X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=moebius2.git;a=blobdiff_plain;f=energy.c;h=aa2dd47fa4364eed4fc5c616ca2336ba9573eee9;hp=1d0360fcc030dafdf62ae7e33c59271f5173bacd;hb=d045b4e5e53daf45808a65f8811a1c6fbf7ecc98;hpb=c3e758476ec10723ccb81a7dd91967d2996665b9 diff --git a/energy.c b/energy.c index 1d0360f..aa2dd47 100644 --- a/energy.c +++ b/energy.c @@ -5,39 +5,158 @@ #include "common.h" #include "minimise.h" #include "mgraph.h" +#include "parallel.h" -double vertex_areas[N], vertex_mean_edge_lengths[N], edge_lengths[N][V6]; +double vertex_mean_edge_lengths[N]; + +static double vertex_areas[N]; +static double edge_lengths[N][V6]; +static double rim_vertex_angles[N]; static double best_energy= DBL_MAX; static void addcost(double *energy, double tweight, double tcost, int pr); -#define COST(weight, compute) addcost(&energy, (weight), (compute), printing) -double density; +/*---------- 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( 2e2, 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 7e-4 + 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( 3e4, vertex_displacement_cost) + COST( 3e4, vertex_edgewise_displ_cost) + COST( 2e-1, rim_proximity_cost) + COST( 1e3, 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) { - density= sqrt(N); + 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); } -/*---------- main energy computation and subroutines ----------*/ +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; cia); - compute_vertex_areas(vs->a); - energy= 0; + double totals[NCOSTS], energy; + int ci, printing; printing= printing_check(pr_cost,0); - if (printing) printf("cost > energy |"); + if (printing) printf("%15lld c>e |", evaluations); - COST(2.25e3, line_bending_adjcost(vs->a)); - COST(1e3, edge_length_variation_cost(vs->a)); - COST(0.2e3, rim_proximity_cost(vs->a)); -// COST(1e2, graph_layout_cost(vs->a)); - COST(1e8, noncircular_rim_cost(vs->a)); + 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(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; } @@ -59,29 +184,30 @@ double compute_energy(const struct Vertices *vs) { flushoutput(); } + evaluations++; return energy; } static void addcost(double *energy, double tweight, double tcost, int pr) { double tenergy= tweight * tcost; - if (pr) printf(" %# e x %# e > %# e* |", tcost, tweight, tenergy); + if (pr) printf(/*" %# e >"*/ " %# e* |", /*tcost,*/ tenergy); *energy += tenergy; } /*---------- Precomputations ----------*/ -void compute_edge_lengths(const Vertices vertices) { +void compute_edge_lengths(const Vertices vertices, int section) { int v1,e,v2; - FOR_EDGE(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) { +void compute_vertex_areas(const Vertices vertices, int section) { int v0,v1,v2, e1,e2; // int k; - FOR_VERTEX(v0) { + FOR_VERTEX(v0, OUTER) { double total= 0.0, edges_total=0; int count= 0; @@ -107,7 +233,118 @@ void compute_vertex_areas(const Vertices vertices) { } } -/*---------- Edgewise vertex displacement ----------*/ +/*---------- displacement of vertices across a midpoint ----------*/ + + /* + * 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. + * + * Details: + * + * Let R' = M + SM + * D = R' - R + * + * 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| ] + * + */ + +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; +} + +/*---------- 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; +} + +/*---------- 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 + */ + +double vertex_edgewise_displ_cost(const Vertices vertices, int section) { + const double inv_lambda= 1.0/1; //2; + const double delta= 6; + + 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 total_cost; +} + + +/*---------- at-vertex edge angles ----------*/ /* * Definition: @@ -141,73 +378,21 @@ void compute_vertex_areas(const Vertices vertices) { * r * cost = delta * Q,e - * - * Normalisation: - * - * We want the minimum energy to remain unchanged with changes in - * triangle densitiy, when the vertices lie evenly spaced on - * circles, and we do this by normalising the force ie the - * derivative of the energy with respect to linear motions of the - * vertices. - * - * We consider only the force on Q due to PQR, wlog. (Forces on - * P qnd R due to PQR are equal and opposite so normalising - * forces on Q will normalise them too.) - * - * Force on Q is in the plnae PQR and normal to PR, so we can - * consider it only linearly in that dimension. WLOG let that be - * the x dimension. So with f' representing df'/dx_Q: - * - * , d - * F = cost = -- - * Q,e Q,e err looks like we can only do - * this if we make some kind of - * assumption about delta or - * something give up - * - * - * Interposing M and N so that we have P-M-Q-N-R - * generates half as much delta for each vertex. So - * - - In that case the force on Q - * due to PQR - * - *Normalising for equal linear - * forces: - * - * d - * linear force on Q due to e = ------- cost - * d coord Q,e - * Q - * - * (we will consider only one e and one coord and hope - * that doesn't lead us astray.) - * - * - * , -r - * cost = D . cost - * Q,e Q,e - * - * where D is the linear density. - * - * , -r - * Sigma cost = N . D . Sigma cost - * Q,e Q,e Q,e Q,e - * - * */ + */ -double line_bending_adjcost(const Vertices vertices) { +double line_bending_cost(const Vertices vertices, int section) { static const double axb_epsilon= 1e-6; - static const double exponent_r= 3; + static const double exponent_r= 4; int pi,e,qi,ri, k; double a[D3], b[D3], axb[D3]; double total_cost= 0; - FOR_EDGE(qi,e,ri) { + 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]; @@ -216,12 +401,9 @@ double line_bending_adjcost(const Vertices vertices) { double delta= atan2(magnD(axb) + axb_epsilon, dotprod(a,b)); double cost= pow(delta,exponent_r); - if (!e && !(qi & YMASK)) - cost *= 10; - total_cost += cost; } - return total_cost / (N / density); + return total_cost; } /*---------- edge length variation ----------*/ @@ -230,18 +412,47 @@ double line_bending_adjcost(const Vertices vertices) { * Definition: * * See the diagram above. - * - * cost = + * r + * cost = ( |PQ| - |QR| ) * Q,e + */ -double edge_length_variation_cost(const Vertices vertices) { - double diff, cost= 0; +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) { + FOR_EDGE(q,e,r, OUTER) { eback= edge_reverse(q,e); diff= edge_lengths[q][e] - edge_lengths[q][eback]; - cost += diff*diff; + 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; } @@ -259,11 +470,11 @@ static void find_nearest_oncircle(double oncircle[D3], const double p[D3]) { oncircle[1] *= mult; } -double rim_proximity_cost(const Vertices vertices) { - double oncircle[3], cost=0; +double rim_proximity_cost(const Vertices vertices, int section) { + double oncircle[D3], cost=0; int v; - FOR_VERTEX(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; @@ -280,12 +491,12 @@ double rim_proximity_cost(const Vertices vertices) { /*---------- noncircular rim cost ----------*/ -double noncircular_rim_cost(const Vertices vertices) { +double noncircular_rim_cost(const Vertices vertices, int section) { int vy,vx,v; double cost= 0.0; double oncircle[3]; - FOR_RIM_VERTEX(vy,vx,v) { + FOR_RIM_VERTEX(vy,vx,v, OUTER) { find_nearest_oncircle(oncircle, vertices[v]); double d2= hypotD2(vertices[v], oncircle); @@ -293,3 +504,190 @@ double noncircular_rim_cost(const Vertices vertices) { } 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[2]; + 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; +}