X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=moebius2.git;a=blobdiff_plain;f=energy.c;h=2bbf0492a5a41312d6819907995857bce9d1e180;hp=aa1c7f4d29ee7820c7abe784e414e8cac99ebd20;hb=7968bc4aca3306473e7ab0a55d4bdc721a3eacd5;hpb=f5fef8bc75d9d5658705763fa7c083ae75a501ba diff --git a/energy.c b/energy.c index aa1c7f4..2bbf049 100644 --- a/energy.c +++ b/energy.c @@ -3,73 +3,87 @@ */ #include "common.h" -#include "bgl.h" +#include "minimise.h" #include "mgraph.h" -#include -#include +double vertex_areas[N], vertex_mean_edge_lengths[N], edge_lengths[N][V6]; -#define BEST_F "best" -#define INITIAL_F "initial" - -static double edgewise_vertex_displacement_cost(const Vertices vertices); -static double noncircular_rim_cost(const Vertices vertices); - -static void compute_vertex_areas(const Vertices vertices, double areas[N]); static double best_energy= DBL_MAX; -static void cost(double *energy, double tweight, double tcost); -#define COST(weight, compute) cost(&energy, (weight), (compute)) +static void addcost(double *energy, double tweight, double tcost, int pr); +#define COST(weight, compute) addcost(&energy, (weight), (compute), printing) /*---------- main energy computation and subroutines ----------*/ -static double compute_energy(const Vertices vertices) { - double vertex_areas[N], energy; +double compute_energy(const struct Vertices *vs) { + double energy; + int printing; - compute_vertex_areas(vertices,vertex_areas); + compute_edge_lengths(vs->a); + compute_vertex_areas(vs->a); energy= 0; - printf("cost > energy |"); - COST(1000.0, edgewise_vertex_displacement_cost(vertices)); - COST(1.0, graph_layout_cost(vertices,vertex_areas)); - COST(1e3, noncircular_rim_cost(vertices)); - - printf("| total %# e |", energy); + printing= printing_check(pr_cost); + + if (printing) printf("cost > energy |"); + + COST(1e2, edgewise_vertex_displacement_cost(vs->a)); + COST(1e2, graph_layout_cost(vs->a)); + COST(1e3, edge_length_variation_cost(vs->a)); +// COST(1e6, noncircular_rim_cost(vs->a)); + + if (printing) printf("| total %# e |", energy); + if (energy < best_energy) { FILE *best_f; int r; - - printf(" BEST"); - - best_f= fopen(BEST_F ".new","wb"); if (!best_f) diee("fopen new best"); - r= fwrite(vertices,sizeof(vertices),1,best_f); if (r!=1) diee("fwrite"); + + if (printing) printf(" BEST"); + + best_f= fopen(output_file_tmp,"wb"); if (!best_f) diee("fopen new out"); + r= fwrite(vs->a,sizeof(vs->a),1,best_f); if (r!=1) diee("fwrite"); if (fclose(best_f)) diee("fclose new best"); - if (rename(BEST_F ".new", BEST_F)) diee("rename install new best"); + if (rename(output_file_tmp,output_file)) diee("rename install new best"); + + best_energy= energy; + } + if (printing) { + putchar('\n'); + flushoutput(); } - putchar('\n'); - flushoutput(); return energy; -} +} -static void cost(double *energy, double tweight, double tcost) { +static void addcost(double *energy, double tweight, double tcost, int pr) { double tenergy= tweight * tcost; - printf(" %# e > %# e |", tcost, tenergy); + if (pr) printf(" %# e > %# e |", tcost, tenergy); *energy += tenergy; } -static void compute_vertex_areas(const Vertices vertices, double areas[N]) { - int v0,v1,v2, e1,e2, k; +/*---------- Precomputations ----------*/ + +void compute_edge_lengths(const Vertices vertices) { + int v1,e,v2; + FOR_EDGE(v1,e,v2) + edge_lengths[v1][e]= hypotD(vertices[v1],vertices[v2]); +} + +void compute_vertex_areas(const Vertices vertices) { + int v0,v1,v2, e1,e2, k; + FOR_VERTEX(v0) { - double total= 0.0; + double total= 0.0, edges_total=0; int count= 0; - + FOR_VEDGE(v0,e1,v1) { e2= (e1+1) % V6; v2= EDGE_END2(v0,e2); if (v2<0) continue; - + + edges_total += edge_lengths[v0][e1]; + double e1v[D3], e2v[D3], av[D3]; K { e1v[k]= vertices[v1][k] - vertices[v0][k]; @@ -77,204 +91,102 @@ static void compute_vertex_areas(const Vertices vertices, double areas[N]) { } xprod(av, e1v, e2v); total += magnD(av); + count++; } - areas[v0]= total / count; + vertex_areas[v0]= total / count; + vertex_mean_edge_lengths[v0]= edges_total / count; } } -/*---------- use of GSL ----------*/ - - /* We want to do multidimensional minimisation. - * - * We don't think there are any local minima. Or at least, if there - * are, the local minimum which will be found from the starting - * state is the one we want. - * - * We don't want to try to provide a derivative of the cost - * function. That's too tedious (and anyway the polynomial - * approximation to our our cost function sometimes has high degree - * in the inputs which means the quadratic model implied by most of - * the gradient descent minimisers is not ideal). - * - * This eliminates most of the algorithms. Nelder and Mead's - * simplex algorithm is still available and we will try that. - * - * In our application we are searching for the optimal locations of - * N actualvertices in D3 (3) dimensions - ie, we are searching for - * the optimal metapoint in an N*D3-dimensional space. - * - * So eg with X=Y=100, the simplex will contain 300 metavertices - * each of which is an array of 300 doubles for the actualvertex - * coordinates. Hopefully this won't be too slow ... - */ - -static void gsldie(const char *what, int status) { - fprintf(stderr,"gsl function failed: %s: %s\n", what, gsl_strerror(status)); - exit(-1); -} - -static gsl_multimin_fminimizer *minimiser; - -static const double stop_epsilon= 1e-4; - -static double minfunc_f(const gsl_vector *x, void *params) { - assert(x->size == DIM); - assert(x->stride == 1); - return compute_energy((const double(*)[D3])x->data); -} - -int main(int argc, const char *const *argv) { - gsl_multimin_function multimin_function; - double size; - Vertices initial, step_size; - FILE *initial_f; - gsl_vector initial_gsl, step_size_gsl; - int r, v, vx,vy, k; - - if (argc>1) { fputs("takes no arguments\n",stderr); exit(8); } - - minimiser= gsl_multimin_fminimizer_alloc - (gsl_multimin_fminimizer_nmsimplex, DIM); - if (!minimiser) { perror("alloc minimiser"); exit(-1); } - - multimin_function.f= minfunc_f; - multimin_function.n= DIM; - multimin_function.params= 0; - - initial_f= fopen(INITIAL_F,"rb"); if (!initial_f) diee("fopen initial"); - errno= 0; r= fread(initial,sizeof(initial),1,initial_f); - if (r!=1) diee("fread"); - fclose(initial_f); - - initial_gsl.size= DIM; - initial_gsl.stride= 1; - initial_gsl.block= 0; - initial_gsl.owner= 0; - step_size_gsl= initial_gsl; - - initial_gsl.data= (double*)initial; - step_size_gsl.data= (double*)step_size; - - FOR_VERTEX(v) - K step_size[v][k]= 1e-3; - FOR_RIM_VERTEX(vx,vy,v) - step_size[v][3] *= 0.1; - - r= gsl_multimin_fminimizer_set(minimiser, &multimin_function, - &initial_gsl, &step_size_gsl); - if (r) { gsldie("fminimizer_set",r); } - - for (;;) { - r= gsl_multimin_fminimizer_iterate(minimiser); - if (r) { gsldie("fminimizer_iterate",r); } - - size= gsl_multimin_fminimizer_size(minimiser); - r= gsl_multimin_test_size(size, stop_epsilon); - - printf("size %# e, r=%d\n", size, r); - flushoutput(); - - if (r==GSL_SUCCESS) break; - assert(r==GSL_CONTINUE); - } - return 0; -} - /*---------- Edgewise vertex displacement ----------*/ /* - * + * * * * Q `-_ * / | `-_ - * R' - _ _ _/_ | `-. - * . / M - - - - - S - * . / | _,-' - * . / | _,-' - * . / , P ' - * . / ,-' - * . /,-' - * . /' + * / | `-. + * / M - - - - - S + * / ' | _,-' + * / ' | _,-' + * / ' , P ' + * / ',-' + * /,-' + * /' * R * + * Let delta = 180deg - angle RMS * - * - * Find R', the `expected' location of R, by - * reflecting S in M (the midpoint of QP). - * - * Let 2d = |RR'| - * b = |PQ| - * l = |RS| + * Let l = |PQ| + * d = |RS| * * Giving energy contribution: * - * 2 - * b d - * E = F . ---- - * vd, edge PQ vd 3 - * l - * - * (The dimensions of this are those of F_vd.) + * 3 + * l delta + * E = F . -------- + * vd, edge PQ vd d * - * By symmetry, this calculation gives the same answer with R and S - * exchanged. Looking at the projection in the RMS plane: * + * (The dimensions of this are those of F_vd.) * - * S' - * ,' - * ,' - * R' ,' 2d" = |SS'| = |RR'| = 2d - * `-._ ,' - * `-._ ,' By congruent triangles, - * ` M with M' = midpoint of RS, - * ,' `-._ |MM'| = |RR'|/2 = d - * ,' `-._ - * ,' ` S So use - * ,' M' _ , - ' d = |MM'| - * ,' _ , - ' - * R - ' - * - * We choose this value for l (rather than |RM|+|MS|, say, or |RM|) - * because we want this symmetry and because we're happy to punish - * bending more than uneveness in the metric. + * We calculate delta as atan2(|AxB|, A.B) + * where A = PQ, B = QR * - * In practice to avoid division by zero we'll add epsilon to l^3 - * and the huge energy ought then to be sufficient for the model to - * avoid being close to R=S. + * In practice to avoid division by zero we'll add epsilon to d and + * |AxB| and the huge energy ought then to be sufficient for the + * model to avoid being close to R=S. */ -static double edgewise_vertex_displacement_cost(const Vertices vertices) { - static const double l3_epsilon= 1e-6; +double edgewise_vertex_displacement_cost(const Vertices vertices) { + static const double axb_epsilon= 1e-6; - int pi,e,qi,ri,si, k; - double m[D3], mprime[D3], b, d2, l, sigma_bd2_l3=0; + int pi,e,qi,ri, k; //,si + double a[D3], b[D3], axb[D3]; //m[D3], + double total_cost= 0; - FOR_EDGE(pi,e,qi) { - ri= EDGE_END2(pi,(e+1)%V6); if (ri<0) continue; - si= EDGE_END2(pi,(e+5)%V6); if (si<0) continue; - assert(ri == EDGE_END2(qi,(e+2)%V6)); - assert(si == EDGE_END2(qi,(e+4)%V6)); + FOR_EDGE(qi,e,ri) { + pi= EDGE_END2(qi,(e+3)%V6); if (pi<0) continue; + +// K m[k]= (vertices[pi][k] + vertices[qi][k]) * 0.5; + K a[k]= -vertices[pi][k] + vertices[qi][k]; + K b[k]= -vertices[qi][k] + vertices[ri][k]; + + xprod(axb,a,b); - K m[k]= (vertices[pi][k] + vertices[qi][k]) * 0.5; - K mprime[k]= (vertices[ri][k] + vertices[si][k]) * 0.5; - b= hypotD(vertices[pi], vertices[qi]); - d2= hypotD2(m, mprime); - l= hypotD(vertices[ri], vertices[si]); - double l3 = l*l*l + l3_epsilon; - - sigma_bd2_l3 += b * d2 / l3; + double delta= atan2(magnD(axb) + axb_epsilon, dotprod(a,b)); + double cost= pow(delta,3); + + if (!e && !(qi & YMASK)) + cost *= 10; + + total_cost += cost; } - return sigma_bd2_l3; + return total_cost; } +/*---------- edge length variation ----------*/ + +double edge_length_variation_cost(const Vertices vertices) { + double diff, cost= 0; + int v0, efwd,vfwd, eback; + + FOR_EDGE(v0,efwd,vfwd) { + eback= edge_reverse(v0,efwd); + diff= edge_lengths[v0][efwd] - edge_lengths[v0][eback]; + cost += diff*diff; + } + return cost; +} + /*---------- noncircular rim cost ----------*/ -static double noncircular_rim_cost(const Vertices vertices) { +double noncircular_rim_cost(const Vertices vertices) { int vy,vx,v; double cost= 0.0; - + FOR_RIM_VERTEX(vy,vx,v) { double oncircle[3]; /* By symmetry, nearest point on circle is the one with