fabs(evalue[1])) <= FTINY*FTINY) ) |
325 |
|
error(INTERNAL, "bad eigenvalue calculation"); |
326 |
|
|
327 |
|
if (evalue[0] > evalue[1]) { |
547 |
|
ambdirgrad(hp, uv, dg); |
548 |
|
|
549 |
|
if (ra != NULL) { /* scale/clamp radii */ |
550 |
+ |
if (pg != NULL) { |
551 |
+ |
if (ra[0]*(d = fabs(pg[0])) > 1.0) |
552 |
+ |
ra[0] = 1.0/d; |
553 |
+ |
if (ra[1]*(d = fabs(pg[1])) > 1.0) |
554 |
+ |
ra[1] = 1.0/d; |
555 |
+ |
if (ra[0] > ra[1]) |
556 |
+ |
ra[0] = ra[1]; |
557 |
+ |
} |
558 |
|
if (ra[0] < minarad) { |
559 |
|
ra[0] = minarad; |
560 |
|
if (ra[1] < minarad) |
561 |
|
ra[1] = minarad; |
559 |
– |
/* cap gradient if necessary */ |
560 |
– |
if (pg != NULL) { |
561 |
– |
d = pg[0]*pg[0]*ra[0]*ra[0] + |
562 |
– |
pg[1]*pg[1]*ra[1]*ra[1]; |
563 |
– |
if (d > 1.0) { |
564 |
– |
d = 1.0/sqrt(d); |
565 |
– |
pg[0] *= d; |
566 |
– |
pg[1] *= d; |
567 |
– |
} |
568 |
– |
} |
562 |
|
} |
563 |
|
ra[0] *= d = 1.0/sqrt(sqrt(wt)); |
564 |
|
if ((ra[1] *= d) > 2.0*ra[0]) |
567 |
|
ra[1] = maxarad; |
568 |
|
if (ra[0] > maxarad) |
569 |
|
ra[0] = maxarad; |
570 |
+ |
} |
571 |
+ |
if (pg != NULL) { /* cap gradient if necessary */ |
572 |
+ |
d = pg[0]*pg[0]*ra[0]*ra[0] + pg[1]*pg[1]*ra[1]*ra[1]; |
573 |
+ |
if (d > 1.0) { |
574 |
+ |
d = 1.0/sqrt(d); |
575 |
+ |
pg[0] *= d; |
576 |
+ |
pg[1] *= d; |
577 |
+ |
} |
578 |
|
} |
579 |
|
} |
580 |
|
free(hp); /* clean up and return */ |