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) {
25 compute_edge_lengths(vs->a);
26 compute_vertex_areas(vs->a);
29 printing= printing_check(pr_cost,0);
31 if (printing) printf("cost > energy |");
33 COST(3e2, line_bending_cost(vs->a));
34 COST(1e3, edge_length_variation_cost(vs->a));
35 COST(0.2e3, rim_proximity_cost(vs->a));
36 // COST(1e2, graph_layout_cost(vs->a));
37 COST(1e8, noncircular_rim_cost(vs->a));
39 if (printing) printf("| total %# e |", energy);
41 if (energy < best_energy) {
45 if (printing) printf(" BEST");
47 best_f= fopen(output_file_tmp,"wb"); if (!best_f) diee("fopen new out");
48 r= fwrite(vs->a,sizeof(vs->a),1,best_f); if (r!=1) diee("fwrite");
49 if (fclose(best_f)) diee("fclose new best");
50 if (rename(output_file_tmp,output_file)) diee("rename install new best");
62 static void addcost(double *energy, double tweight, double tcost, int pr) {
63 double tenergy= tweight * tcost;
64 if (pr) printf(" %# e x %# e > %# e* |", tcost, tweight, tenergy);
68 /*---------- Precomputations ----------*/
70 void compute_edge_lengths(const Vertices vertices) {
74 edge_lengths[v1][e]= hypotD(vertices[v1],vertices[v2]);
77 void compute_vertex_areas(const Vertices vertices) {
82 double total= 0.0, edges_total=0;
90 edges_total += edge_lengths[v0][e1];
92 // double e1v[D3], e2v[D3], av[D3];
94 // e1v[k]= vertices[v1][k] - vertices[v0][k];
95 // e2v[k]= vertices[v2][k] - vertices[v0][k];
97 // xprod(av, e1v, e2v);
98 // total += magnD(av);
102 vertex_areas[v0]= total / count;
103 vertex_mean_edge_lengths[v0]= edges_total / count;
107 /*---------- Edgewise vertex displacement ----------*/
112 * At each vertex Q, in each direction e:
121 * cost = delta (we use r=3)
131 * delta = tan -------
134 * which is always in the range 0..pi because the denominator
135 * is nonnegative. We add epsilon to |AxB| to avoid division
143 double line_bending_cost(const Vertices vertices) {
144 static const double axb_epsilon= 1e-6;
145 static const double exponent_r= 3;
148 double a[D3], b[D3], axb[D3];
149 double total_cost= 0;
152 pi= EDGE_END2(qi,(e+3)%V6); if (pi<0) continue;
154 K a[k]= -vertices[pi][k] + vertices[qi][k];
155 K b[k]= -vertices[qi][k] + vertices[ri][k];
159 double delta= atan2(magnD(axb) + axb_epsilon, dotprod(a,b));
160 double cost= pow(delta,exponent_r);
162 if (!e && !(qi & YMASK))
170 /*---------- edge length variation ----------*/
175 * See the diagram above.
177 * cost = ( |PQ| - |QR| )
181 double edge_length_variation_cost(const Vertices vertices) {
182 double diff, cost= 0, exponent_r= 2;
186 eback= edge_reverse(q,e);
187 diff= edge_lengths[q][e] - edge_lengths[q][eback];
188 cost += pow(diff,exponent_r);
193 /*---------- rim proximity cost ----------*/
195 static void find_nearest_oncircle(double oncircle[D3], const double p[D3]) {
196 /* By symmetry, nearest point on circle is the one with
197 * the same angle subtended at the z axis. */
201 double mult= 1.0/ magnD(oncircle);
206 double rim_proximity_cost(const Vertices vertices) {
207 double oncircle[3], cost=0;
212 int nominal_edge_distance= y <= Y/2 ? y : Y-1-y;
213 if (nominal_edge_distance==0) continue;
215 find_nearest_oncircle(oncircle, vertices[v]);
218 vertex_mean_edge_lengths[v] *
219 (nominal_edge_distance*nominal_edge_distance) /
220 (hypotD2(vertices[v], oncircle) + 1e-6);
225 /*---------- noncircular rim cost ----------*/
227 double noncircular_rim_cost(const Vertices vertices) {
232 FOR_RIM_VERTEX(vy,vx,v) {
233 find_nearest_oncircle(oncircle, vertices[v]);
235 double d2= hypotD2(vertices[v], oncircle);