| 1 |
#ifndef lint |
| 2 |
static const char RCSid[] = "$Id: bsdfmesh.c,v 2.9 2013/06/28 23:18:51 greg Exp $"; |
| 3 |
#endif |
| 4 |
/* |
| 5 |
* Create BSDF advection mesh from radial basis functions. |
| 6 |
* |
| 7 |
* G. Ward |
| 8 |
*/ |
| 9 |
|
| 10 |
#ifndef _WIN32 |
| 11 |
#include <unistd.h> |
| 12 |
#include <sys/wait.h> |
| 13 |
#include <sys/mman.h> |
| 14 |
#endif |
| 15 |
#define _USE_MATH_DEFINES |
| 16 |
#include <stdio.h> |
| 17 |
#include <stdlib.h> |
| 18 |
#include <string.h> |
| 19 |
#include <math.h> |
| 20 |
#include "bsdfrep.h" |
| 21 |
/* number of processes to run */ |
| 22 |
int nprocs = 1; |
| 23 |
/* number of children (-1 in child) */ |
| 24 |
static int nchild = 0; |
| 25 |
|
| 26 |
typedef struct { |
| 27 |
int nrows, ncols; /* array size (matches migration) */ |
| 28 |
float *price; /* migration prices */ |
| 29 |
short *sord; /* sort for each row, low to high */ |
| 30 |
float *prow; /* current price row */ |
| 31 |
} PRICEMAT; /* sorted pricing matrix */ |
| 32 |
|
| 33 |
#define pricerow(p,i) ((p)->price + (i)*(p)->ncols) |
| 34 |
#define psortrow(p,i) ((p)->sord + (i)*(p)->ncols) |
| 35 |
|
| 36 |
/* Create a new migration holder (sharing memory for multiprocessing) */ |
| 37 |
static MIGRATION * |
| 38 |
new_migration(RBFNODE *from_rbf, RBFNODE *to_rbf) |
| 39 |
{ |
| 40 |
size_t memlen = sizeof(MIGRATION) + |
| 41 |
sizeof(float)*(from_rbf->nrbf*to_rbf->nrbf - 1); |
| 42 |
MIGRATION *newmig; |
| 43 |
#ifdef _WIN32 |
| 44 |
if (nprocs > 1) |
| 45 |
fprintf(stderr, "%s: warning - multiprocessing not supported\n", |
| 46 |
progname); |
| 47 |
nprocs = 1; |
| 48 |
newmig = (MIGRATION *)malloc(memlen); |
| 49 |
#else |
| 50 |
if (nprocs <= 1) { /* single process? */ |
| 51 |
newmig = (MIGRATION *)malloc(memlen); |
| 52 |
} else { /* else need to share memory */ |
| 53 |
newmig = (MIGRATION *)mmap(NULL, memlen, PROT_READ|PROT_WRITE, |
| 54 |
MAP_ANON|MAP_SHARED, -1, 0); |
| 55 |
if ((void *)newmig == MAP_FAILED) |
| 56 |
newmig = NULL; |
| 57 |
} |
| 58 |
#endif |
| 59 |
if (newmig == NULL) { |
| 60 |
fprintf(stderr, "%s: cannot allocate new migration\n", progname); |
| 61 |
exit(1); |
| 62 |
} |
| 63 |
newmig->rbfv[0] = from_rbf; |
| 64 |
newmig->rbfv[1] = to_rbf; |
| 65 |
/* insert in edge lists */ |
| 66 |
newmig->enxt[0] = from_rbf->ejl; |
| 67 |
from_rbf->ejl = newmig; |
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newmig->enxt[1] = to_rbf->ejl; |
| 69 |
to_rbf->ejl = newmig; |
| 70 |
newmig->next = mig_list; /* push onto global list */ |
| 71 |
return(mig_list = newmig); |
| 72 |
} |
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|
| 74 |
#ifdef _WIN32 |
| 75 |
#define await_children(n) (void)(n) |
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#define run_subprocess() 0 |
| 77 |
#define end_subprocess() (void)0 |
| 78 |
#else |
| 79 |
|
| 80 |
/* Wait for the specified number of child processes to complete */ |
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static void |
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await_children(int n) |
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{ |
| 84 |
int exit_status = 0; |
| 85 |
|
| 86 |
if (n > nchild) |
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n = nchild; |
| 88 |
while (n-- > 0) { |
| 89 |
int status; |
| 90 |
if (wait(&status) < 0) { |
| 91 |
fprintf(stderr, "%s: missing child(ren)!\n", progname); |
| 92 |
nchild = 0; |
| 93 |
break; |
| 94 |
} |
| 95 |
--nchild; |
| 96 |
if (status) { /* something wrong */ |
| 97 |
if ((status = WEXITSTATUS(status))) |
| 98 |
exit_status = status; |
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else |
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exit_status += !exit_status; |
| 101 |
fprintf(stderr, "%s: subprocess died\n", progname); |
| 102 |
n = nchild; /* wait for the rest */ |
| 103 |
} |
| 104 |
} |
| 105 |
if (exit_status) |
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exit(exit_status); |
| 107 |
} |
| 108 |
|
| 109 |
/* Start child process if multiprocessing selected */ |
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static pid_t |
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run_subprocess(void) |
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{ |
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int status; |
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pid_t pid; |
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|
| 116 |
if (nprocs <= 1) /* any children requested? */ |
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return(0); |
| 118 |
await_children(nchild + 1 - nprocs); /* free up child process */ |
| 119 |
if ((pid = fork())) { |
| 120 |
if (pid < 0) { |
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fprintf(stderr, "%s: cannot fork subprocess\n", |
| 122 |
progname); |
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await_children(nchild); |
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exit(1); |
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} |
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++nchild; /* subprocess started */ |
| 127 |
return(pid); |
| 128 |
} |
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nchild = -1; |
| 130 |
return(0); /* put child to work */ |
| 131 |
} |
| 132 |
|
| 133 |
/* If we are in subprocess, call exit */ |
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#define end_subprocess() if (nchild < 0) _exit(0); else |
| 135 |
|
| 136 |
#endif /* ! _WIN32 */ |
| 137 |
|
| 138 |
/* Comparison routine needed for sorting price row */ |
| 139 |
static int |
| 140 |
msrt_cmp(void *b, const void *p1, const void *p2) |
| 141 |
{ |
| 142 |
PRICEMAT *pm = (PRICEMAT *)b; |
| 143 |
float c1 = pm->prow[*(const short *)p1]; |
| 144 |
float c2 = pm->prow[*(const short *)p2]; |
| 145 |
|
| 146 |
if (c1 > c2) return(1); |
| 147 |
if (c1 < c2) return(-1); |
| 148 |
return(0); |
| 149 |
} |
| 150 |
|
| 151 |
/* Compute (and allocate) migration price matrix for optimization */ |
| 152 |
static void |
| 153 |
price_routes(PRICEMAT *pm, const RBFNODE *from_rbf, const RBFNODE *to_rbf) |
| 154 |
{ |
| 155 |
FVECT *vto = (FVECT *)malloc(sizeof(FVECT) * to_rbf->nrbf); |
| 156 |
int i, j; |
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|
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pm->nrows = from_rbf->nrbf; |
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pm->ncols = to_rbf->nrbf; |
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pm->price = (float *)malloc(sizeof(float) * pm->nrows*pm->ncols); |
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pm->sord = (short *)malloc(sizeof(short) * pm->nrows*pm->ncols); |
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|
| 163 |
if ((pm->price == NULL) | (pm->sord == NULL) | (vto == NULL)) { |
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fprintf(stderr, "%s: Out of memory in migration_costs()\n", |
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progname); |
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exit(1); |
| 167 |
} |
| 168 |
for (j = to_rbf->nrbf; j--; ) /* save repetitive ops. */ |
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ovec_from_pos(vto[j], to_rbf->rbfa[j].gx, to_rbf->rbfa[j].gy); |
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|
| 171 |
for (i = from_rbf->nrbf; i--; ) { |
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const double from_ang = R2ANG(from_rbf->rbfa[i].crad); |
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FVECT vfrom; |
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short *srow; |
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ovec_from_pos(vfrom, from_rbf->rbfa[i].gx, from_rbf->rbfa[i].gy); |
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pm->prow = pricerow(pm,i); |
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srow = psortrow(pm,i); |
| 178 |
for (j = to_rbf->nrbf; j--; ) { |
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double dprod = DOT(vfrom, vto[j]); |
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pm->prow[j] = ((dprod >= 1.) ? .0 : acos(dprod)) + |
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fabs(R2ANG(to_rbf->rbfa[j].crad) - from_ang); |
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srow[j] = j; |
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} |
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qsort_r(srow, pm->ncols, sizeof(short), pm, &msrt_cmp); |
| 185 |
} |
| 186 |
free(vto); |
| 187 |
} |
| 188 |
|
| 189 |
/* Free price matrix */ |
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static void |
| 191 |
free_routes(PRICEMAT *pm) |
| 192 |
{ |
| 193 |
free(pm->price); pm->price = NULL; |
| 194 |
free(pm->sord); pm->sord = NULL; |
| 195 |
} |
| 196 |
|
| 197 |
/* Compute minimum (optimistic) cost for moving the given source material */ |
| 198 |
static double |
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min_cost(double amt2move, const double *avail, const PRICEMAT *pm, int s) |
| 200 |
{ |
| 201 |
double total_cost = 0; |
| 202 |
int j; |
| 203 |
|
| 204 |
if (amt2move <= FTINY) /* pre-emptive check */ |
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return(.0); |
| 206 |
/* move cheapest first */ |
| 207 |
for (j = 0; j < pm->ncols && amt2move > FTINY; j++) { |
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int d = psortrow(pm,s)[j]; |
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double amt = (amt2move < avail[d]) ? amt2move : avail[d]; |
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|
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total_cost += amt * pricerow(pm,s)[d]; |
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amt2move -= amt; |
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} |
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return(total_cost); |
| 215 |
} |
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|
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/* Take a step in migration by choosing optimal bucket to transfer */ |
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static double |
| 219 |
migration_step(MIGRATION *mig, double *src_rem, double *dst_rem, const PRICEMAT *pm) |
| 220 |
{ |
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const double maxamt = 1./(double)pm->ncols; |
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const double minamt = maxamt*5e-6; |
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double *src_cost; |
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struct { |
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int s, d; /* source and destination */ |
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double price; /* price estimate per amount moved */ |
| 227 |
double amt; /* amount we can move */ |
| 228 |
} cur, best; |
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int i; |
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/* allocate cost array */ |
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src_cost = (double *)malloc(sizeof(double)*pm->nrows); |
| 232 |
if (src_cost == NULL) { |
| 233 |
fprintf(stderr, "%s: Out of memory in migration_step()\n", |
| 234 |
progname); |
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exit(1); |
| 236 |
} |
| 237 |
for (i = pm->nrows; i--; ) /* starting costs for diff. */ |
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src_cost[i] = min_cost(src_rem[i], dst_rem, pm, i); |
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|
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/* find best source & dest. */ |
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best.s = best.d = -1; best.price = FHUGE; best.amt = 0; |
| 242 |
for (cur.s = pm->nrows; cur.s--; ) { |
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double cost_others = 0; |
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|
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if (src_rem[cur.s] <= minamt) |
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continue; |
| 247 |
/* examine cheapest dest. */ |
| 248 |
for (i = 0; i < pm->ncols; i++) |
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if (dst_rem[ cur.d = psortrow(pm,cur.s)[i] ] > minamt) |
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break; |
| 251 |
if (i >= pm->ncols) |
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break; |
| 253 |
if ((cur.price = pricerow(pm,cur.s)[cur.d]) >= best.price) |
| 254 |
continue; /* no point checking further */ |
| 255 |
cur.amt = (src_rem[cur.s] < dst_rem[cur.d]) ? |
| 256 |
src_rem[cur.s] : dst_rem[cur.d]; |
| 257 |
if (cur.amt > maxamt) cur.amt = maxamt; |
| 258 |
dst_rem[cur.d] -= cur.amt; /* add up differential costs */ |
| 259 |
for (i = pm->nrows; i--; ) |
| 260 |
if (i != cur.s) |
| 261 |
cost_others += min_cost(src_rem[i], dst_rem, pm, i) |
| 262 |
- src_cost[i]; |
| 263 |
dst_rem[cur.d] += cur.amt; /* undo trial move */ |
| 264 |
cur.price += cost_others/cur.amt; /* adjust effective price */ |
| 265 |
if (cur.price < best.price) /* are we better than best? */ |
| 266 |
best = cur; |
| 267 |
} |
| 268 |
free(src_cost); /* finish up */ |
| 269 |
|
| 270 |
if ((best.s < 0) | (best.d < 0)) /* nothing left to move? */ |
| 271 |
return(.0); |
| 272 |
/* else make the actual move */ |
| 273 |
mtx_coef(mig,best.s,best.d) += best.amt; |
| 274 |
src_rem[best.s] -= best.amt; |
| 275 |
dst_rem[best.d] -= best.amt; |
| 276 |
return(best.amt); |
| 277 |
} |
| 278 |
|
| 279 |
/* Compute and insert migration along directed edge (may fork child) */ |
| 280 |
static MIGRATION * |
| 281 |
create_migration(RBFNODE *from_rbf, RBFNODE *to_rbf) |
| 282 |
{ |
| 283 |
const double end_thresh = 5e-6; |
| 284 |
PRICEMAT pmtx; |
| 285 |
MIGRATION *newmig; |
| 286 |
double *src_rem, *dst_rem; |
| 287 |
double total_rem = 1., move_amt; |
| 288 |
int i, j; |
| 289 |
/* check if exists already */ |
| 290 |
for (newmig = from_rbf->ejl; newmig != NULL; |
| 291 |
newmig = nextedge(from_rbf,newmig)) |
| 292 |
if (newmig->rbfv[1] == to_rbf) |
| 293 |
return(NULL); |
| 294 |
/* else allocate */ |
| 295 |
#ifdef DEBUG |
| 296 |
fprintf(stderr, "Building path from (theta,phi) (%.0f,%.0f) ", |
| 297 |
get_theta180(from_rbf->invec), |
| 298 |
get_phi360(from_rbf->invec)); |
| 299 |
fprintf(stderr, "to (%.0f,%.0f) with %d x %d matrix\n", |
| 300 |
get_theta180(to_rbf->invec), |
| 301 |
get_phi360(to_rbf->invec), |
| 302 |
from_rbf->nrbf, to_rbf->nrbf); |
| 303 |
#endif |
| 304 |
newmig = new_migration(from_rbf, to_rbf); |
| 305 |
if (run_subprocess()) |
| 306 |
return(newmig); /* child continues */ |
| 307 |
price_routes(&pmtx, from_rbf, to_rbf); |
| 308 |
src_rem = (double *)malloc(sizeof(double)*from_rbf->nrbf); |
| 309 |
dst_rem = (double *)malloc(sizeof(double)*to_rbf->nrbf); |
| 310 |
if ((src_rem == NULL) | (dst_rem == NULL)) { |
| 311 |
fprintf(stderr, "%s: Out of memory in create_migration()\n", |
| 312 |
progname); |
| 313 |
exit(1); |
| 314 |
} |
| 315 |
/* starting quantities */ |
| 316 |
memset(newmig->mtx, 0, sizeof(float)*from_rbf->nrbf*to_rbf->nrbf); |
| 317 |
for (i = from_rbf->nrbf; i--; ) |
| 318 |
src_rem[i] = rbf_volume(&from_rbf->rbfa[i]) / from_rbf->vtotal; |
| 319 |
for (j = to_rbf->nrbf; j--; ) |
| 320 |
dst_rem[j] = rbf_volume(&to_rbf->rbfa[j]) / to_rbf->vtotal; |
| 321 |
|
| 322 |
do { /* move a bit at a time */ |
| 323 |
move_amt = migration_step(newmig, src_rem, dst_rem, &pmtx); |
| 324 |
total_rem -= move_amt; |
| 325 |
} while ((total_rem > end_thresh) & (move_amt > 0)); |
| 326 |
|
| 327 |
for (i = from_rbf->nrbf; i--; ) { /* normalize final matrix */ |
| 328 |
double nf = rbf_volume(&from_rbf->rbfa[i]); |
| 329 |
if (nf <= FTINY) continue; |
| 330 |
nf = from_rbf->vtotal / nf; |
| 331 |
for (j = to_rbf->nrbf; j--; ) |
| 332 |
mtx_coef(newmig,i,j) *= nf; /* row now sums to 1.0 */ |
| 333 |
} |
| 334 |
end_subprocess(); /* exit here if subprocess */ |
| 335 |
free_routes(&pmtx); /* free working arrays */ |
| 336 |
free(src_rem); |
| 337 |
free(dst_rem); |
| 338 |
return(newmig); |
| 339 |
} |
| 340 |
|
| 341 |
/* Check if prospective vertex would create overlapping triangle */ |
| 342 |
static int |
| 343 |
overlaps_tri(const RBFNODE *bv0, const RBFNODE *bv1, const RBFNODE *pv) |
| 344 |
{ |
| 345 |
const MIGRATION *ej; |
| 346 |
RBFNODE *vother[2]; |
| 347 |
int im_rev; |
| 348 |
/* find shared edge in mesh */ |
| 349 |
for (ej = pv->ejl; ej != NULL; ej = nextedge(pv,ej)) { |
| 350 |
const RBFNODE *tv = opp_rbf(pv,ej); |
| 351 |
if (tv == bv0) { |
| 352 |
im_rev = is_rev_tri(ej->rbfv[0]->invec, |
| 353 |
ej->rbfv[1]->invec, bv1->invec); |
| 354 |
break; |
| 355 |
} |
| 356 |
if (tv == bv1) { |
| 357 |
im_rev = is_rev_tri(ej->rbfv[0]->invec, |
| 358 |
ej->rbfv[1]->invec, bv0->invec); |
| 359 |
break; |
| 360 |
} |
| 361 |
} |
| 362 |
if (!get_triangles(vother, ej)) /* triangle on same side? */ |
| 363 |
return(0); |
| 364 |
return(vother[im_rev] != NULL); |
| 365 |
} |
| 366 |
|
| 367 |
/* Find context hull vertex to complete triangle (oriented call) */ |
| 368 |
static RBFNODE * |
| 369 |
find_chull_vert(const RBFNODE *rbf0, const RBFNODE *rbf1) |
| 370 |
{ |
| 371 |
FVECT vmid, vejn, vp; |
| 372 |
RBFNODE *rbf, *rbfbest = NULL; |
| 373 |
double dprod, area2, bestarea2 = FHUGE, bestdprod = -.5; |
| 374 |
|
| 375 |
VSUB(vejn, rbf1->invec, rbf0->invec); |
| 376 |
VADD(vmid, rbf0->invec, rbf1->invec); |
| 377 |
if (normalize(vejn) == 0 || normalize(vmid) == 0) |
| 378 |
return(NULL); |
| 379 |
/* XXX exhaustive search */ |
| 380 |
/* Find triangle with minimum rotation from perpendicular */ |
| 381 |
for (rbf = dsf_list; rbf != NULL; rbf = rbf->next) { |
| 382 |
if ((rbf == rbf0) | (rbf == rbf1)) |
| 383 |
continue; |
| 384 |
tri_orient(vp, rbf0->invec, rbf1->invec, rbf->invec); |
| 385 |
if (DOT(vp, vmid) <= FTINY) |
| 386 |
continue; /* wrong orientation */ |
| 387 |
area2 = .25*DOT(vp,vp); |
| 388 |
VSUB(vp, rbf->invec, rbf0->invec); |
| 389 |
dprod = -DOT(vp, vejn); |
| 390 |
VSUM(vp, vp, vejn, dprod); /* above guarantees non-zero */ |
| 391 |
dprod = DOT(vp, vmid) / VLEN(vp); |
| 392 |
if (dprod <= bestdprod + FTINY*(1 - 2*(area2 < bestarea2))) |
| 393 |
continue; /* found better already */ |
| 394 |
if (overlaps_tri(rbf0, rbf1, rbf)) |
| 395 |
continue; /* overlaps another triangle */ |
| 396 |
rbfbest = rbf; |
| 397 |
bestdprod = dprod; /* new one to beat */ |
| 398 |
bestarea2 = area2; |
| 399 |
} |
| 400 |
return(rbfbest); |
| 401 |
} |
| 402 |
|
| 403 |
/* Create new migration edge and grow mesh recursively around it */ |
| 404 |
static void |
| 405 |
mesh_from_edge(MIGRATION *edge) |
| 406 |
{ |
| 407 |
MIGRATION *ej0, *ej1; |
| 408 |
RBFNODE *tvert[2]; |
| 409 |
|
| 410 |
if (edge == NULL) |
| 411 |
return; |
| 412 |
/* triangle on either side? */ |
| 413 |
get_triangles(tvert, edge); |
| 414 |
if (tvert[0] == NULL) { /* grow mesh on right */ |
| 415 |
tvert[0] = find_chull_vert(edge->rbfv[0], edge->rbfv[1]); |
| 416 |
if (tvert[0] != NULL) { |
| 417 |
if (tvert[0]->ord > edge->rbfv[0]->ord) |
| 418 |
ej0 = create_migration(edge->rbfv[0], tvert[0]); |
| 419 |
else |
| 420 |
ej0 = create_migration(tvert[0], edge->rbfv[0]); |
| 421 |
if (tvert[0]->ord > edge->rbfv[1]->ord) |
| 422 |
ej1 = create_migration(edge->rbfv[1], tvert[0]); |
| 423 |
else |
| 424 |
ej1 = create_migration(tvert[0], edge->rbfv[1]); |
| 425 |
mesh_from_edge(ej0); |
| 426 |
mesh_from_edge(ej1); |
| 427 |
} |
| 428 |
} else if (tvert[1] == NULL) { /* grow mesh on left */ |
| 429 |
tvert[1] = find_chull_vert(edge->rbfv[1], edge->rbfv[0]); |
| 430 |
if (tvert[1] != NULL) { |
| 431 |
if (tvert[1]->ord > edge->rbfv[0]->ord) |
| 432 |
ej0 = create_migration(edge->rbfv[0], tvert[1]); |
| 433 |
else |
| 434 |
ej0 = create_migration(tvert[1], edge->rbfv[0]); |
| 435 |
if (tvert[1]->ord > edge->rbfv[1]->ord) |
| 436 |
ej1 = create_migration(edge->rbfv[1], tvert[1]); |
| 437 |
else |
| 438 |
ej1 = create_migration(tvert[1], edge->rbfv[1]); |
| 439 |
mesh_from_edge(ej0); |
| 440 |
mesh_from_edge(ej1); |
| 441 |
} |
| 442 |
} |
| 443 |
} |
| 444 |
|
| 445 |
/* Build our triangle mesh from recorded RBFs */ |
| 446 |
void |
| 447 |
build_mesh(void) |
| 448 |
{ |
| 449 |
double best2 = M_PI*M_PI; |
| 450 |
RBFNODE *shrt_edj[2]; |
| 451 |
RBFNODE *rbf0, *rbf1; |
| 452 |
/* check if isotropic */ |
| 453 |
if (single_plane_incident) { |
| 454 |
for (rbf0 = dsf_list; rbf0 != NULL; rbf0 = rbf0->next) |
| 455 |
if (rbf0->next != NULL) |
| 456 |
create_migration(rbf0, rbf0->next); |
| 457 |
await_children(nchild); |
| 458 |
return; |
| 459 |
} |
| 460 |
shrt_edj[0] = shrt_edj[1] = NULL; /* start w/ shortest edge */ |
| 461 |
for (rbf0 = dsf_list; rbf0 != NULL; rbf0 = rbf0->next) |
| 462 |
for (rbf1 = rbf0->next; rbf1 != NULL; rbf1 = rbf1->next) { |
| 463 |
double dist2 = 2. - 2.*DOT(rbf0->invec,rbf1->invec); |
| 464 |
if (dist2 < best2) { |
| 465 |
shrt_edj[0] = rbf0; |
| 466 |
shrt_edj[1] = rbf1; |
| 467 |
best2 = dist2; |
| 468 |
} |
| 469 |
} |
| 470 |
if (shrt_edj[0] == NULL) { |
| 471 |
fprintf(stderr, "%s: Cannot find shortest edge\n", progname); |
| 472 |
exit(1); |
| 473 |
} |
| 474 |
/* build mesh from this edge */ |
| 475 |
if (shrt_edj[0]->ord < shrt_edj[1]->ord) |
| 476 |
mesh_from_edge(create_migration(shrt_edj[0], shrt_edj[1])); |
| 477 |
else |
| 478 |
mesh_from_edge(create_migration(shrt_edj[1], shrt_edj[0])); |
| 479 |
/* complete migrations */ |
| 480 |
await_children(nchild); |
| 481 |
} |
