2 * We try to find an optimal triangle grid
9 double vertex_areas[N], vertex_mean_edge_lengths[N], edge_lengths[N][V6];
11 static double best_energy= DBL_MAX;
13 static void addcost(double *energy, double tweight, double tcost, int pr);
14 #define COST(weight, compute) addcost(&energy, (weight), (compute), printing)
16 void energy_init(void) {
19 /*---------- main energy computation and subroutines ----------*/
21 double compute_energy(const struct Vertices *vs) {
22 static int bests_unprinted;
27 compute_edge_lengths(vs->a);
28 compute_vertex_areas(vs->a);
31 printing= printing_check(pr_cost,0);
33 if (printing) printf("%15lld c>e |", evaluations);
36 COST( 3e2, line_bending_cost(vs->a));
37 COST( 1e3, edge_length_variation_cost(vs->a));
38 COST( 0.2e3, rim_proximity_cost(vs->a));
39 COST( 1e8, noncircular_rim_cost(vs->a));
41 COST( 3e3, line_bending_cost(vs->a));
42 COST( 1e4, edge_length_variation_cost(vs->a));
43 COST( 0.2e3, rim_proximity_cost(vs->a));
44 COST( 1e8, noncircular_rim_cost(vs->a));
47 if (printing) printf("| total %# e |", energy);
49 if (energy < best_energy) {
55 if (bests_unprinted) printf(" [%4d]",bests_unprinted);
61 best_f= fopen(best_file_tmp,"wb"); if (!best_f) diee("fopen new out");
62 r= fwrite(vs->a,sizeof(vs->a),1,best_f); if (r!=1) diee("fwrite");
63 if (fclose(best_f)) diee("fclose new best");
64 if (rename(best_file_tmp,best_file)) diee("rename install new best");
77 static void addcost(double *energy, double tweight, double tcost, int pr) {
78 double tenergy= tweight * tcost;
79 if (pr) printf(" %# e x %g > %# e* |", tcost, tweight, tenergy);
83 /*---------- Precomputations ----------*/
85 void compute_edge_lengths(const Vertices vertices) {
89 edge_lengths[v1][e]= hypotD(vertices[v1],vertices[v2]);
92 void compute_vertex_areas(const Vertices vertices) {
97 double total= 0.0, edges_total=0;
100 FOR_VEDGE(v0,e1,v1) {
102 v2= EDGE_END2(v0,e2);
105 edges_total += edge_lengths[v0][e1];
107 // double e1v[D3], e2v[D3], av[D3];
109 // e1v[k]= vertices[v1][k] - vertices[v0][k];
110 // e2v[k]= vertices[v2][k] - vertices[v0][k];
112 // xprod(av, e1v, e2v);
113 // total += magnD(av);
117 vertex_areas[v0]= total / count;
118 vertex_mean_edge_lengths[v0]= edges_total / count;
122 /*---------- Edgewise vertex displacement ----------*/
127 * At each vertex Q, in each direction e:
136 * cost = delta (we use r=3)
146 * delta = tan -------
149 * which is always in the range 0..pi because the denominator
150 * is nonnegative. We add epsilon to |AxB| to avoid division
158 double line_bending_cost(const Vertices vertices) {
159 static const double axb_epsilon= 1e-6;
160 static const double exponent_r= 3;
163 double a[D3], b[D3], axb[D3];
164 double total_cost= 0;
167 pi= EDGE_END2(qi,(e+3)%V6); if (pi<0) continue;
169 K a[k]= -vertices[pi][k] + vertices[qi][k];
170 K b[k]= -vertices[qi][k] + vertices[ri][k];
174 double delta= atan2(magnD(axb) + axb_epsilon, dotprod(a,b));
175 double cost= pow(delta,exponent_r);
177 if (!e && !(qi & ~XMASK))
185 /*---------- edge length variation ----------*/
190 * See the diagram above.
192 * cost = ( |PQ| - |QR| )
196 double edge_length_variation_cost(const Vertices vertices) {
197 double diff, cost= 0, exponent_r= 2;
201 eback= edge_reverse(q,e);
202 diff= edge_lengths[q][e] - edge_lengths[q][eback];
203 cost += pow(diff,exponent_r);
208 /*---------- rim proximity cost ----------*/
210 static void find_nearest_oncircle(double oncircle[D3], const double p[D3]) {
211 /* By symmetry, nearest point on circle is the one with
212 * the same angle subtended at the z axis. */
216 double mult= 1.0/ magnD(oncircle);
221 double rim_proximity_cost(const Vertices vertices) {
222 double oncircle[3], cost=0;
227 int nominal_edge_distance= y <= Y/2 ? y : Y-1-y;
228 if (nominal_edge_distance==0) continue;
230 find_nearest_oncircle(oncircle, vertices[v]);
233 vertex_mean_edge_lengths[v] *
234 (nominal_edge_distance*nominal_edge_distance) /
235 (hypotD2(vertices[v], oncircle) + 1e-6);
240 /*---------- noncircular rim cost ----------*/
242 double noncircular_rim_cost(const Vertices vertices) {
247 FOR_RIM_VERTEX(vy,vx,v) {
248 find_nearest_oncircle(oncircle, vertices[v]);
250 double d2= hypotD2(vertices[v], oncircle);