2 * We try to find an optimal triangle grid
9 #include <gsl/gsl_errno.h>
10 #include <gsl/gsl_multimin.h>
12 static const char *input_file, *output_file;
13 static char *output_file_tmp;
15 static void compute_vertex_areas(const Vertices vertices, double areas[N]);
16 static double best_energy= DBL_MAX;
18 static void addcost(double *energy, double tweight, double tcost);
19 #define COST(weight, compute) addcost(&energy, (weight), (compute))
21 /*---------- main energy computation and subroutines ----------*/
23 static double compute_energy(const Vertices vertices) {
24 double vertex_areas[N], energy;
26 compute_vertex_areas(vertices,vertex_areas);
28 printf("cost > energy |");
30 COST(1e4, edgewise_vertex_displacement_cost(vertices));
31 // COST(1e2, graph_layout_cost(vertices,vertex_areas));
32 // COST(1e4, noncircular_rim_cost(vertices));
34 printf("| total %# e |", energy);
35 if (energy < best_energy) {
41 best_f= fopen(output_file_tmp,"wb"); if (!best_f) diee("fopen new out");
42 r= fwrite(vertices,sizeof(Vertices),1,best_f); if (r!=1) diee("fwrite");
43 if (fclose(best_f)) diee("fclose new best");
44 if (rename(output_file_tmp,output_file)) diee("rename install new best");
54 static void addcost(double *energy, double tweight, double tcost) {
55 double tenergy= tweight * tcost;
56 printf(" %# e > %# e |", tcost, tenergy);
60 static void compute_vertex_areas(const Vertices vertices, double areas[N]) {
61 int v0,v1,v2, e1,e2, k;
72 double e1v[D3], e2v[D3], av[D3];
74 e1v[k]= vertices[v1][k] - vertices[v0][k];
75 e2v[k]= vertices[v2][k] - vertices[v0][k];
81 areas[v0]= total / count;
85 /*---------- use of GSL ----------*/
87 /* We want to do multidimensional minimisation.
89 * We don't think there are any local minima. Or at least, if there
90 * are, the local minimum which will be found from the starting
91 * state is the one we want.
93 * We don't want to try to provide a derivative of the cost
94 * function. That's too tedious (and anyway the polynomial
95 * approximation to our our cost function sometimes has high degree
96 * in the inputs which means the quadratic model implied by most of
97 * the gradient descent minimisers is not ideal).
99 * This eliminates most of the algorithms. Nelder and Mead's
100 * simplex algorithm is still available and we will try that.
102 * In our application we are searching for the optimal locations of
103 * N actualvertices in D3 (3) dimensions - ie, we are searching for
104 * the optimal metapoint in an N*D3-dimensional space.
106 * So eg with X=Y=100, the simplex will contain 300 metavertices
107 * each of which is an array of 300 doubles for the actualvertex
108 * coordinates. Hopefully this won't be too slow ...
111 static gsl_multimin_fminimizer *minimiser;
113 static const double stop_epsilon= 1e-4;
115 static double minfunc_f(const gsl_vector *x, void *params) {
116 assert(x->size == DIM);
117 assert(x->stride == 1);
118 return compute_energy((const double(*)[D3])x->data);
121 int main(int argc, const char *const *argv) {
122 gsl_multimin_function multimin_function;
124 Vertices initial, step_size;
126 gsl_vector initial_gsl, step_size_gsl;
129 if (argc!=3 || argv[1][0]=='-' || strncmp(argv[2],"-o",2))
130 { fputs("usage: minimise <input> -o<output\n",stderr); exit(8); }
133 output_file= argv[2]+2;
134 if (asprintf(&output_file_tmp,"%s.new",output_file) <= 0) diee("asprintf");
136 minimiser= gsl_multimin_fminimizer_alloc
137 (gsl_multimin_fminimizer_nmsimplex, DIM);
138 if (!minimiser) { perror("alloc minimiser"); exit(-1); }
140 multimin_function.f= minfunc_f;
141 multimin_function.n= DIM;
142 multimin_function.params= 0;
144 initial_f= fopen(input_file,"rb"); if (!initial_f) diee("fopen initial");
145 errno= 0; r= fread(initial,sizeof(initial),1,initial_f);
146 if (r!=1) diee("fread");
149 initial_gsl.size= DIM;
150 initial_gsl.stride= 1;
151 initial_gsl.block= 0;
152 initial_gsl.owner= 0;
153 step_size_gsl= initial_gsl;
155 initial_gsl.data= &initial[0][0];
156 step_size_gsl.data= &step_size[0][0];
159 K step_size[v][k]= 0.03;
161 // FOR_RIM_VERTEX(vx,vy,v)
162 // step_size[v][3] *= 0.1;
164 GA( gsl_multimin_fminimizer_set(minimiser, &multimin_function,
165 &initial_gsl, &step_size_gsl) );
168 GA( gsl_multimin_fminimizer_iterate(minimiser) );
170 size= gsl_multimin_fminimizer_size(minimiser);
171 r= gsl_multimin_test_size(size, stop_epsilon);
173 printf("%*s size %# e, r=%d\n", 135,"", size, r);
176 if (r==GSL_SUCCESS) break;
177 assert(r==GSL_CONTINUE);
182 /*---------- Edgewise vertex displacement ----------*/
200 * Let delta = 180deg - angle RMS
205 * Giving energy contribution:
213 * (The dimensions of this are those of F_vd.)
215 * We calculate delta as atan2(|AxB|, A.B)
216 * where A = RM, B = MS
218 * In practice to avoid division by zero we'll add epsilon to d and
219 * |AxB| and the huge energy ought then to be sufficient for the
220 * model to avoid being close to R=S.
223 double edgewise_vertex_displacement_cost(const Vertices vertices) {
224 static const double /*d_epsilon= 1e-6,*/ axb_epsilon= 1e-6;
226 int pi,e,qi,ri,si, k;
227 double m[D3], a[D3], b[D3], axb[D3];
228 double total_cost= 0;
231 ri= EDGE_END2(pi,(e+1)%V6); if (ri<0) continue;
232 si= EDGE_END2(pi,(e+5)%V6); if (si<0) continue;
234 K m[k]= (vertices[pi][k] + vertices[qi][k]) * 0.5;
235 K a[k]= -vertices[ri][k] + m[k];
236 K b[k]= -m[k] + vertices[si][k];
240 double l= 1; //hypotD(vertices[pi], vertices[qi]);
241 double d= 1; //hypotD(vertices[ri], vertices[si]) + d_epsilon;
242 double delta= atan2(magnD(axb) + axb_epsilon, dotprod(a,b));
244 double cost= l * delta * delta / d;
251 /*---------- noncircular rim cost ----------*/
253 double noncircular_rim_cost(const Vertices vertices) {
257 FOR_RIM_VERTEX(vy,vx,v) {
259 /* By symmetry, nearest point on circle is the one with
260 * the same angle subtended at the z axis. */
261 oncircle[0]= vertices[v][0];
262 oncircle[1]= vertices[v][1];
264 double mult= 1.0/ magnD(oncircle);
267 double d2= hypotD2(vertices[v], oncircle);