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greg |
2.1 |
#ifndef lint |
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static const char RCSid[] = "$Id$"; |
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#endif |
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/* |
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* Create BSDF advection mesh from radial basis functions. |
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* |
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* G. Ward |
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*/ |
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#ifndef _WIN32 |
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#include <unistd.h> |
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#include <sys/wait.h> |
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#include <sys/mman.h> |
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#endif |
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#define _USE_MATH_DEFINES |
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#include <stdio.h> |
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#include <stdlib.h> |
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#include <string.h> |
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#include <math.h> |
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#include "bsdfrep.h" |
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/* number of processes to run */ |
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int nprocs = 1; |
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/* number of children (-1 in child) */ |
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static int nchild = 0; |
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/* Compute (and allocate) migration price matrix for optimization */ |
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static float * |
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price_routes(const RBFNODE *from_rbf, const RBFNODE *to_rbf) |
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{ |
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float *pmtx = (float *)malloc(sizeof(float) * |
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from_rbf->nrbf * to_rbf->nrbf); |
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FVECT *vto = (FVECT *)malloc(sizeof(FVECT) * to_rbf->nrbf); |
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int i, j; |
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if ((pmtx == 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); |
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} |
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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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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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ovec_from_pos(vfrom, from_rbf->rbfa[i].gx, from_rbf->rbfa[i].gy); |
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for (j = to_rbf->nrbf; j--; ) |
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pmtx[i*to_rbf->nrbf + j] = acos(DOT(vfrom, vto[j])) + |
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fabs(R2ANG(to_rbf->rbfa[j].crad) - from_ang); |
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} |
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free(vto); |
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return(pmtx); |
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} |
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/* Comparison routine needed for sorting price row */ |
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static const float *price_arr; |
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static int |
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msrt_cmp(const void *p1, const void *p2) |
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{ |
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float c1 = price_arr[*(const int *)p1]; |
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float c2 = price_arr[*(const int *)p2]; |
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if (c1 > c2) return(1); |
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if (c1 < c2) return(-1); |
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return(0); |
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} |
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/* Compute minimum (optimistic) cost for moving the given source material */ |
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static double |
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min_cost(double amt2move, const double *avail, const float *price, int n) |
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{ |
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static int *price_sort = NULL; |
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static int n_alloc = 0; |
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double total_cost = 0; |
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int i; |
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if (amt2move <= FTINY) /* pre-emptive check */ |
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return(0.); |
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if (n > n_alloc) { /* (re)allocate sort array */ |
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if (n_alloc) free(price_sort); |
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price_sort = (int *)malloc(sizeof(int)*n); |
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if (price_sort == NULL) { |
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fprintf(stderr, "%s: Out of memory in min_cost()\n", |
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progname); |
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exit(1); |
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} |
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n_alloc = n; |
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} |
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for (i = n; i--; ) |
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price_sort[i] = i; |
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price_arr = price; |
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qsort(price_sort, n, sizeof(int), &msrt_cmp); |
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/* move cheapest first */ |
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for (i = 0; i < n && amt2move > FTINY; i++) { |
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int d = price_sort[i]; |
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double amt = (amt2move < avail[d]) ? amt2move : avail[d]; |
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total_cost += amt * price[d]; |
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amt2move -= amt; |
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} |
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return(total_cost); |
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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 |
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migration_step(MIGRATION *mig, double *src_rem, double *dst_rem, const float *pmtx) |
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{ |
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const double maxamt = .1; |
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const double minamt = maxamt*.0001; |
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static double *src_cost = NULL; |
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static int n_alloc = 0; |
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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 */ |
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double amt; /* amount we can move */ |
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} cur, best; |
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int i; |
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if (mtx_nrows(mig) > n_alloc) { /* allocate cost array */ |
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if (n_alloc) |
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free(src_cost); |
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src_cost = (double *)malloc(sizeof(double)*mtx_nrows(mig)); |
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if (src_cost == NULL) { |
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fprintf(stderr, "%s: Out of memory in migration_step()\n", |
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progname); |
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exit(1); |
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} |
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n_alloc = mtx_nrows(mig); |
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} |
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for (i = mtx_nrows(mig); i--; ) /* starting costs for diff. */ |
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src_cost[i] = min_cost(src_rem[i], dst_rem, |
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pmtx+i*mtx_ncols(mig), mtx_ncols(mig)); |
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/* find best source & dest. */ |
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best.s = best.d = -1; best.price = FHUGE; best.amt = 0; |
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for (cur.s = mtx_nrows(mig); cur.s--; ) { |
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const float *price = pmtx + cur.s*mtx_ncols(mig); |
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double cost_others = 0; |
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if (src_rem[cur.s] < minamt) |
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continue; |
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cur.d = -1; /* examine cheapest dest. */ |
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for (i = mtx_ncols(mig); i--; ) |
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if (dst_rem[i] > minamt && |
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(cur.d < 0 || price[i] < price[cur.d])) |
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cur.d = i; |
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if (cur.d < 0) |
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return(.0); |
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if ((cur.price = price[cur.d]) >= best.price) |
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continue; /* no point checking further */ |
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cur.amt = (src_rem[cur.s] < dst_rem[cur.d]) ? |
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src_rem[cur.s] : dst_rem[cur.d]; |
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if (cur.amt > maxamt) cur.amt = maxamt; |
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dst_rem[cur.d] -= cur.amt; /* add up differential costs */ |
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for (i = mtx_nrows(mig); i--; ) |
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if (i != cur.s) |
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cost_others += min_cost(src_rem[i], dst_rem, |
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price, mtx_ncols(mig)) |
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- src_cost[i]; |
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dst_rem[cur.d] += cur.amt; /* undo trial move */ |
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cur.price += cost_others/cur.amt; /* adjust effective price */ |
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if (cur.price < best.price) /* are we better than best? */ |
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best = cur; |
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} |
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if ((best.s < 0) | (best.d < 0)) |
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return(.0); |
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/* make the actual move */ |
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mig->mtx[mtx_ndx(mig,best.s,best.d)] += best.amt; |
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src_rem[best.s] -= best.amt; |
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dst_rem[best.d] -= best.amt; |
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return(best.amt); |
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} |
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#ifdef DEBUG |
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static char * |
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thetaphi(const FVECT v) |
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{ |
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static char buf[128]; |
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double theta, phi; |
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theta = 180./M_PI*acos(v[2]); |
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phi = 180./M_PI*atan2(v[1],v[0]); |
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sprintf(buf, "(%.0f,%.0f)", theta, phi); |
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return(buf); |
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} |
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#endif |
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/* Create a new migration holder (sharing memory for multiprocessing) */ |
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static MIGRATION * |
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new_migration(RBFNODE *from_rbf, RBFNODE *to_rbf) |
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{ |
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size_t memlen = sizeof(MIGRATION) + |
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sizeof(float)*(from_rbf->nrbf*to_rbf->nrbf - 1); |
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MIGRATION *newmig; |
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#ifdef _WIN32 |
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if (nprocs > 1) |
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fprintf(stderr, "%s: warning - multiprocessing not supported\n", |
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progname); |
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nprocs = 1; |
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newmig = (MIGRATION *)malloc(memlen); |
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#else |
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if (nprocs <= 1) { /* single process? */ |
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newmig = (MIGRATION *)malloc(memlen); |
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} else { /* else need to share memory */ |
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newmig = (MIGRATION *)mmap(NULL, memlen, PROT_READ|PROT_WRITE, |
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MAP_ANON|MAP_SHARED, -1, 0); |
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if ((void *)newmig == MAP_FAILED) |
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newmig = NULL; |
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} |
| 210 |
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#endif |
| 211 |
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if (newmig == NULL) { |
| 212 |
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fprintf(stderr, "%s: cannot allocate new migration\n", progname); |
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exit(1); |
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} |
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newmig->rbfv[0] = from_rbf; |
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newmig->rbfv[1] = to_rbf; |
| 217 |
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/* insert in edge lists */ |
| 218 |
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newmig->enxt[0] = from_rbf->ejl; |
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from_rbf->ejl = newmig; |
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newmig->enxt[1] = to_rbf->ejl; |
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to_rbf->ejl = newmig; |
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newmig->next = mig_list; /* push onto global list */ |
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return(mig_list = newmig); |
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} |
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#ifdef _WIN32 |
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#define await_children(n) (void)(n) |
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#define run_subprocess() 0 |
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#define end_subprocess() (void)0 |
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#else |
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| 232 |
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/* Wait for the specified number of child processes to complete */ |
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static void |
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await_children(int n) |
| 235 |
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{ |
| 236 |
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int exit_status = 0; |
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| 238 |
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if (n > nchild) |
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n = nchild; |
| 240 |
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while (n-- > 0) { |
| 241 |
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int status; |
| 242 |
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if (wait(&status) < 0) { |
| 243 |
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fprintf(stderr, "%s: missing child(ren)!\n", progname); |
| 244 |
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nchild = 0; |
| 245 |
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break; |
| 246 |
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} |
| 247 |
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--nchild; |
| 248 |
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if (status) { /* something wrong */ |
| 249 |
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if ((status = WEXITSTATUS(status))) |
| 250 |
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exit_status = status; |
| 251 |
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else |
| 252 |
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exit_status += !exit_status; |
| 253 |
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fprintf(stderr, "%s: subprocess died\n", progname); |
| 254 |
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n = nchild; /* wait for the rest */ |
| 255 |
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} |
| 256 |
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} |
| 257 |
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if (exit_status) |
| 258 |
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exit(exit_status); |
| 259 |
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} |
| 260 |
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| 261 |
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/* Start child process if multiprocessing selected */ |
| 262 |
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static pid_t |
| 263 |
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run_subprocess(void) |
| 264 |
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{ |
| 265 |
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int status; |
| 266 |
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pid_t pid; |
| 267 |
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| 268 |
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if (nprocs <= 1) /* any children requested? */ |
| 269 |
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return(0); |
| 270 |
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await_children(nchild + 1 - nprocs); /* free up child process */ |
| 271 |
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if ((pid = fork())) { |
| 272 |
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if (pid < 0) { |
| 273 |
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fprintf(stderr, "%s: cannot fork subprocess\n", |
| 274 |
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progname); |
| 275 |
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exit(1); |
| 276 |
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} |
| 277 |
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++nchild; /* subprocess started */ |
| 278 |
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return(pid); |
| 279 |
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} |
| 280 |
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nchild = -1; |
| 281 |
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return(0); /* put child to work */ |
| 282 |
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} |
| 283 |
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| 284 |
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/* If we are in subprocess, call exit */ |
| 285 |
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#define end_subprocess() if (nchild < 0) _exit(0); else |
| 286 |
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| 287 |
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#endif /* ! _WIN32 */ |
| 288 |
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| 289 |
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/* Compute and insert migration along directed edge (may fork child) */ |
| 290 |
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static MIGRATION * |
| 291 |
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create_migration(RBFNODE *from_rbf, RBFNODE *to_rbf) |
| 292 |
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{ |
| 293 |
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const double end_thresh = 0.1/(from_rbf->nrbf*to_rbf->nrbf); |
| 294 |
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const double check_thresh = 0.01; |
| 295 |
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const double rel_thresh = 5e-6; |
| 296 |
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float *pmtx; |
| 297 |
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MIGRATION *newmig; |
| 298 |
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double *src_rem, *dst_rem; |
| 299 |
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double total_rem = 1., move_amt; |
| 300 |
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int i; |
| 301 |
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/* check if exists already */ |
| 302 |
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for (newmig = from_rbf->ejl; newmig != NULL; |
| 303 |
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newmig = nextedge(from_rbf,newmig)) |
| 304 |
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if (newmig->rbfv[1] == to_rbf) |
| 305 |
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return(NULL); |
| 306 |
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/* else allocate */ |
| 307 |
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newmig = new_migration(from_rbf, to_rbf); |
| 308 |
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if (run_subprocess()) |
| 309 |
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return(newmig); /* child continues */ |
| 310 |
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pmtx = price_routes(from_rbf, to_rbf); |
| 311 |
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src_rem = (double *)malloc(sizeof(double)*from_rbf->nrbf); |
| 312 |
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dst_rem = (double *)malloc(sizeof(double)*to_rbf->nrbf); |
| 313 |
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if ((src_rem == NULL) | (dst_rem == NULL)) { |
| 314 |
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fprintf(stderr, "%s: Out of memory in create_migration()\n", |
| 315 |
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progname); |
| 316 |
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exit(1); |
| 317 |
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} |
| 318 |
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#ifdef DEBUG |
| 319 |
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fprintf(stderr, "Building path from (theta,phi) %s ", |
| 320 |
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thetaphi(from_rbf->invec)); |
| 321 |
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fprintf(stderr, "to %s", thetaphi(to_rbf->invec)); |
| 322 |
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/* if (nchild) */ fputc('\n', stderr); |
| 323 |
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#endif |
| 324 |
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/* starting quantities */ |
| 325 |
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memset(newmig->mtx, 0, sizeof(float)*from_rbf->nrbf*to_rbf->nrbf); |
| 326 |
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for (i = from_rbf->nrbf; i--; ) |
| 327 |
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src_rem[i] = rbf_volume(&from_rbf->rbfa[i]) / from_rbf->vtotal; |
| 328 |
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for (i = to_rbf->nrbf; i--; ) |
| 329 |
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dst_rem[i] = rbf_volume(&to_rbf->rbfa[i]) / to_rbf->vtotal; |
| 330 |
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do { /* move a bit at a time */ |
| 331 |
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move_amt = migration_step(newmig, src_rem, dst_rem, pmtx); |
| 332 |
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total_rem -= move_amt; |
| 333 |
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#ifdef DEBUG |
| 334 |
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if (!nchild) |
| 335 |
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/* fputc('.', stderr); */ |
| 336 |
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fprintf(stderr, "%.9f remaining...\r", total_rem); |
| 337 |
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#endif |
| 338 |
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} while (total_rem > end_thresh && (total_rem > check_thresh) | |
| 339 |
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(move_amt > rel_thresh*total_rem)); |
| 340 |
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#ifdef DEBUG |
| 341 |
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if (!nchild) fputs("\ndone.\n", stderr); |
| 342 |
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else fprintf(stderr, "finished with %.9f remaining\n", total_rem); |
| 343 |
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#endif |
| 344 |
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for (i = from_rbf->nrbf; i--; ) { /* normalize final matrix */ |
| 345 |
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|
float nf = rbf_volume(&from_rbf->rbfa[i]); |
| 346 |
|
|
int j; |
| 347 |
|
|
if (nf <= FTINY) continue; |
| 348 |
|
|
nf = from_rbf->vtotal / nf; |
| 349 |
|
|
for (j = to_rbf->nrbf; j--; ) |
| 350 |
|
|
newmig->mtx[mtx_ndx(newmig,i,j)] *= nf; |
| 351 |
|
|
} |
| 352 |
|
|
end_subprocess(); /* exit here if subprocess */ |
| 353 |
|
|
free(pmtx); /* free working arrays */ |
| 354 |
|
|
free(src_rem); |
| 355 |
|
|
free(dst_rem); |
| 356 |
|
|
return(newmig); |
| 357 |
|
|
} |
| 358 |
|
|
|
| 359 |
|
|
/* Check if prospective vertex would create overlapping triangle */ |
| 360 |
|
|
static int |
| 361 |
|
|
overlaps_tri(const RBFNODE *bv0, const RBFNODE *bv1, const RBFNODE *pv) |
| 362 |
|
|
{ |
| 363 |
|
|
const MIGRATION *ej; |
| 364 |
|
|
RBFNODE *vother[2]; |
| 365 |
|
|
int im_rev; |
| 366 |
|
|
/* find shared edge in mesh */ |
| 367 |
|
|
for (ej = pv->ejl; ej != NULL; ej = nextedge(pv,ej)) { |
| 368 |
|
|
const RBFNODE *tv = opp_rbf(pv,ej); |
| 369 |
|
|
if (tv == bv0) { |
| 370 |
|
|
im_rev = is_rev_tri(ej->rbfv[0]->invec, |
| 371 |
|
|
ej->rbfv[1]->invec, bv1->invec); |
| 372 |
|
|
break; |
| 373 |
|
|
} |
| 374 |
|
|
if (tv == bv1) { |
| 375 |
|
|
im_rev = is_rev_tri(ej->rbfv[0]->invec, |
| 376 |
|
|
ej->rbfv[1]->invec, bv0->invec); |
| 377 |
|
|
break; |
| 378 |
|
|
} |
| 379 |
|
|
} |
| 380 |
|
|
if (!get_triangles(vother, ej)) /* triangle on same side? */ |
| 381 |
|
|
return(0); |
| 382 |
|
|
return(vother[im_rev] != NULL); |
| 383 |
|
|
} |
| 384 |
|
|
|
| 385 |
|
|
/* Find context hull vertex to complete triangle (oriented call) */ |
| 386 |
|
|
static RBFNODE * |
| 387 |
|
|
find_chull_vert(const RBFNODE *rbf0, const RBFNODE *rbf1) |
| 388 |
|
|
{ |
| 389 |
|
|
FVECT vmid, vejn, vp; |
| 390 |
|
|
RBFNODE *rbf, *rbfbest = NULL; |
| 391 |
|
|
double dprod, area2, bestarea2 = FHUGE, bestdprod = -.5; |
| 392 |
|
|
|
| 393 |
|
|
VSUB(vejn, rbf1->invec, rbf0->invec); |
| 394 |
|
|
VADD(vmid, rbf0->invec, rbf1->invec); |
| 395 |
|
|
if (normalize(vejn) == 0 || normalize(vmid) == 0) |
| 396 |
|
|
return(NULL); |
| 397 |
|
|
/* XXX exhaustive search */ |
| 398 |
|
|
/* Find triangle with minimum rotation from perpendicular */ |
| 399 |
|
|
for (rbf = dsf_list; rbf != NULL; rbf = rbf->next) { |
| 400 |
|
|
if ((rbf == rbf0) | (rbf == rbf1)) |
| 401 |
|
|
continue; |
| 402 |
|
|
tri_orient(vp, rbf0->invec, rbf1->invec, rbf->invec); |
| 403 |
|
|
if (DOT(vp, vmid) <= FTINY) |
| 404 |
|
|
continue; /* wrong orientation */ |
| 405 |
|
|
area2 = .25*DOT(vp,vp); |
| 406 |
|
|
VSUB(vp, rbf->invec, rbf0->invec); |
| 407 |
|
|
dprod = -DOT(vp, vejn); |
| 408 |
|
|
VSUM(vp, vp, vejn, dprod); /* above guarantees non-zero */ |
| 409 |
|
|
dprod = DOT(vp, vmid) / VLEN(vp); |
| 410 |
|
|
if (dprod <= bestdprod + FTINY*(1 - 2*(area2 < bestarea2))) |
| 411 |
|
|
continue; /* found better already */ |
| 412 |
|
|
if (overlaps_tri(rbf0, rbf1, rbf)) |
| 413 |
|
|
continue; /* overlaps another triangle */ |
| 414 |
|
|
rbfbest = rbf; |
| 415 |
|
|
bestdprod = dprod; /* new one to beat */ |
| 416 |
|
|
bestarea2 = area2; |
| 417 |
|
|
} |
| 418 |
|
|
return(rbfbest); |
| 419 |
|
|
} |
| 420 |
|
|
|
| 421 |
|
|
/* Create new migration edge and grow mesh recursively around it */ |
| 422 |
|
|
static void |
| 423 |
|
|
mesh_from_edge(MIGRATION *edge) |
| 424 |
|
|
{ |
| 425 |
|
|
MIGRATION *ej0, *ej1; |
| 426 |
|
|
RBFNODE *tvert[2]; |
| 427 |
|
|
|
| 428 |
|
|
if (edge == NULL) |
| 429 |
|
|
return; |
| 430 |
|
|
/* triangle on either side? */ |
| 431 |
|
|
get_triangles(tvert, edge); |
| 432 |
|
|
if (tvert[0] == NULL) { /* grow mesh on right */ |
| 433 |
|
|
tvert[0] = find_chull_vert(edge->rbfv[0], edge->rbfv[1]); |
| 434 |
|
|
if (tvert[0] != NULL) { |
| 435 |
|
|
if (tvert[0]->ord > edge->rbfv[0]->ord) |
| 436 |
|
|
ej0 = create_migration(edge->rbfv[0], tvert[0]); |
| 437 |
|
|
else |
| 438 |
|
|
ej0 = create_migration(tvert[0], edge->rbfv[0]); |
| 439 |
|
|
if (tvert[0]->ord > edge->rbfv[1]->ord) |
| 440 |
|
|
ej1 = create_migration(edge->rbfv[1], tvert[0]); |
| 441 |
|
|
else |
| 442 |
|
|
ej1 = create_migration(tvert[0], edge->rbfv[1]); |
| 443 |
|
|
mesh_from_edge(ej0); |
| 444 |
|
|
mesh_from_edge(ej1); |
| 445 |
|
|
} |
| 446 |
|
|
} else if (tvert[1] == NULL) { /* grow mesh on left */ |
| 447 |
|
|
tvert[1] = find_chull_vert(edge->rbfv[1], edge->rbfv[0]); |
| 448 |
|
|
if (tvert[1] != NULL) { |
| 449 |
|
|
if (tvert[1]->ord > edge->rbfv[0]->ord) |
| 450 |
|
|
ej0 = create_migration(edge->rbfv[0], tvert[1]); |
| 451 |
|
|
else |
| 452 |
|
|
ej0 = create_migration(tvert[1], edge->rbfv[0]); |
| 453 |
|
|
if (tvert[1]->ord > edge->rbfv[1]->ord) |
| 454 |
|
|
ej1 = create_migration(edge->rbfv[1], tvert[1]); |
| 455 |
|
|
else |
| 456 |
|
|
ej1 = create_migration(tvert[1], edge->rbfv[1]); |
| 457 |
|
|
mesh_from_edge(ej0); |
| 458 |
|
|
mesh_from_edge(ej1); |
| 459 |
|
|
} |
| 460 |
|
|
} |
| 461 |
|
|
} |
| 462 |
|
|
|
| 463 |
|
|
/* Build our triangle mesh from recorded RBFs */ |
| 464 |
|
|
void |
| 465 |
|
|
build_mesh(void) |
| 466 |
|
|
{ |
| 467 |
|
|
double best2 = M_PI*M_PI; |
| 468 |
|
|
RBFNODE *shrt_edj[2]; |
| 469 |
|
|
RBFNODE *rbf0, *rbf1; |
| 470 |
|
|
/* check if isotropic */ |
| 471 |
|
|
if (single_plane_incident) { |
| 472 |
|
|
for (rbf0 = dsf_list; rbf0 != NULL; rbf0 = rbf0->next) |
| 473 |
|
|
if (rbf0->next != NULL) |
| 474 |
|
|
create_migration(rbf0, rbf0->next); |
| 475 |
|
|
await_children(nchild); |
| 476 |
|
|
return; |
| 477 |
|
|
} |
| 478 |
|
|
shrt_edj[0] = shrt_edj[1] = NULL; /* start w/ shortest edge */ |
| 479 |
|
|
for (rbf0 = dsf_list; rbf0 != NULL; rbf0 = rbf0->next) |
| 480 |
|
|
for (rbf1 = rbf0->next; rbf1 != NULL; rbf1 = rbf1->next) { |
| 481 |
|
|
double dist2 = 2. - 2.*DOT(rbf0->invec,rbf1->invec); |
| 482 |
|
|
if (dist2 < best2) { |
| 483 |
|
|
shrt_edj[0] = rbf0; |
| 484 |
|
|
shrt_edj[1] = rbf1; |
| 485 |
|
|
best2 = dist2; |
| 486 |
|
|
} |
| 487 |
|
|
} |
| 488 |
|
|
if (shrt_edj[0] == NULL) { |
| 489 |
|
|
fprintf(stderr, "%s: Cannot find shortest edge\n", progname); |
| 490 |
|
|
exit(1); |
| 491 |
|
|
} |
| 492 |
|
|
/* build mesh from this edge */ |
| 493 |
|
|
if (shrt_edj[0]->ord < shrt_edj[1]->ord) |
| 494 |
|
|
mesh_from_edge(create_migration(shrt_edj[0], shrt_edj[1])); |
| 495 |
|
|
else |
| 496 |
|
|
mesh_from_edge(create_migration(shrt_edj[1], shrt_edj[0])); |
| 497 |
|
|
/* complete migrations */ |
| 498 |
|
|
await_children(nchild); |
| 499 |
|
|
} |
