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 } else if (XBITS==4) {
42 COST( 3e2, line_bending_cost(vs->a));
43 COST( 3e3, edge_length_variation_cost(vs->a));
44 COST( 3.8e1, rim_proximity_cost(vs->a)); // 5e1 is too much
45 // 2.5e1 is too little
46 // 0.2e1 grows compared to previous ?
47 // 0.6e0 shrinks compared to previous ?
48 COST( 1e12, noncircular_rim_cost(vs->a));
54 if (printing) printf("| total %# e |", energy);
56 if (energy < best_energy) {
62 if (bests_unprinted) printf(" [%4d]",bests_unprinted);
68 best_f= fopen(best_file_tmp,"wb"); if (!best_f) diee("fopen new out");
69 r= fwrite(vs->a,sizeof(vs->a),1,best_f); if (r!=1) diee("fwrite");
70 if (fclose(best_f)) diee("fclose new best");
71 if (rename(best_file_tmp,best_file)) diee("rename install new best");
84 static void addcost(double *energy, double tweight, double tcost, int pr) {
85 double tenergy= tweight * tcost;
86 if (pr) printf(" %# e x %g > %# e* |", tcost, tweight, tenergy);
90 /*---------- Precomputations ----------*/
92 void compute_edge_lengths(const Vertices vertices) {
96 edge_lengths[v1][e]= hypotD(vertices[v1],vertices[v2]);
99 void compute_vertex_areas(const Vertices vertices) {
104 double total= 0.0, edges_total=0;
107 FOR_VEDGE(v0,e1,v1) {
109 v2= EDGE_END2(v0,e2);
112 edges_total += edge_lengths[v0][e1];
114 // double e1v[D3], e2v[D3], av[D3];
116 // e1v[k]= vertices[v1][k] - vertices[v0][k];
117 // e2v[k]= vertices[v2][k] - vertices[v0][k];
119 // xprod(av, e1v, e2v);
120 // total += magnD(av);
124 vertex_areas[v0]= total / count;
125 vertex_mean_edge_lengths[v0]= edges_total / count;
129 /*---------- Edgewise vertex displacement ----------*/
134 * At each vertex Q, in each direction e:
143 * cost = delta (we use r=3)
153 * delta = tan -------
156 * which is always in the range 0..pi because the denominator
157 * is nonnegative. We add epsilon to |AxB| to avoid division
165 double line_bending_cost(const Vertices vertices) {
166 static const double axb_epsilon= 1e-6;
167 static const double exponent_r= 3;
170 double a[D3], b[D3], axb[D3];
171 double total_cost= 0;
174 pi= EDGE_END2(qi,(e+3)%V6); if (pi<0) continue;
176 K a[k]= -vertices[pi][k] + vertices[qi][k];
177 K b[k]= -vertices[qi][k] + vertices[ri][k];
181 double delta= atan2(magnD(axb) + axb_epsilon, dotprod(a,b));
182 double cost= pow(delta,exponent_r);
184 if (!e && !(qi & ~XMASK))
192 /*---------- edge length variation ----------*/
197 * See the diagram above.
199 * cost = ( |PQ| - |QR| )
203 double edge_length_variation_cost(const Vertices vertices) {
204 double diff, cost= 0, exponent_r= 2;
208 eback= edge_reverse(q,e);
209 diff= edge_lengths[q][e] - edge_lengths[q][eback];
210 cost += pow(diff,exponent_r);
215 /*---------- rim proximity cost ----------*/
217 static void find_nearest_oncircle(double oncircle[D3], const double p[D3]) {
218 /* By symmetry, nearest point on circle is the one with
219 * the same angle subtended at the z axis. */
223 double mult= 1.0/ magnD(oncircle);
228 double rim_proximity_cost(const Vertices vertices) {
229 double oncircle[3], cost=0;
234 int nominal_edge_distance= y <= Y/2 ? y : Y-1-y;
235 if (nominal_edge_distance==0) continue;
237 find_nearest_oncircle(oncircle, vertices[v]);
240 vertex_mean_edge_lengths[v] *
241 (nominal_edge_distance*nominal_edge_distance) /
242 (hypotD2(vertices[v], oncircle) + 1e-6);
247 /*---------- noncircular rim cost ----------*/
249 double noncircular_rim_cost(const Vertices vertices) {
254 FOR_RIM_VERTEX(vy,vx,v) {
255 find_nearest_oncircle(oncircle, vertices[v]);
257 double d2= hypotD2(vertices[v], oncircle);