static const char *input_file, *output_file;
static char *output_file_tmp;
-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;
printf("cost > energy |");
COST(1e4, edgewise_vertex_displacement_cost(vertices));
- COST(1e2, graph_layout_cost(vertices,vertex_areas));
- COST(1e4, noncircular_rim_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 (fclose(best_f)) diee("fclose new best");
flushoutput();
return energy;
-}
+}
static void addcost(double *energy, double tweight, double tcost) {
double tenergy= tweight * tcost;
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;
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];
* 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 ...
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); }
GA( gsl_multimin_fminimizer_set(minimiser, &multimin_function,
&initial_gsl, &step_size_gsl) );
-
+
for (;;) {
GA( gsl_multimin_fminimizer_iterate(minimiser) );
/*---------- Edgewise vertex displacement ----------*/
/*
- *
+ *
*
*
* Q `-_
* / | `-_
- * R' - _ _ _/_ | `-.
- * . / M - - - - - S
- * . / | _,-'
- * . / | _,-'
- * . / , P '
- * . / ,-'
- * . /,-'
- * . /'
+ * / | `-.
+ * / M - - - - - S
+ * / ' | _,-'
+ * / ' | _,-'
+ * / ' , P '
+ * / ',-'
+ * /,-'
+ * /'
* R
*
+ * Let delta = 180deg - angle RMS
*
- *
- * Find R', the `expected' location of R, by
- * reflecting S in M (the midpoint of QP).
- *
- * Let 2d = |RR'|
- * b = |PQ|
- * l = |RS|
+ * Let l = |PQ|
+ * d = |RS|
*
* Giving energy contribution:
*
- * 2
- * b d
- * E = F . ----
- * vd, edge PQ vd 3
- * l
+ * 2
+ * l delta
+ * E = F . --------
+ * vd, edge PQ vd d
*
- * (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 - '
+ * (The dimensions of this are those of F_vd.)
*
- * 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.
+ * We calculate delta as atan2(|AxB|, A.B)
+ * where A = RM, B = MS
*
- * 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.
+ * In practice to avoid division by zero we'll add epsilon to d and
+ * |AxB| and the huge energy ought then to be sufficient for the
+ * model to avoid being close to R=S.
*/
-static double edgewise_vertex_displacement_cost(const Vertices vertices) {
- static const double l3_epsilon= 1e-6;
+double edgewise_vertex_displacement_cost(const Vertices vertices) {
+ static const double /*d_epsilon= 1e-6,*/ axb_epsilon= 1e-6;
int pi,e,qi,ri,si, k;
- double m[D3], mprime[D3], b, d2, l, sigma_bd2_l3=0;
+ double m[D3], 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;
+ K a[k]= -vertices[ri][k] + m[k];
+ K b[k]= -m[k] + vertices[si][k];
+
+ xprod(axb,a,b);
+
+ double l= 1; //hypotD(vertices[pi], vertices[qi]);
+ double d= 1; //hypotD(vertices[ri], vertices[si]) + d_epsilon;
+ double delta= atan2(magnD(axb) + axb_epsilon, dotprod(a,b));
+
+ double cost= l * delta * delta / d;
- sigma_bd2_l3 += b * d2 / l3;
+ total_cost += cost;
}
- return sigma_bd2_l3;
+ return total_cost;
}
/*---------- noncircular rim cost ----------*/
-static double noncircular_rim_cost(const Vertices vertices) {
+double noncircular_rim_cost(const Vertices vertices) {
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
~ian / moebius2.git / commitdiff