--- ray/src/cv/bsdfmesh.c 2012/10/19 04:14:29 2.1 +++ ray/src/cv/bsdfmesh.c 2014/03/24 06:07:46 2.25 @@ -1,5 +1,5 @@ #ifndef lint -static const char RCSid[] = "$Id: bsdfmesh.c,v 2.1 2012/10/19 04:14:29 greg Exp $"; +static const char RCSid[] = "$Id: bsdfmesh.c,v 2.25 2014/03/24 06:07:46 greg Exp $"; #endif /* * Create BSDF advection mesh from radial basis functions. @@ -18,173 +18,25 @@ static const char RCSid[] = "$Id: bsdfmesh.c,v 2.1 201 #include #include #include "bsdfrep.h" + +#ifndef NEIGH_FACT2 +#define NEIGH_FACT2 0.1 /* empirical neighborhood distance weight */ +#endif /* number of processes to run */ int nprocs = 1; /* number of children (-1 in child) */ static int nchild = 0; -/* Compute (and allocate) migration price matrix for optimization */ -static float * -price_routes(const RBFNODE *from_rbf, const RBFNODE *to_rbf) -{ - float *pmtx = (float *)malloc(sizeof(float) * - from_rbf->nrbf * to_rbf->nrbf); - FVECT *vto = (FVECT *)malloc(sizeof(FVECT) * to_rbf->nrbf); - int i, j; +typedef struct { + int nrows, ncols; /* array size (matches migration) */ + float *price; /* migration prices */ + short *sord; /* sort for each row, low to high */ + float *prow; /* current price row */ +} PRICEMAT; /* sorted pricing matrix */ - if ((pmtx == NULL) | (vto == NULL)) { - fprintf(stderr, "%s: Out of memory in migration_costs()\n", - progname); - exit(1); - } - for (j = to_rbf->nrbf; j--; ) /* save repetitive ops. */ - ovec_from_pos(vto[j], to_rbf->rbfa[j].gx, to_rbf->rbfa[j].gy); +#define pricerow(p,i) ((p)->price + (i)*(p)->ncols) +#define psortrow(p,i) ((p)->sord + (i)*(p)->ncols) - for (i = from_rbf->nrbf; i--; ) { - const double from_ang = R2ANG(from_rbf->rbfa[i].crad); - FVECT vfrom; - ovec_from_pos(vfrom, from_rbf->rbfa[i].gx, from_rbf->rbfa[i].gy); - for (j = to_rbf->nrbf; j--; ) - pmtx[i*to_rbf->nrbf + j] = acos(DOT(vfrom, vto[j])) + - fabs(R2ANG(to_rbf->rbfa[j].crad) - from_ang); - } - free(vto); - return(pmtx); -} - -/* Comparison routine needed for sorting price row */ -static const float *price_arr; -static int -msrt_cmp(const void *p1, const void *p2) -{ - float c1 = price_arr[*(const int *)p1]; - float c2 = price_arr[*(const int *)p2]; - - if (c1 > c2) return(1); - if (c1 < c2) return(-1); - return(0); -} - -/* Compute minimum (optimistic) cost for moving the given source material */ -static double -min_cost(double amt2move, const double *avail, const float *price, int n) -{ - static int *price_sort = NULL; - static int n_alloc = 0; - double total_cost = 0; - int i; - - if (amt2move <= FTINY) /* pre-emptive check */ - return(0.); - if (n > n_alloc) { /* (re)allocate sort array */ - if (n_alloc) free(price_sort); - price_sort = (int *)malloc(sizeof(int)*n); - if (price_sort == NULL) { - fprintf(stderr, "%s: Out of memory in min_cost()\n", - progname); - exit(1); - } - n_alloc = n; - } - for (i = n; i--; ) - price_sort[i] = i; - price_arr = price; - qsort(price_sort, n, sizeof(int), &msrt_cmp); - /* move cheapest first */ - for (i = 0; i < n && amt2move > FTINY; i++) { - int d = price_sort[i]; - double amt = (amt2move < avail[d]) ? amt2move : avail[d]; - - total_cost += amt * price[d]; - amt2move -= amt; - } - return(total_cost); -} - -/* Take a step in migration by choosing optimal bucket to transfer */ -static double -migration_step(MIGRATION *mig, double *src_rem, double *dst_rem, const float *pmtx) -{ - const double maxamt = .1; - const double minamt = maxamt*.0001; - static double *src_cost = NULL; - static int n_alloc = 0; - struct { - int s, d; /* source and destination */ - double price; /* price estimate per amount moved */ - double amt; /* amount we can move */ - } cur, best; - int i; - - if (mtx_nrows(mig) > n_alloc) { /* allocate cost array */ - if (n_alloc) - free(src_cost); - src_cost = (double *)malloc(sizeof(double)*mtx_nrows(mig)); - if (src_cost == NULL) { - fprintf(stderr, "%s: Out of memory in migration_step()\n", - progname); - exit(1); - } - n_alloc = mtx_nrows(mig); - } - for (i = mtx_nrows(mig); i--; ) /* starting costs for diff. */ - src_cost[i] = min_cost(src_rem[i], dst_rem, - pmtx+i*mtx_ncols(mig), mtx_ncols(mig)); - - /* find best source & dest. */ - best.s = best.d = -1; best.price = FHUGE; best.amt = 0; - for (cur.s = mtx_nrows(mig); cur.s--; ) { - const float *price = pmtx + cur.s*mtx_ncols(mig); - double cost_others = 0; - if (src_rem[cur.s] < minamt) - continue; - cur.d = -1; /* examine cheapest dest. */ - for (i = mtx_ncols(mig); i--; ) - if (dst_rem[i] > minamt && - (cur.d < 0 || price[i] < price[cur.d])) - cur.d = i; - if (cur.d < 0) - return(.0); - if ((cur.price = price[cur.d]) >= best.price) - continue; /* no point checking further */ - cur.amt = (src_rem[cur.s] < dst_rem[cur.d]) ? - src_rem[cur.s] : dst_rem[cur.d]; - if (cur.amt > maxamt) cur.amt = maxamt; - dst_rem[cur.d] -= cur.amt; /* add up differential costs */ - for (i = mtx_nrows(mig); i--; ) - if (i != cur.s) - cost_others += min_cost(src_rem[i], dst_rem, - price, mtx_ncols(mig)) - - src_cost[i]; - dst_rem[cur.d] += cur.amt; /* undo trial move */ - cur.price += cost_others/cur.amt; /* adjust effective price */ - if (cur.price < best.price) /* are we better than best? */ - best = cur; - } - if ((best.s < 0) | (best.d < 0)) - return(.0); - /* make the actual move */ - mig->mtx[mtx_ndx(mig,best.s,best.d)] += best.amt; - src_rem[best.s] -= best.amt; - dst_rem[best.d] -= best.amt; - return(best.amt); -} - -#ifdef DEBUG -static char * -thetaphi(const FVECT v) -{ - static char buf[128]; - double theta, phi; - - theta = 180./M_PI*acos(v[2]); - phi = 180./M_PI*atan2(v[1],v[0]); - sprintf(buf, "(%.0f,%.0f)", theta, phi); - - return(buf); -} -#endif - /* Create a new migration holder (sharing memory for multiprocessing) */ static MIGRATION * new_migration(RBFNODE *from_rbf, RBFNODE *to_rbf) @@ -272,6 +124,7 @@ run_subprocess(void) if (pid < 0) { fprintf(stderr, "%s: cannot fork subprocess\n", progname); + await_children(nchild); exit(1); } ++nchild; /* subprocess started */ @@ -286,28 +139,279 @@ run_subprocess(void) #endif /* ! _WIN32 */ +/* Compute normalized distribution scattering functions for comparison */ +static void +compute_nDSFs(const RBFNODE *rbf0, const RBFNODE *rbf1) +{ + const double nf0 = (GRIDRES*GRIDRES) / rbf0->vtotal; + const double nf1 = (GRIDRES*GRIDRES) / rbf1->vtotal; + int x, y; + FVECT dv; + + for (x = GRIDRES; x--; ) + for (y = GRIDRES; y--; ) { + ovec_from_pos(dv, x, y); /* cube root (brightness) */ + dsf_grid[x][y].val[0] = pow(nf0*eval_rbfrep(rbf0, dv), .3333); + dsf_grid[x][y].val[1] = pow(nf1*eval_rbfrep(rbf1, dv), .3333); + } +} + +/* Compute neighborhood distance-squared (dissimilarity) */ +static double +neighborhood_dist2(int x0, int y0, int x1, int y1) +{ + int rad = GRIDRES>>5; + double sum2 = 0.; + double d; + int p[4]; + int i, j; + /* check radius */ + p[0] = x0; p[1] = y0; p[2] = x1; p[3] = y1; + for (i = 4; i--; ) { + if (p[i] < rad) rad = p[i]; + if (GRIDRES-1-p[i] < rad) rad = GRIDRES-1-p[i]; + } + for (i = -rad; i <= rad; i++) + for (j = -rad; j <= rad; j++) { + d = dsf_grid[x0+i][y0+j].val[0] - + dsf_grid[x1+i][y1+j].val[1]; + sum2 += d*d; + } + return(sum2 / (4*rad*(rad+1) + 1)); +} + +/* Comparison routine needed for sorting price row */ +static int +msrt_cmp(void *b, const void *p1, const void *p2) +{ + PRICEMAT *pm = (PRICEMAT *)b; + float c1 = pm->prow[*(const short *)p1]; + float c2 = pm->prow[*(const short *)p2]; + + if (c1 > c2) return(1); + if (c1 < c2) return(-1); + return(0); +} + +/* Compute (and allocate) migration price matrix for optimization */ +static void +price_routes(PRICEMAT *pm, const RBFNODE *from_rbf, const RBFNODE *to_rbf) +{ + FVECT *vto = (FVECT *)malloc(sizeof(FVECT) * to_rbf->nrbf); + int i, j; + + compute_nDSFs(from_rbf, to_rbf); + pm->nrows = from_rbf->nrbf; + pm->ncols = to_rbf->nrbf; + pm->price = (float *)malloc(sizeof(float) * pm->nrows*pm->ncols); + pm->sord = (short *)malloc(sizeof(short) * pm->nrows*pm->ncols); + + if ((pm->price == NULL) | (pm->sord == NULL) | (vto == NULL)) { + fprintf(stderr, "%s: Out of memory in migration_costs()\n", + progname); + exit(1); + } + for (j = to_rbf->nrbf; j--; ) /* save repetitive ops. */ + ovec_from_pos(vto[j], to_rbf->rbfa[j].gx, to_rbf->rbfa[j].gy); + + for (i = from_rbf->nrbf; i--; ) { + const double from_ang = R2ANG(from_rbf->rbfa[i].crad); + FVECT vfrom; + short *srow; + ovec_from_pos(vfrom, from_rbf->rbfa[i].gx, from_rbf->rbfa[i].gy); + pm->prow = pricerow(pm,i); + srow = psortrow(pm,i); + for (j = to_rbf->nrbf; j--; ) { + double d; /* quadratic cost function */ + d = Acos(DOT(vfrom, vto[j])); + pm->prow[j] = d*d; + d = R2ANG(to_rbf->rbfa[j].crad) - from_ang; + pm->prow[j] += d*d; + /* neighborhood difference */ + pm->prow[j] += NEIGH_FACT2 * neighborhood_dist2( + from_rbf->rbfa[i].gx, from_rbf->rbfa[i].gy, + to_rbf->rbfa[j].gx, to_rbf->rbfa[j].gy ); + srow[j] = j; + } + qsort_r(srow, pm->ncols, sizeof(short), pm, &msrt_cmp); + } + free(vto); +} + +/* Free price matrix */ +static void +free_routes(PRICEMAT *pm) +{ + free(pm->price); pm->price = NULL; + free(pm->sord); pm->sord = NULL; +} + +/* Compute minimum (optimistic) cost for moving the given source material */ +static double +min_cost(double amt2move, const double *avail, const PRICEMAT *pm, int s) +{ + const short *srow = psortrow(pm,s); + const float *prow = pricerow(pm,s); + double total_cost = 0; + int j; + /* move cheapest first */ + for (j = 0; (j < pm->ncols) & (amt2move > FTINY); j++) { + int d = srow[j]; + double amt = (amt2move < avail[d]) ? amt2move : avail[d]; + + total_cost += amt * prow[d]; + amt2move -= amt; + } + return(total_cost); +} + +typedef struct { + short s, d; /* source and destination */ + float dc; /* discount to push inventory */ +} ROWSENT; /* row sort entry */ + +/* Compare entries by discounted moving price */ +static int +rmovcmp(void *b, const void *p1, const void *p2) +{ + PRICEMAT *pm = (PRICEMAT *)b; + const ROWSENT *re1 = (const ROWSENT *)p1; + const ROWSENT *re2 = (const ROWSENT *)p2; + double price_diff; + + if (re1->d < 0) return(re2->d >= 0); + if (re2->d < 0) return(-1); + price_diff = re1->dc*pricerow(pm,re1->s)[re1->d] - + re2->dc*pricerow(pm,re2->s)[re2->d]; + if (price_diff > 0) return(1); + if (price_diff < 0) return(-1); + return(0); +} + +/* Take a step in migration by choosing reasonable bucket to transfer */ +static double +migration_step(MIGRATION *mig, double *src_rem, double *dst_rem, PRICEMAT *pm) +{ + const int max2check = 100; + const double maxamt = 1./(double)pm->ncols; + const double minamt = maxamt*1e-4; + double *src_cost; + ROWSENT *rord; + struct { + int s, d; /* source and destination */ + double price; /* cost per amount moved */ + double amt; /* amount we can move */ + } cur, best; + int r2check, i, ri; + /* + * Check cheapest available routes only -- a higher adjusted + * destination price implies that another source is closer, so + * we can hold off considering more expensive options until + * some other (hopefully better) moves have been made. + * A discount based on source remaining is supposed to prioritize + * movement from large lobes, but it doesn't seem to do much, + * so we have it set to 1.0 at the moment. + */ +#define discount(qr) 1.0 + /* most promising row order */ + rord = (ROWSENT *)malloc(sizeof(ROWSENT)*pm->nrows); + if (rord == NULL) + goto memerr; + for (ri = pm->nrows; ri--; ) { + rord[ri].s = ri; + rord[ri].d = -1; + rord[ri].dc = 1.f; + if (src_rem[ri] <= minamt) /* enough source material? */ + continue; + for (i = 0; i < pm->ncols; i++) + if (dst_rem[ rord[ri].d = psortrow(pm,ri)[i] ] > minamt) + break; + if (i >= pm->ncols) { /* moved all we can? */ + free(rord); + return(.0); + } + rord[ri].dc = discount(src_rem[ri]); + } + if (pm->nrows > max2check) /* sort if too many sources */ + qsort_r(rord, pm->nrows, sizeof(ROWSENT), pm, &rmovcmp); + /* allocate cost array */ + src_cost = (double *)malloc(sizeof(double)*pm->nrows); + if (src_cost == NULL) + goto memerr; + for (i = pm->nrows; i--; ) /* starting costs for diff. */ + src_cost[i] = min_cost(src_rem[i], dst_rem, pm, i); + /* find best source & dest. */ + best.s = best.d = -1; best.price = FHUGE; best.amt = 0; + if ((r2check = pm->nrows) > max2check) + r2check = max2check; /* put a limit on search */ + for (ri = 0; ri < r2check; ri++) { /* check each source row */ + double cost_others = 0; + cur.s = rord[ri].s; + if ((cur.d = rord[ri].d) < 0 || + rord[ri].dc*pricerow(pm,cur.s)[cur.d] >= best.price) { + if (pm->nrows > max2check) break; /* sorted end */ + continue; /* else skip this one */ + } + cur.amt = (src_rem[cur.s] < dst_rem[cur.d]) ? + src_rem[cur.s] : dst_rem[cur.d]; + /* don't just leave smidgen */ + if (cur.amt > maxamt*1.02) cur.amt = maxamt; + dst_rem[cur.d] -= cur.amt; /* add up opportunity costs */ + for (i = pm->nrows; i--; ) + if (i != cur.s) + cost_others += min_cost(src_rem[i], dst_rem, pm, i) + - src_cost[i]; + dst_rem[cur.d] += cur.amt; /* undo trial move */ + /* discount effective price */ + cur.price = ( pricerow(pm,cur.s)[cur.d] + cost_others/cur.amt ) * + rord[ri].dc; + if (cur.price < best.price) /* are we better than best? */ + best = cur; + } + free(src_cost); /* clean up */ + free(rord); + if ((best.s < 0) | (best.d < 0)) /* nothing left to move? */ + return(.0); + /* else make the actual move */ + mtx_coef(mig,best.s,best.d) += best.amt; + src_rem[best.s] -= best.amt; + dst_rem[best.d] -= best.amt; + return(best.amt); +memerr: + fprintf(stderr, "%s: Out of memory in migration_step()\n", progname); + exit(1); +#undef discount +} + /* Compute and insert migration along directed edge (may fork child) */ static MIGRATION * create_migration(RBFNODE *from_rbf, RBFNODE *to_rbf) { - const double end_thresh = 0.1/(from_rbf->nrbf*to_rbf->nrbf); - const double check_thresh = 0.01; - const double rel_thresh = 5e-6; - float *pmtx; + const double end_thresh = 5e-6; + PRICEMAT pmtx; MIGRATION *newmig; double *src_rem, *dst_rem; double total_rem = 1., move_amt; - int i; + int i, j; /* check if exists already */ for (newmig = from_rbf->ejl; newmig != NULL; newmig = nextedge(from_rbf,newmig)) if (newmig->rbfv[1] == to_rbf) return(NULL); /* else allocate */ +#ifdef DEBUG + fprintf(stderr, "Building path from (theta,phi) (%.1f,%.1f) ", + get_theta180(from_rbf->invec), + get_phi360(from_rbf->invec)); + fprintf(stderr, "to (%.1f,%.1f) with %d x %d matrix\n", + get_theta180(to_rbf->invec), + get_phi360(to_rbf->invec), + from_rbf->nrbf, to_rbf->nrbf); +#endif newmig = new_migration(from_rbf, to_rbf); if (run_subprocess()) return(newmig); /* child continues */ - pmtx = price_routes(from_rbf, to_rbf); + price_routes(&pmtx, from_rbf, to_rbf); src_rem = (double *)malloc(sizeof(double)*from_rbf->nrbf); dst_rem = (double *)malloc(sizeof(double)*to_rbf->nrbf); if ((src_rem == NULL) | (dst_rem == NULL)) { @@ -315,42 +419,27 @@ create_migration(RBFNODE *from_rbf, RBFNODE *to_rbf) progname); exit(1); } -#ifdef DEBUG - fprintf(stderr, "Building path from (theta,phi) %s ", - thetaphi(from_rbf->invec)); - fprintf(stderr, "to %s", thetaphi(to_rbf->invec)); - /* if (nchild) */ fputc('\n', stderr); -#endif /* starting quantities */ memset(newmig->mtx, 0, sizeof(float)*from_rbf->nrbf*to_rbf->nrbf); for (i = from_rbf->nrbf; i--; ) src_rem[i] = rbf_volume(&from_rbf->rbfa[i]) / from_rbf->vtotal; - for (i = to_rbf->nrbf; i--; ) - dst_rem[i] = rbf_volume(&to_rbf->rbfa[i]) / to_rbf->vtotal; + for (j = to_rbf->nrbf; j--; ) + dst_rem[j] = rbf_volume(&to_rbf->rbfa[j]) / to_rbf->vtotal; + do { /* move a bit at a time */ - move_amt = migration_step(newmig, src_rem, dst_rem, pmtx); + move_amt = migration_step(newmig, src_rem, dst_rem, &pmtx); total_rem -= move_amt; -#ifdef DEBUG - if (!nchild) - /* fputc('.', stderr); */ - fprintf(stderr, "%.9f remaining...\r", total_rem); -#endif - } while (total_rem > end_thresh && (total_rem > check_thresh) | - (move_amt > rel_thresh*total_rem)); -#ifdef DEBUG - if (!nchild) fputs("\ndone.\n", stderr); - else fprintf(stderr, "finished with %.9f remaining\n", total_rem); -#endif + } while ((total_rem > end_thresh) & (move_amt > 0)); + for (i = from_rbf->nrbf; i--; ) { /* normalize final matrix */ - float nf = rbf_volume(&from_rbf->rbfa[i]); - int j; + double nf = rbf_volume(&from_rbf->rbfa[i]); if (nf <= FTINY) continue; nf = from_rbf->vtotal / nf; for (j = to_rbf->nrbf; j--; ) - newmig->mtx[mtx_ndx(newmig,i,j)] *= nf; + mtx_coef(newmig,i,j) *= nf; /* row now sums to 1.0 */ } end_subprocess(); /* exit here if subprocess */ - free(pmtx); /* free working arrays */ + free_routes(&pmtx); /* free working arrays */ free(src_rem); free(dst_rem); return(newmig); @@ -382,7 +471,7 @@ overlaps_tri(const RBFNODE *bv0, const RBFNODE *bv1, c return(vother[im_rev] != NULL); } -/* Find context hull vertex to complete triangle (oriented call) */ +/* Find convex hull vertex to complete triangle (oriented call) */ static RBFNODE * find_chull_vert(const RBFNODE *rbf0, const RBFNODE *rbf1) { @@ -403,7 +492,7 @@ find_chull_vert(const RBFNODE *rbf0, const RBFNODE *rb if (DOT(vp, vmid) <= FTINY) continue; /* wrong orientation */ area2 = .25*DOT(vp,vp); - VSUB(vp, rbf->invec, rbf0->invec); + VSUB(vp, rbf->invec, vmid); dprod = -DOT(vp, vejn); VSUM(vp, vp, vejn, dprod); /* above guarantees non-zero */ dprod = DOT(vp, vmid) / VLEN(vp); @@ -459,6 +548,79 @@ mesh_from_edge(MIGRATION *edge) } } } + +/* Add normal direction if missing */ +static void +check_normal_incidence(void) +{ + static FVECT norm_vec = {.0, .0, 1.}; + const int saved_nprocs = nprocs; + RBFNODE *near_rbf, *mir_rbf, *rbf; + double bestd; + int n; + + if (dsf_list == NULL) + return; /* XXX should be error? */ + near_rbf = dsf_list; + bestd = input_orient*near_rbf->invec[2]; + if (single_plane_incident) { /* ordered plane incidence? */ + if (bestd >= 1.-2.*FTINY) + return; /* already have normal */ + } else { + switch (inp_coverage) { + case INP_QUAD1: + case INP_QUAD2: + case INP_QUAD3: + case INP_QUAD4: + break; /* quadrilateral symmetry? */ + default: + return; /* else we can interpolate */ + } + for (rbf = near_rbf->next; rbf != NULL; rbf = rbf->next) { + const double d = input_orient*rbf->invec[2]; + if (d >= 1.-2.*FTINY) + return; /* seems we have normal */ + if (d > bestd) { + near_rbf = rbf; + bestd = d; + } + } + } + if (mig_list != NULL) { /* need to be called first */ + fprintf(stderr, "%s: Late call to check_normal_incidence()\n", + progname); + exit(1); + } +#ifdef DEBUG + fprintf(stderr, "Interpolating normal incidence by mirroring (%.1f,%.1f)\n", + get_theta180(near_rbf->invec), get_phi360(near_rbf->invec)); +#endif + /* mirror nearest incidence */ + n = sizeof(RBFNODE) + sizeof(RBFVAL)*(near_rbf->nrbf-1); + mir_rbf = (RBFNODE *)malloc(n); + if (mir_rbf == NULL) + goto memerr; + memcpy(mir_rbf, near_rbf, n); + mir_rbf->ord = near_rbf->ord - 1; /* not used, I think */ + mir_rbf->next = NULL; + mir_rbf->ejl = NULL; + rev_rbf_symmetry(mir_rbf, MIRROR_X|MIRROR_Y); + nprocs = 1; /* compute migration matrix */ + if (create_migration(mir_rbf, near_rbf) == NULL) + exit(1); /* XXX should never happen! */ + norm_vec[2] = input_orient; /* interpolate normal dist. */ + rbf = e_advect_rbf(mig_list, norm_vec, 2*near_rbf->nrbf); + nprocs = saved_nprocs; /* final clean-up */ + free(mir_rbf); + free(mig_list); + mig_list = near_rbf->ejl = NULL; + insert_dsf(rbf); /* insert interpolated normal */ + return; +memerr: + fprintf(stderr, "%s: Out of memory in check_normal_incidence()\n", + progname); + exit(1); +} /* Build our triangle mesh from recorded RBFs */ void @@ -467,6 +629,8 @@ build_mesh(void) double best2 = M_PI*M_PI; RBFNODE *shrt_edj[2]; RBFNODE *rbf0, *rbf1; + /* add normal if needed */ + check_normal_incidence(); /* check if isotropic */ if (single_plane_incident) { for (rbf0 = dsf_list; rbf0 != NULL; rbf0 = rbf0->next)