1 |
#ifndef lint |
2 |
static const char RCSid[] = "$Id: bsdfrbf.c,v 2.16 2013/11/08 23:49:07 greg Exp $"; |
3 |
#endif |
4 |
/* |
5 |
* Radial basis function representation for BSDF data. |
6 |
* |
7 |
* G. Ward |
8 |
*/ |
9 |
|
10 |
/**************************************************************** |
11 |
1) Collect samples into a grid using the Shirley-Chiu |
12 |
angular mapping from a hemisphere to a square. |
13 |
|
14 |
2) Compute an adaptive quadtree by subdividing the grid so that |
15 |
each leaf node has at least one sample up to as many |
16 |
samples as fit nicely on a plane to within a certain |
17 |
MSE tolerance. |
18 |
|
19 |
3) Place one Gaussian lobe at each leaf node in the quadtree, |
20 |
sizing it to have a radius equal to the leaf size and |
21 |
a volume equal to the energy in that node. |
22 |
*****************************************************************/ |
23 |
|
24 |
#define _USE_MATH_DEFINES |
25 |
#include <stdio.h> |
26 |
#include <stdlib.h> |
27 |
#include <string.h> |
28 |
#include <math.h> |
29 |
#include "bsdfrep.h" |
30 |
|
31 |
#ifndef RSCA |
32 |
#define RSCA 2.2 /* radius scaling factor (empirical) */ |
33 |
#endif |
34 |
#ifndef SMOOTH_MSE |
35 |
#define SMOOTH_MSE 5e-5 /* acceptable mean squared error */ |
36 |
#endif |
37 |
#ifndef SMOOTH_MSER |
38 |
#define SMOOTH_MSER 0.07 /* acceptable relative MSE */ |
39 |
#endif |
40 |
#define MAX_RAD (GRIDRES/8) /* maximum lobe radius */ |
41 |
|
42 |
#define RBFALLOCB 10 /* RBF allocation block size */ |
43 |
|
44 |
/* our loaded grid for this incident angle */ |
45 |
GRIDVAL dsf_grid[GRIDRES][GRIDRES]; |
46 |
|
47 |
/* Start new DSF input grid */ |
48 |
void |
49 |
new_bsdf_data(double new_theta, double new_phi) |
50 |
{ |
51 |
if (!new_input_direction(new_theta, new_phi)) |
52 |
exit(1); |
53 |
memset(dsf_grid, 0, sizeof(dsf_grid)); |
54 |
} |
55 |
|
56 |
/* Add BSDF data point */ |
57 |
void |
58 |
add_bsdf_data(double theta_out, double phi_out, double val, int isDSF) |
59 |
{ |
60 |
FVECT ovec; |
61 |
int pos[2]; |
62 |
|
63 |
if (!output_orient) /* check output orientation */ |
64 |
output_orient = 1 - 2*(theta_out > 90.); |
65 |
else if (output_orient > 0 ^ theta_out < 90.) { |
66 |
fputs("Cannot handle output angles on both sides of surface\n", |
67 |
stderr); |
68 |
exit(1); |
69 |
} |
70 |
ovec[2] = sin((M_PI/180.)*theta_out); |
71 |
ovec[0] = cos((M_PI/180.)*phi_out) * ovec[2]; |
72 |
ovec[1] = sin((M_PI/180.)*phi_out) * ovec[2]; |
73 |
ovec[2] = sqrt(1. - ovec[2]*ovec[2]); |
74 |
|
75 |
if (val <= 0) /* truncate to zero */ |
76 |
val = 0; |
77 |
else if (!isDSF) |
78 |
val *= ovec[2]; /* convert from BSDF to DSF */ |
79 |
|
80 |
/* update BSDF histogram */ |
81 |
if (val < BSDF2BIG*ovec[2] && val > BSDF2SML*ovec[2]) |
82 |
++bsdf_hist[histndx(val/ovec[2])]; |
83 |
|
84 |
pos_from_vec(pos, ovec); |
85 |
|
86 |
dsf_grid[pos[0]][pos[1]].vsum += val; |
87 |
dsf_grid[pos[0]][pos[1]].nval++; |
88 |
} |
89 |
|
90 |
/* Compute minimum BSDF from histogram (does not clear) */ |
91 |
static void |
92 |
comp_bsdf_min() |
93 |
{ |
94 |
unsigned long cnt, target; |
95 |
int i; |
96 |
|
97 |
cnt = 0; |
98 |
for (i = HISTLEN; i--; ) |
99 |
cnt += bsdf_hist[i]; |
100 |
if (!cnt) { /* shouldn't happen */ |
101 |
bsdf_min = 0; |
102 |
return; |
103 |
} |
104 |
target = cnt/100; /* ignore bottom 1% */ |
105 |
cnt = 0; |
106 |
for (i = 0; cnt <= target; i++) |
107 |
cnt += bsdf_hist[i]; |
108 |
bsdf_min = histval(i-1); |
109 |
} |
110 |
|
111 |
/* Determine if the given region is empty of grid samples */ |
112 |
static int |
113 |
empty_region(int x0, int x1, int y0, int y1) |
114 |
{ |
115 |
int x, y; |
116 |
|
117 |
for (x = x0; x < x1; x++) |
118 |
for (y = y0; y < y1; y++) |
119 |
if (dsf_grid[x][y].nval) |
120 |
return(0); |
121 |
return(1); |
122 |
} |
123 |
|
124 |
/* Determine if the given region is smooth enough to be a single lobe */ |
125 |
static int |
126 |
smooth_region(int x0, int x1, int y0, int y1) |
127 |
{ |
128 |
RREAL rMtx[3][3]; |
129 |
FVECT xvec; |
130 |
double A, B, C, nvs, sqerr; |
131 |
int x, y, n; |
132 |
/* compute planar regression */ |
133 |
memset(rMtx, 0, sizeof(rMtx)); |
134 |
memset(xvec, 0, sizeof(xvec)); |
135 |
for (x = x0; x < x1; x++) |
136 |
for (y = y0; y < y1; y++) |
137 |
if ((n = dsf_grid[x][y].nval) > 0) { |
138 |
double z = dsf_grid[x][y].vsum; |
139 |
rMtx[0][0] += x*x*(double)n; |
140 |
rMtx[0][1] += x*y*(double)n; |
141 |
rMtx[0][2] += x*(double)n; |
142 |
rMtx[1][1] += y*y*(double)n; |
143 |
rMtx[1][2] += y*(double)n; |
144 |
rMtx[2][2] += (double)n; |
145 |
xvec[0] += x*z; |
146 |
xvec[1] += y*z; |
147 |
xvec[2] += z; |
148 |
} |
149 |
rMtx[1][0] = rMtx[0][1]; |
150 |
rMtx[2][0] = rMtx[0][2]; |
151 |
rMtx[2][1] = rMtx[1][2]; |
152 |
nvs = rMtx[2][2]; |
153 |
if (SDinvXform(rMtx, rMtx) != SDEnone) |
154 |
return(1); /* colinear values */ |
155 |
A = DOT(rMtx[0], xvec); |
156 |
B = DOT(rMtx[1], xvec); |
157 |
C = DOT(rMtx[2], xvec); |
158 |
sqerr = 0.0; /* compute mean squared error */ |
159 |
for (x = x0; x < x1; x++) |
160 |
for (y = y0; y < y1; y++) |
161 |
if ((n = dsf_grid[x][y].nval) > 0) { |
162 |
double d = A*x + B*y + C - dsf_grid[x][y].vsum/n; |
163 |
sqerr += n*d*d; |
164 |
} |
165 |
if (sqerr <= nvs*SMOOTH_MSE) /* below absolute MSE threshold? */ |
166 |
return(1); |
167 |
/* OR below relative MSE threshold? */ |
168 |
return(sqerr*nvs <= xvec[2]*xvec[2]*SMOOTH_MSER); |
169 |
} |
170 |
|
171 |
/* Create new lobe based on integrated samples in region */ |
172 |
static void |
173 |
create_lobe(RBFVAL *rvp, int x0, int x1, int y0, int y1) |
174 |
{ |
175 |
double vtot = 0.0; |
176 |
int nv = 0; |
177 |
double rad; |
178 |
int x, y; |
179 |
/* compute average for region */ |
180 |
for (x = x0; x < x1; x++) |
181 |
for (y = y0; y < y1; y++) { |
182 |
vtot += dsf_grid[x][y].vsum; |
183 |
nv += dsf_grid[x][y].nval; |
184 |
} |
185 |
if (!nv) { |
186 |
fprintf(stderr, "%s: internal - missing samples in create_lobe\n", |
187 |
progname); |
188 |
exit(1); |
189 |
} |
190 |
/* peak value based on integral */ |
191 |
vtot *= (x1-x0)*(y1-y0)*(2.*M_PI/GRIDRES/GRIDRES)/(double)nv; |
192 |
rad = (RSCA/(double)GRIDRES)*(x1-x0); |
193 |
rvp->peak = vtot / ((2.*M_PI) * rad*rad); |
194 |
rvp->crad = ANG2R(rad); |
195 |
rvp->gx = (x0+x1)>>1; |
196 |
rvp->gy = (y0+y1)>>1; |
197 |
} |
198 |
|
199 |
/* Recursive function to build radial basis function representation */ |
200 |
static int |
201 |
build_rbfrep(RBFVAL **arp, int *np, int x0, int x1, int y0, int y1) |
202 |
{ |
203 |
int xmid = (x0+x1)>>1; |
204 |
int ymid = (y0+y1)>>1; |
205 |
int branched[4]; |
206 |
int nadded, nleaves; |
207 |
/* need to make this a leaf? */ |
208 |
if (empty_region(x0, xmid, y0, ymid) || |
209 |
empty_region(xmid, x1, y0, ymid) || |
210 |
empty_region(x0, xmid, ymid, y1) || |
211 |
empty_region(xmid, x1, ymid, y1)) |
212 |
return(0); |
213 |
/* add children (branches+leaves) */ |
214 |
if ((branched[0] = build_rbfrep(arp, np, x0, xmid, y0, ymid)) < 0) |
215 |
return(-1); |
216 |
if ((branched[1] = build_rbfrep(arp, np, xmid, x1, y0, ymid)) < 0) |
217 |
return(-1); |
218 |
if ((branched[2] = build_rbfrep(arp, np, x0, xmid, ymid, y1)) < 0) |
219 |
return(-1); |
220 |
if ((branched[3] = build_rbfrep(arp, np, xmid, x1, ymid, y1)) < 0) |
221 |
return(-1); |
222 |
nadded = branched[0] + branched[1] + branched[2] + branched[3]; |
223 |
nleaves = !branched[0] + !branched[1] + !branched[2] + !branched[3]; |
224 |
if (!nleaves) /* nothing but branches? */ |
225 |
return(nadded); |
226 |
/* combine 4 leaves into 1? */ |
227 |
if ((nleaves == 4) & (x1-x0 <= MAX_RAD) && |
228 |
smooth_region(x0, x1, y0, y1)) |
229 |
return(0); |
230 |
/* need more array space? */ |
231 |
if ((*np+nleaves-1)>>RBFALLOCB != (*np-1)>>RBFALLOCB) { |
232 |
*arp = (RBFVAL *)realloc(*arp, |
233 |
sizeof(RBFVAL)*(*np+nleaves-1+(1<<RBFALLOCB))); |
234 |
if (*arp == NULL) |
235 |
return(-1); |
236 |
} |
237 |
/* create lobes for leaves */ |
238 |
if (!branched[0]) |
239 |
create_lobe(*arp+(*np)++, x0, xmid, y0, ymid); |
240 |
if (!branched[1]) |
241 |
create_lobe(*arp+(*np)++, xmid, x1, y0, ymid); |
242 |
if (!branched[2]) |
243 |
create_lobe(*arp+(*np)++, x0, xmid, ymid, y1); |
244 |
if (!branched[3]) |
245 |
create_lobe(*arp+(*np)++, xmid, x1, ymid, y1); |
246 |
nadded += nleaves; |
247 |
return(nadded); |
248 |
} |
249 |
|
250 |
/* Count up filled nodes and build RBF representation from current grid */ |
251 |
RBFNODE * |
252 |
make_rbfrep() |
253 |
{ |
254 |
RBFNODE *newnode; |
255 |
RBFVAL *rbfarr; |
256 |
int nn; |
257 |
/* compute minimum BSDF */ |
258 |
comp_bsdf_min(); |
259 |
/* create RBF node list */ |
260 |
rbfarr = NULL; nn = 0; |
261 |
if (build_rbfrep(&rbfarr, &nn, 0, GRIDRES, 0, GRIDRES) <= 0) |
262 |
goto memerr; |
263 |
/* (re)allocate RBF array */ |
264 |
newnode = (RBFNODE *)realloc(rbfarr, |
265 |
sizeof(RBFNODE) + sizeof(RBFVAL)*(nn-1)); |
266 |
if (newnode == NULL) |
267 |
goto memerr; |
268 |
/* copy computed lobes into RBF node */ |
269 |
memmove(newnode->rbfa, newnode, sizeof(RBFVAL)*nn); |
270 |
newnode->ord = -1; |
271 |
newnode->next = NULL; |
272 |
newnode->ejl = NULL; |
273 |
newnode->invec[2] = sin((M_PI/180.)*theta_in_deg); |
274 |
newnode->invec[0] = cos((M_PI/180.)*phi_in_deg)*newnode->invec[2]; |
275 |
newnode->invec[1] = sin((M_PI/180.)*phi_in_deg)*newnode->invec[2]; |
276 |
newnode->invec[2] = input_orient*sqrt(1. - newnode->invec[2]*newnode->invec[2]); |
277 |
newnode->vtotal = .0; |
278 |
newnode->nrbf = nn; |
279 |
/* compute sum for normalization */ |
280 |
while (nn-- > 0) |
281 |
newnode->vtotal += rbf_volume(&newnode->rbfa[nn]); |
282 |
#ifdef DEBUG |
283 |
fprintf(stderr, "Built RBF with %d lobes\n", newnode->nrbf); |
284 |
fprintf(stderr, "Integrated DSF at (%.1f,%.1f) deg. is %.2f\n", |
285 |
get_theta180(newnode->invec), get_phi360(newnode->invec), |
286 |
newnode->vtotal); |
287 |
#endif |
288 |
insert_dsf(newnode); |
289 |
|
290 |
return(newnode); |
291 |
memerr: |
292 |
fprintf(stderr, "%s: Out of memory in make_rbfrep()\n", progname); |
293 |
exit(1); |
294 |
} |