*/
#include "common.h"
-#include "bgl.h"
+#include "minimise.h"
#include "mgraph.h"
+#include "parallel.h"
-#include <gsl/gsl_errno.h>
-#include <gsl/gsl_multimin.h>
+double vertex_mean_edge_lengths[N];
-static const char *input_file, *output_file;
-static char *output_file_tmp;
+static double vertex_areas[N];
+static double edge_lengths[N][V6];
+static double rim_vertex_angles[N];
-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);
+
+/*---------- main energy computation, weights, etc. ----------*/
+
+typedef double CostComputation(const Vertices vertices, int section);
+typedef void PreComputation(const Vertices vertices, int section);
+
+typedef struct {
+ double weight;
+ CostComputation *fn;
+} CostContribution;
+
+#define NPRECOMPS ((sizeof(precomps)/sizeof(precomps[0])))
+#define NCOSTS ((sizeof(costs)/sizeof(costs[0])))
+#define COST(weight, compute) { (weight),(compute) },
+
+static PreComputation *const precomps[]= {
+ compute_edge_lengths,
+ compute_vertex_areas,
+ compute_rim_twist_angles
+};
+
+static const CostContribution costs[]= {
+
+#if XBITS==3
+#define STOP_EPSILON 1e-6
+ COST( 3e3, vertex_displacement_cost)
+ COST( 0.4e3, rim_proximity_cost)
+ COST( 1e7, edge_angle_cost)
+ #define EDGE_ANGLE_COST_CIRCCIRCRAT (0.2/1.7)
+ COST( 1e2, small_triangles_cost)
+ COST( 1e12, noncircular_rim_cost)
+#endif
+
+#if XBITS==4
+#define STOP_EPSILON 5e-3
+ COST( 3e4, vertex_displacement_cost) // NB this is probably wrong now
+ COST( 3e4, vertex_edgewise_displ_cost) // we have changed the power
+ COST( 0.2e3, rim_proximity_cost)
+ COST( 1e4, rim_twist_cost)
+ COST( 1e12, noncircular_rim_cost)
+ COST( 10e1, nonequilateral_triangles_cost)
+// COST( 1e1, small_triangles_cost)
+// COST( 1e6, edge_angle_cost)
+ #define EDGE_ANGLE_COST_CIRCCIRCRAT (0.5/1.7)
+#endif
+
+#if XBITS==5
+#define STOP_EPSILON 1e-5
+ COST( 3e4, vertex_displacement_cost)
+ COST( 3e4, vertex_edgewise_displ_cost)
+ COST( 2e-1, rim_proximity_cost)
+ COST( 3e3, rim_twist_cost)
+ COST( 1e12, noncircular_rim_cost)
+ COST( 3e2, nonequilateral_triangles_cost)
+// COST( 1e1, small_triangles_cost)
+// COST( 1e6, edge_angle_cost)
+ #define EDGE_ANGLE_COST_CIRCCIRCRAT (0.5/1.7)
+#endif
+
+#if XBITS==6
+#define STOP_EPSILON 1.2e-4
+ COST( 3e3, vertex_displacement_cost)
+ COST( 3e3, vertex_edgewise_displ_cost)
+ COST( 0.02e0, rim_proximity_cost)
+ COST( 1e4, rim_twist_cost)
+ COST( 1e12, noncircular_rim_cost)
+ COST( 10e1, nonequilateral_triangles_cost)
+// COST( 1e1, small_triangles_cost)
+// COST( 1e6, edge_angle_cost)
+ #define EDGE_ANGLE_COST_CIRCCIRCRAT (0.5/1.7)
+#endif
+
+#if XBITS>=7 /* nonsense follows but never mind */
+#define STOP_EPSILON 1e-6
+ COST( 3e5, line_bending_cost)
+ COST( 10e2, edge_length_variation_cost)
+ COST( 9.0e1, rim_proximity_cost) // 5e1 is too much
+ // 2.5e1 is too little
+ // 0.2e1 grows compared to previous ?
+ // 0.6e0 shrinks compared to previous ?
+
+ COST( 1e12, edge_angle_cost)
+ #define EDGE_ANGLE_COST_CIRCCIRCRAT (0.5/1.3)
+ COST( 1e18, noncircular_rim_cost)
+#endif
+
+};
+
+const double edge_angle_cost_circcircrat= EDGE_ANGLE_COST_CIRCCIRCRAT;
+
+void energy_init(void) {
+ stop_epsilon= STOP_EPSILON;
+}
+
+/*---------- energy computation machinery ----------*/
+
+void compute_energy_separately(const struct Vertices *vs,
+ int section, void *energies_v, void *totals_v) {
+ double *energies= energies_v;
+ int ci;
+
+ for (ci=0; ci<NPRECOMPS; ci++) {
+ precomps[ci](vs->a, section);
+ inparallel_barrier();
+ }
+ for (ci=0; ci<NCOSTS; ci++)
+ energies[ci]= costs[ci].fn(vs->a, section);
+}
+
+void compute_energy_combine(const struct Vertices *vertices,
+ int section, void *energies_v, void *totals_v) {
+ int ci;
+ double *energies= energies_v;
+ double *totals= totals_v;
+
+ for (ci=0; ci<NCOSTS; ci++)
+ totals[ci] += energies[ci];
+}
+
+double compute_energy(const struct Vertices *vs) {
+ static int bests_unprinted;
-/*---------- main energy computation and subroutines ----------*/
+ double totals[NCOSTS], energy;
+ int ci, printing;
-static double compute_energy(const Vertices vertices) {
- double vertex_areas[N], energy;
+ printing= printing_check(pr_cost,0);
+
+ if (printing) printf("%15lld c>e |", evaluations);
+
+ for (ci=0; ci<NCOSTS; ci++)
+ totals[ci]= 0;
+
+ inparallel(vs,
+ compute_energy_separately,
+ compute_energy_combine,
+ sizeof(totals) /* really, size of energies */,
+ totals);
- compute_vertex_areas(vertices,vertex_areas);
energy= 0;
- printf("cost > energy |");
+ for (ci=0; ci<NCOSTS; ci++)
+ addcost(&energy, costs[ci].weight, totals[ci], printing);
+
+ if (printing) printf("| total %# e |", 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);
if (energy < best_energy) {
FILE *best_f;
int r;
-
- 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");
+
+ if (printing) {
+ printf(" BEST");
+ if (bests_unprinted) printf(" [%4d]",bests_unprinted);
+ bests_unprinted= 0;
+ } else {
+ bests_unprinted++;
+ }
+
+ best_f= fopen(best_file_tmp,"wb"); if (!best_f) diee("fopen new out");
+ 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");
+ if (rename(best_file_tmp,best_file)) diee("rename install new best");
best_energy= energy;
}
- putchar('\n');
- flushoutput();
+ if (printing) {
+ putchar('\n');
+ flushoutput();
+ }
+ evaluations++;
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;
-
- FOR_VERTEX(v0) {
- double total= 0.0;
+/*---------- Precomputations ----------*/
+
+void compute_edge_lengths(const Vertices vertices, int section) {
+ int v1,e,v2;
+
+ FOR_EDGE(v1,e,v2, OUTER)
+ edge_lengths[v1][e]= hypotD(vertices[v1],vertices[v2]);
+}
+
+void compute_vertex_areas(const Vertices vertices, int section) {
+ int v0,v1,v2, e1,e2;
+// int k;
+
+ FOR_VERTEX(v0, OUTER) {
+ 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;
-
- double e1v[D3], e2v[D3], av[D3];
- K {
- e1v[k]= vertices[v1][k] - vertices[v0][k];
- e2v[k]= vertices[v2][k] - vertices[v0][k];
- }
- xprod(av, e1v, e2v);
- total += magnD(av);
+
+ edges_total += edge_lengths[v0][e1];
+
+// double e1v[D3], e2v[D3], av[D3];
+// K {
+// e1v[k]= vertices[v1][k] - vertices[v0][k];
+// e2v[k]= vertices[v2][k] - vertices[v0][k];
+// }
+// xprod(av, e1v, e2v);
+// total += magnD(av);
+
count++;
}
- areas[v0]= total / count;
+ vertex_areas[v0]= total / count;
+ vertex_mean_edge_lengths[v0]= edges_total / count;
}
}
-/*---------- use of GSL ----------*/
+/*---------- displacement of vertices across a midpoint ----------*/
- /* We want to do multidimensional minimisation.
+ /*
+ * Subroutine used where we have
+ *
+ * R - - - - - - - M . - - - - R'
+ * ` .
+ * ` .
+ * S
+ *
+ * and wish to say that the vector RM should be similar to MS
+ * or to put it another way S = M + RM
+ *
+ * NB this is not symmetric wrt R and S since it divides by
+ * |SM| but not |RM| so you probably want to call it twice.
*
- * 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.
+ * Details:
*
- * 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).
+ * Let R' = M + SM
+ * D = R' - R
*
- * This eliminates most of the algorithms. Nelder and Mead's
- * simplex algorithm is still available and we will try that.
+ * Then the (1/delta)th power of the cost is
+ * proportional to |D|, and
+ * inversely proportional to |SM|
+ * except that |D| is measured in a wierd way which counts
+ * distance in the same direction as SM 1/lambda times as much
+ * ie the equipotential surfaces are ellipsoids around R',
+ * lengthened by lambda in the direction of RM.
+ *
+ * So
+ * delta
+ * [ -1 ]
+ * cost = [ lambda . ( D . SM/|SM| ) + | D x SM/|SM| | ]
+ * R,S,M [ ------------------------------------------- ]
+ * [ |SM| ]
*
- * 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 double vertex_one_displ_cost(const double r[D3], const double s[D3],
+ const double midpoint[D3],
+ double delta, double inv_lambda) {
+ const double smlen2_epsilon= 1e-12;
+ double sm[D3], d[D3], ddot, dcross[D3];
+ int k;
+
+ K sm[k]= -s[k] + midpoint[k];
+ K d[k]= midpoint[k] + sm[k] - r[k];
+ ddot= dotprod(d,sm);
+ xprod(dcross, d,sm);
+ double smlen2= magnD2(sm);
+ double cost_basis= inv_lambda * ddot + magnD(dcross);
+ double cost= pow(cost_basis / (smlen2 + smlen2_epsilon), delta);
-static const double stop_epsilon= 1e-4;
+ return cost;
+}
-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);
+/*---------- displacement of vertices opposite at a vertex ----------*/
+
+ /*
+ * At vertex Q considering edge direction e to R
+ * and corresponding opposite edge to S.
+ *
+ * This is vertex displacement as above with M=Q
+ */
+
+double vertex_displacement_cost(const Vertices vertices, int section) {
+ const double inv_lambda= 1.0/1; //2;
+ const double delta= 6;
+
+ int si,e,qi,ri;
+ double total_cost= 0;
+
+ FOR_EDGE(qi,e,ri, OUTER) {
+ si= EDGE_END2(qi,(e+3)%V6); if (si<0) continue;
+
+ total_cost += vertex_one_displ_cost(vertices[ri], vertices[si], vertices[qi],
+ delta, inv_lambda);
+ }
+ return total_cost;
}
-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) );
+/*---------- displacement of vertices opposite at an edge ----------*/
+
+ /*
+ * At edge PQ considering vertices R and S (see diagram
+ * below for overly sharp edge cost).
+ *
+ * Let M = midpoint of PQ
+ */
- size= gsl_multimin_fminimizer_size(minimiser);
- r= gsl_multimin_test_size(size, stop_epsilon);
+double vertex_edgewise_displ_cost(const Vertices vertices, int section) {
+ const double inv_lambda= 1.0/1; //2;
+ const double delta= 6;
- printf("%*s size %# e, r=%d\n", 135,"", size, r);
- flushoutput();
+ int pi,e,qi,ri,si, k;
+ double m[D3];
+ double total_cost= 0;
+
+ FOR_EDGE(pi,e,qi, OUTER) {
+ si= EDGE_END2(pi,(e+V6-1)%V6); if (si<0) continue;
+ ri= EDGE_END2(pi,(e +1)%V6); if (ri<0) continue;
- if (r==GSL_SUCCESS) break;
- assert(r==GSL_CONTINUE);
+ K m[k]= 0.5 * (vertices[pi][k] + vertices[qi][k]);
+
+ total_cost += vertex_one_displ_cost(vertices[ri], vertices[si], m,
+ delta, inv_lambda);
}
- return 0;
+ return total_cost;
}
-/*---------- Edgewise vertex displacement ----------*/
+
+/*---------- at-vertex edge angles ----------*/
/*
- *
+ * Definition:
*
+ * At each vertex Q, in each direction e:
*
- * Q `-_
- * / | `-_
- * R' - _ _ _/_ | `-.
- * . / M - - - - - S
- * . / | _,-'
- * . / | _,-'
- * . / , P '
- * . / ,-'
- * . /,-'
- * . /'
- * R
+ * e
+ * Q ----->----- R
+ * _,-'\__/
+ * _,-' delta
+ * P '
*
+ * r
+ * cost = delta (we use r=3)
+ * Q,e
*
*
- * Find R', the `expected' location of R, by
- * reflecting S in M (the midpoint of QP).
+ * Calculation:
*
- * Let 2d = |RR'|
- * b = |PQ|
- * l = |RS|
+ * Let vector A = PQ
+ * B = QR
*
- * Giving energy contribution:
+ * -1 A . B
+ * delta = tan -------
+ * | A x B |
+ *
+ * which is always in the range 0..pi because the denominator
+ * is nonnegative. We add epsilon to |AxB| to avoid division
+ * by zero.
*
- * 2
- * b d
- * E = F . ----
- * vd, edge PQ vd 3
- * l
- *
- * (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:
- *
- *
- * 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.
- *
- * 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.
+ * r
+ * cost = delta
+ * Q,e
*/
-static double edgewise_vertex_displacement_cost(const Vertices vertices) {
- static const double l3_epsilon= 1e-6;
+double line_bending_cost(const Vertices vertices, int section) {
+ static const double axb_epsilon= 1e-6;
+ static const double exponent_r= 4;
- 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;
+ double a[D3], b[D3], axb[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;
-
- 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;
+ FOR_EDGE(qi,e,ri, OUTER) {
+ pi= EDGE_END2(qi,(e+3)%V6); if (pi<0) continue;
+
+//if (!(qi&XMASK)) fprintf(stderr,"%02x-%02x-%02x (%d)\n",pi,qi,ri,e);
+
+ K a[k]= -vertices[pi][k] + vertices[qi][k];
+ K b[k]= -vertices[qi][k] + vertices[ri][k];
+
+ xprod(axb,a,b);
+
+ double delta= atan2(magnD(axb) + axb_epsilon, dotprod(a,b));
+ double cost= pow(delta,exponent_r);
+
+ total_cost += cost;
+ }
+ return total_cost;
+}
+
+/*---------- edge length variation ----------*/
+
+ /*
+ * Definition:
+ *
+ * See the diagram above.
+ * r
+ * cost = ( |PQ| - |QR| )
+ * Q,e
+ */
+
+double edge_length_variation_cost(const Vertices vertices, int section) {
+ double diff, cost= 0, exponent_r= 2;
+ int q, e,r, eback;
+
+ FOR_EDGE(q,e,r, OUTER) {
+ eback= edge_reverse(q,e);
+ diff= edge_lengths[q][e] - edge_lengths[q][eback];
+ cost += pow(diff,exponent_r);
+ }
+ return cost;
+}
+
+/*---------- proportional edge length variation ----------*/
+
+ /*
+ * Definition:
+ *
+ * See the diagram above.
+ * r
+ * cost = ( |PQ| - |QR| )
+ * Q,e
+ */
+
+double prop_edge_length_variation_cost(const Vertices vertices, int section) {
+ const double num_epsilon= 1e-6;
+
+ double cost= 0, exponent_r= 2;
+ int q, e,r, eback;
+
+ FOR_EDGE(q,e,r, OUTER) {
+ eback= edge_reverse(q,e);
+ double le= edge_lengths[q][e];
+ double leback= edge_lengths[q][eback];
+ double diff= le - leback;
+ double num= MIN(le, leback);
+ cost += pow(diff / (num + num_epsilon), exponent_r);
+ }
+ return cost;
+}
+
+/*---------- rim proximity cost ----------*/
+
+static void find_nearest_oncircle(double oncircle[D3], const double p[D3]) {
+ /* By symmetry, nearest point on circle is the one with
+ * the same angle subtended at the z axis. */
+ oncircle[0]= p[0];
+ oncircle[1]= p[1];
+ oncircle[2]= 0;
+ double mult= 1.0/ magnD(oncircle);
+ oncircle[0] *= mult;
+ oncircle[1] *= mult;
+}
+
+double rim_proximity_cost(const Vertices vertices, int section) {
+ double oncircle[D3], cost=0;
+ int v;
+
+ FOR_VERTEX(v, OUTER) {
+ int y= v >> YSHIFT;
+ int nominal_edge_distance= y <= Y/2 ? y : Y-1-y;
+ if (nominal_edge_distance==0) continue;
+
+ find_nearest_oncircle(oncircle, vertices[v]);
+
+ cost +=
+ vertex_mean_edge_lengths[v] *
+ (nominal_edge_distance*nominal_edge_distance) /
+ (hypotD2(vertices[v], oncircle) + 1e-6);
}
- return sigma_bd2_l3;
+ return cost;
}
/*---------- noncircular rim cost ----------*/
-static double noncircular_rim_cost(const Vertices vertices) {
+double noncircular_rim_cost(const Vertices vertices, int section) {
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
- * the same angle subtended at the z axis. */
- oncircle[0]= vertices[v][0];
- oncircle[1]= vertices[v][1];
- oncircle[2]= 0;
- double mult= 1.0/ magnD(oncircle);
- oncircle[0] *= mult;
- oncircle[1] *= mult;
+ double oncircle[3];
+
+ FOR_RIM_VERTEX(vy,vx,v, OUTER) {
+ find_nearest_oncircle(oncircle, vertices[v]);
+
double d2= hypotD2(vertices[v], oncircle);
cost += d2*d2;
}
return cost;
}
+
+/*---------- rim contact angle rotation ----------*/
+
+void compute_rim_twist_angles(const Vertices vertices, int section) {
+ double oncircle[D3], distance[D3];
+ int vpy,vpx,v,k;
+
+ FOR_NEAR_RIM_VERTEX(vpy,vpx,v, 1,OUTER) {
+ find_nearest_oncircle(oncircle, vertices[v]);
+ /* we are interested in the angle subtended at the rim, from the
+ * rim's point of view. */
+ K distance[k]= vertices[v][k] - oncircle[k];
+ double distance_positive_z= distance[3];
+ double distance_radial_outwards= dotprod(distance, oncircle);
+ rim_vertex_angles[v]= atan2(distance_positive_z, distance_radial_outwards);
+ }
+}
+
+double rim_twist_cost(const Vertices vertices, int section) {
+ double total_cost= 0;
+ int vpy,vpx,v0,v1;
+
+ FOR_NEAR_RIM_VERTEX(vpy,vpx,v0, 1,OUTER) {
+ v1= EDGE_END2(v0,0); assert(v1!=0);
+ double delta= rim_vertex_angles[v0] - rim_vertex_angles[v1];
+ if (delta < M_PI) delta += 2*M_PI;
+ if (delta > M_PI) delta -= 2*M_PI;
+
+ double cost= pow(delta, 4);
+ total_cost += cost;
+ }
+
+ return total_cost;
+}
+
+/*---------- overly sharp edge cost ----------*/
+
+ /*
+ *
+ * Q `-_
+ * / | `-_ P'Q' ------ S'
+ * / | `-. _,' `. .
+ * / | S _,' : .
+ * / | _,-' _,' :r .r
+ * / | _,-' R' ' `. .
+ * / , P ' ` . r : .
+ * / ,-' ` . :
+ * /,-' ` C'
+ * /'
+ * R
+ *
+ *
+ *
+ * Let delta = angle between two triangles' normals
+ *
+ * Giving energy contribution:
+ *
+ * 2
+ * E = F . delta
+ * vd, edge PQ vd
+ */
+
+double edge_angle_cost(const Vertices vertices, int section) {
+ double pq1[D3], rp[D3], ps[D3], rp_2d[D3], ps_2d[D3], rs_2d[D3];
+ double a,b,c,s,r;
+ const double minradius_base= 0.2;
+
+ int pi,e,qi,ri,si, k;
+// double our_epsilon=1e-6;
+ double total_cost= 0;
+
+ FOR_EDGE(pi,e,qi, OUTER) {
+// if (!(RIM_VERTEX_P(pi) || RIM_VERTEX_P(qi))) continue;
+
+ si= EDGE_END2(pi,(e+V6-1)%V6); if (si<0) continue;
+ ri= EDGE_END2(pi,(e +1)%V6); if (ri<0) continue;
+
+ K {
+ pq1[k]= -vertices[pi][k] + vertices[qi][k];
+ rp[k]= -vertices[ri][k] + vertices[pi][k];
+ ps[k]= -vertices[pi][k] + vertices[si][k];
+ }
+
+ normalise(pq1,1,1e-6);
+ xprod(rp_2d, rp,pq1); /* projects RP into plane normal to PQ */
+ xprod(ps_2d, ps,pq1); /* likewise PS */
+ K rs_2d[k]= rp_2d[k] + ps_2d[k];
+ /* radius of circumcircle of R'P'S' from Wikipedia
+ * `Circumscribed circle' */
+ a= magnD(rp_2d);
+ b= magnD(ps_2d);
+ c= magnD(rs_2d);
+ s= 0.5*(a+b+c);
+ r= a*b*c / sqrt((a+b+c)*(a-b+c)*(b-c+a)*(c-a+b) + 1e-6);
+
+ double minradius= minradius_base + edge_angle_cost_circcircrat*(a+b);
+ double deficit= minradius - r;
+ if (deficit < 0) continue;
+ double cost= deficit*deficit;
+
+ total_cost += cost;
+ }
+
+ return total_cost;
+}
+
+/*---------- small triangles cost ----------*/
+
+ /*
+ * Consider a triangle PQS
+ *
+ * Cost is 1/( area^2 )
+ */
+
+double small_triangles_cost(const Vertices vertices, int section) {
+ double pq[D3], ps[D3];
+ double x[D3];
+ int pi,e,qi,si, k;
+// double our_epsilon=1e-6;
+ double total_cost= 0;
+
+ FOR_EDGE(pi,e,qi, OUTER) {
+// if (!(RIM_VERTEX_P(pi) || RIM_VERTEX_P(qi))) continue;
+
+ si= EDGE_END2(pi,(e+V6-1)%V6); if (si<0) continue;
+
+ K {
+ pq[k]= vertices[qi][k] - vertices[pi][k];
+ ps[k]= vertices[si][k] - vertices[pi][k];
+ }
+ xprod(x, pq,ps);
+
+ double cost= 1/(magnD2(x) + 0.01);
+
+//double cost= pow(magnD(spqxpqr), 3);
+//assert(dot>=-1 && dot <=1);
+//double cost= 1-dot;
+ total_cost += cost;
+ }
+
+ return total_cost;
+}
+
+/*---------- nonequilateral triangles cost ----------*/
+
+ /*
+ * Consider a triangle PQR
+ *
+ * let edge lengths a=|PQ| b=|QR| c=|RP|
+ *
+ * predicted edge length p = 1/3 * (a+b+c)
+ *
+ * compute cost for each x in {a,b,c}
+ *
+ *
+ * cost = (x-p)^2 / p^2
+ * PQR,x
+ */
+
+double nonequilateral_triangles_cost(const Vertices vertices, int section) {
+ double pr[D3], abc[3];
+ int pi,e0,e1,qi,ri, k,i;
+ double our_epsilon=1e-6;
+ double total_cost= 0;
+
+ FOR_EDGE(pi,e0,qi, OUTER) {
+ e1= (e0+V6-1)%V6;
+ ri= EDGE_END2(pi,e1); if (ri<0) continue;
+
+ K pr[k]= -vertices[pi][k] + vertices[ri][k];
+
+ abc[0]= edge_lengths[pi][e0]; /* PQ */
+ abc[1]= edge_lengths[qi][e1]; /* QR */
+ abc[2]= magnD(pr);
+
+ double p= (1/3.0) * (abc[0]+abc[1]+abc[2]);
+ double p_inv2= 1/(p*p + our_epsilon);
+
+ for (i=0; i<3; i++) {
+ double diff= (abc[i] - p);
+ double cost= diff*diff * p_inv2;
+ total_cost += cost;
+ }
+ }
+
+ return total_cost;
+}
~ian / moebius2.git / blobdiff