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( 3e3, line_bending_cost(vs->a));
37 COST( 3e3, edge_length_variation_cost(vs->a));
38 COST( 0.4e3, rim_proximity_cost(vs->a));
39 COST( 1e6, edge_angle_cost(vs->a, 0.5/1.7));
40 // COST( 1e1, small_triangles_cost(vs->a));
41 COST( 1e12, noncircular_rim_cost(vs->a));
43 } else if (XBITS==4) {
44 COST( 3e5, line_bending_cost(vs->a));
45 COST( 10e2, edge_length_variation_cost(vs->a));
46 COST( 9.0e1, rim_proximity_cost(vs->a)); // 5e1 is too much
47 // 2.5e1 is too little
48 // 0.2e1 grows compared to previous ?
49 // 0.6e0 shrinks compared to previous ?
50 COST( 1e12, edge_angle_cost(vs->a, 0.5/1.3));
51 COST( 1e18, noncircular_rim_cost(vs->a));
57 if (printing) printf("| total %# e |", energy);
59 if (energy < best_energy) {
65 if (bests_unprinted) printf(" [%4d]",bests_unprinted);
71 best_f= fopen(best_file_tmp,"wb"); if (!best_f) diee("fopen new out");
72 r= fwrite(vs->a,sizeof(vs->a),1,best_f); if (r!=1) diee("fwrite");
73 if (fclose(best_f)) diee("fclose new best");
74 if (rename(best_file_tmp,best_file)) diee("rename install new best");
87 static void addcost(double *energy, double tweight, double tcost, int pr) {
88 double tenergy= tweight * tcost;
89 if (pr) printf(" %# e x %g > %# e* |", tcost, tweight, tenergy);
93 /*---------- Precomputations ----------*/
95 void compute_edge_lengths(const Vertices vertices) {
99 edge_lengths[v1][e]= hypotD(vertices[v1],vertices[v2]);
102 void compute_vertex_areas(const Vertices vertices) {
107 double total= 0.0, edges_total=0;
110 FOR_VEDGE(v0,e1,v1) {
112 v2= EDGE_END2(v0,e2);
115 edges_total += edge_lengths[v0][e1];
117 // double e1v[D3], e2v[D3], av[D3];
119 // e1v[k]= vertices[v1][k] - vertices[v0][k];
120 // e2v[k]= vertices[v2][k] - vertices[v0][k];
122 // xprod(av, e1v, e2v);
123 // total += magnD(av);
127 vertex_areas[v0]= total / count;
128 vertex_mean_edge_lengths[v0]= edges_total / count;
132 /*---------- Edgewise vertex displacement ----------*/
137 * At each vertex Q, in each direction e:
146 * cost = delta (we use r=3)
156 * delta = tan -------
159 * which is always in the range 0..pi because the denominator
160 * is nonnegative. We add epsilon to |AxB| to avoid division
168 double line_bending_cost(const Vertices vertices) {
169 static const double axb_epsilon= 1e-6;
170 static const double exponent_r= 4;
173 double a[D3], b[D3], axb[D3];
174 double total_cost= 0;
177 pi= EDGE_END2(qi,(e+3)%V6); if (pi<0) continue;
179 //if (!(qi&XMASK)) fprintf(stderr,"%02x-%02x-%02x (%d)\n",pi,qi,ri,e);
181 K a[k]= -vertices[pi][k] + vertices[qi][k];
182 K b[k]= -vertices[qi][k] + vertices[ri][k];
186 double delta= atan2(magnD(axb) + axb_epsilon, dotprod(a,b));
187 double cost= pow(delta,exponent_r);
194 /*---------- edge length variation ----------*/
199 * See the diagram above.
201 * cost = ( |PQ| - |QR| )
205 double edge_length_variation_cost(const Vertices vertices) {
206 double diff, cost= 0, exponent_r= 2;
210 eback= edge_reverse(q,e);
211 diff= edge_lengths[q][e] - edge_lengths[q][eback];
212 cost += pow(diff,exponent_r);
217 /*---------- rim proximity cost ----------*/
219 static void find_nearest_oncircle(double oncircle[D3], const double p[D3]) {
220 /* By symmetry, nearest point on circle is the one with
221 * the same angle subtended at the z axis. */
225 double mult= 1.0/ magnD(oncircle);
230 double rim_proximity_cost(const Vertices vertices) {
231 double oncircle[3], cost=0;
236 int nominal_edge_distance= y <= Y/2 ? y : Y-1-y;
237 if (nominal_edge_distance==0) continue;
239 find_nearest_oncircle(oncircle, vertices[v]);
242 vertex_mean_edge_lengths[v] *
243 (nominal_edge_distance*nominal_edge_distance) /
244 (hypotD2(vertices[v], oncircle) + 1e-6);
249 /*---------- noncircular rim cost ----------*/
251 double noncircular_rim_cost(const Vertices vertices) {
256 FOR_RIM_VERTEX(vy,vx,v) {
257 find_nearest_oncircle(oncircle, vertices[v]);
259 double d2= hypotD2(vertices[v], oncircle);
265 /*---------- overly sharp edge cost ----------*/
270 * / | `-_ P'Q' ------ S'
283 * Let delta = angle between two triangles' normals
285 * Giving energy contribution:
292 double edge_angle_cost(const Vertices vertices, double circcircrat) {
293 double pq1[D3], rp[D3], ps[D3], rp_2d[D3], ps_2d[D3], rs_2d[D3];
295 const double minradius_base= 0.2;
297 int pi,e,qi,ri,si, k;
298 // double our_epsilon=1e-6;
299 double total_cost= 0;
302 // if (!(RIM_VERTEX_P(pi) || RIM_VERTEX_P(qi))) continue;
304 si= EDGE_END2(pi,(e+V6-1)%V6); if (si<0) continue;
305 ri= EDGE_END2(pi,(e +1)%V6); if (ri<0) continue;
308 pq1[k]= -vertices[pi][k] + vertices[qi][k];
309 rp[k]= -vertices[ri][k] + vertices[pi][k];
310 ps[k]= -vertices[pi][k] + vertices[si][k];
313 normalise(pq1,1,1e-6);
314 xprod(rp_2d, rp,pq1); /* projects RP into plane normal to PQ */
315 xprod(ps_2d, ps,pq1); /* likewise PS */
316 K rs_2d[k]= rp_2d[k] + ps_2d[k];
317 /* radius of circumcircle of R'P'S' from Wikipedia
318 * `Circumscribed circle' */
323 r= a*b*c / sqrt((a+b+c)*(a-b+c)*(b-c+a)*(c-a+b) + 1e-6);
325 double minradius= minradius_base + circcircrat*(a+b);
326 double deficit= minradius - r;
327 if (deficit < 0) continue;
328 double cost= deficit*deficit;
336 /*---------- small triangles cost ----------*/
352 * Let delta = angle between two triangles' normals
354 * Giving energy contribution:
361 double small_triangles_cost(const Vertices vertices) {
362 double pq[D3], ps[D3];
365 // double our_epsilon=1e-6;
366 double total_cost= 0;
369 // if (!(RIM_VERTEX_P(pi) || RIM_VERTEX_P(qi))) continue;
371 si= EDGE_END2(pi,(e+V6-1)%V6); if (si<0) continue;
374 pq[k]= vertices[qi][k] - vertices[pi][k];
375 ps[k]= vertices[si][k] - vertices[pi][k];
379 double cost= 1/(magnD2(x) + 0.01);
381 //double cost= pow(magnD(spqxpqr), 3);
382 //assert(dot>=-1 && dot <=1);
383 //double cost= 1-dot;