*/
#include "common.h"
-#include "bgl.h"
+#include "minimise.h"
#include "mgraph.h"
-#include <gsl/gsl_errno.h>
-#include <gsl/gsl_multimin.h>
+double vertex_areas[N], vertex_mean_edge_lengths[N], edge_lengths[N][V6];
-static const char *input_file, *output_file;
-static char *output_file_tmp;
-
-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 addcost(double *energy, double tweight, double tcost);
-#define COST(weight, compute) addcost(&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(1e4, edgewise_vertex_displacement_cost(vertices));
- COST(1e2, graph_layout_cost(vertices,vertex_areas));
- COST(1e4, 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");
-
+
+ if (printing) printf(" BEST");
+
best_f= fopen(output_file_tmp,"wb"); if (!best_f) diee("fopen new out");
- r= fwrite(vertices,sizeof(Vertices),1,best_f); if (r!=1) diee("fwrite");
+ 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(output_file_tmp,output_file)) diee("rename install new best");
best_energy= energy;
}
- putchar('\n');
- flushoutput();
+ if (printing) {
+ putchar('\n');
+ flushoutput();
+ }
return energy;
-}
+}
-static void addcost(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];
}
xprod(av, e1v, e2v);
total += magnD(av);
+
count++;
}
- areas[v0]= 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 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, k;
-
- if (argc!=3 || argv[1][0]=='-' || strncmp(argv[2],"-o",2))
- { fputs("usage: minimise <input> -o<output\n",stderr); exit(8); }
-
- input_file= argv[1];
- output_file= argv[2]+2;
- if (asprintf(&output_file_tmp,"%s.new",output_file) <= 0) diee("asprintf");
-
- 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(input_file,"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= &initial[0][0];
- step_size_gsl.data= &step_size[0][0];
-
- FOR_VERTEX(v)
- K step_size[v][k]= 0.03;
-//int vx,vy;
-// FOR_RIM_VERTEX(vx,vy,v)
-// step_size[v][3] *= 0.1;
-
- GA( gsl_multimin_fminimizer_set(minimiser, &multimin_function,
- &initial_gsl, &step_size_gsl) );
-
- for (;;) {
- GA( gsl_multimin_fminimizer_iterate(minimiser) );
-
- size= gsl_multimin_fminimizer_size(minimiser);
- r= gsl_multimin_test_size(size, stop_epsilon);
-
- printf("%*s size %# e, r=%d\n", 135,"", size, r);
- flushoutput();
-
- if (r==GSL_SUCCESS) break;
- assert(r==GSL_CONTINUE);
+ vertex_areas[v0]= total / count;
+ vertex_mean_edge_lengths[v0]= edges_total / count;
}
- 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
+ * 3
+ * l delta
+ * E = F . --------
+ * vd, edge PQ vd d
*
- * (The dimensions of this are those of F_vd.)
- *
- * 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;
+ 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
~ian / moebius2.git / blobdiff