X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=moebius2.git;a=blobdiff_plain;f=energy.c;h=09c54811520c45ca3a43a79464afa15ebe262619;hp=f28135a3bf4d2bc02ce9f700c89d0d6c77dfba20;hb=5cb1a1aa2036ff015feafa61691c9dfde9fa4395;hpb=62710d55de09f02e31a9fc2cc7e3ec5de44651e4 diff --git a/energy.c b/energy.c index f28135a..09c5481 100644 --- a/energy.c +++ b/energy.c @@ -3,298 +3,691 @@ */ #include "common.h" -#include "bgl.h" +#include "minimise.h" #include "mgraph.h" +#include "parallel.h" -#include -#include +double vertex_mean_edge_lengths[N]; -#define BEST_F "best" -#define INITIAL_F "initial" +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 flushoutput(void); -static void diee(const char *what) { perror(what); exit(16); } -static void cost(double *energy, double tweight, double tcost); -#define COST(weight, compute) cost(&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 8e-4 + COST( 3e4, vertex_displacement_cost) + COST( 3e4, vertex_edgewise_displ_cost) + COST( 3e-2, 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; cia, section); + inparallel_barrier(); + } + for (ci=0; cia, 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; cie |", evaluations); + + for (ci=0; ci energy |"); + for (ci=0; cia,sizeof(vs->a),1,best_f); if (r!=1) diee("fwrite"); if (fclose(best_f)) diee("fclose new best"); - if (rename(BEST_F ".new", BEST_F)) diee("rename install new best"); + if (rename(best_file_tmp,best_file)) diee("rename install new best"); + + best_energy= energy; + } + if (printing) { + putchar('\n'); + flushoutput(); } - putchar('\n'); - flushoutput(); + evaluations++; return energy; -} +} -static void cost(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 flushoutput(void) { - if (fflush(stdout) || ferror(stdout)) diee("stdout"); +/*---------- 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]); } -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; +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 void gsldie(const char *what, int status) { - fprintf(stderr,"gsl function failed: %s: %s\n", what, gsl_strerror(status)); - exit(-1); +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); + + return cost; } -static gsl_multimin_fminimizer *minimiser; +/*---------- displacement of vertices opposite at a vertex ----------*/ -static const double stop_epsilon= 1e-4; + /* + * 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; -#define DIM (N*D3) + FOR_EDGE(qi,e,ri, OUTER) { + si= EDGE_END2(qi,(e+3)%V6); if (si<0) continue; -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); + 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, vx,vy, k; - - if (argc>1) { fputs("takes no arguments\n",stderr); exit(8); } - - 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(INITIAL_F,"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= (double*)initial; - step_size_gsl.data= (double*)step_size; - - FOR_VERTEX(v) - K step_size[v][k]= 1e-3; - FOR_RIM_VERTEX(vx,vy,v) - step_size[v][3] *= 0.1; - - r= gsl_multimin_fminimizer_set(minimiser, &multimin_function, - &initial_gsl, &step_size_gsl); - if (r) { gsldie("fminimizer_set",r); } - - for (;;) { - r= gsl_multimin_fminimizer_iterate(minimiser); - if (r) { gsldie("fminimizer_iterate",r); } +/*---------- displacement of vertices opposite at an edge ----------*/ - size= gsl_multimin_fminimizer_size(minimiser); - r= gsl_multimin_test_size(size, stop_epsilon); + /* + * At edge PQ considering vertices R and S (see diagram + * below for overly sharp edge cost). + * + * Let M = midpoint of PQ + */ - printf("size %# e, r=%d\n", size, r); - flushoutput(); +double vertex_edgewise_displ_cost(const Vertices vertices, int section) { + const double inv_lambda= 1.0/1; //2; + const double delta= 6; - if (r==GSL_SUCCESS) break; - assert(r==GSL_CONTINUE); + 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; + + 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; + 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; - assert(ri == EDGE_END2(qi,(e+2)%V6)); - assert(si == EDGE_END2(qi,(e+4)%V6)); - - 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; +}