X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?a=blobdiff_plain;f=energy.c;h=db13fbffcf866a23b87d308914bcc8362b9e6728;hb=23c346bb18366c8e9509743aacc5d777bd7f85cb;hp=a54cfe2f93bf07ab70d0f9bce02639a868bd9b1b;hpb=190a54bc07e4c1497938a31373543650d3f19c55;p=moebius2.git diff --git a/energy.c b/energy.c index a54cfe2..db13fbf 100644 --- a/energy.c +++ b/energy.c @@ -6,28 +6,38 @@ #include "minimise.h" #include "mgraph.h" -static void compute_vertex_areas(const Vertices vertices, double areas[N]); +double vertex_areas[N], vertex_mean_edge_lengths[N], edge_lengths[N][V6]; + 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; + +void energy_init(void) { + density= sqrt(N); +} + /*---------- main energy computation and subroutines ----------*/ double compute_energy(const struct Vertices *vs) { - double vertex_areas[N], energy; + double energy; int printing; - compute_vertex_areas(vs->a, vertex_areas); + compute_edge_lengths(vs->a); + compute_vertex_areas(vs->a); energy= 0; - printing= printing_check(pr_cost); + printing= printing_check(pr_cost,0); if (printing) printf("cost > energy |"); - COST(1e2, edgewise_vertex_displacement_cost(vs->a)); - COST(1e2, graph_layout_cost(vs->a,vertex_areas)); - COST(1e6, noncircular_rim_cost(vs->a)); + 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)); if (printing) printf("| total %# e |", energy); @@ -54,15 +64,25 @@ double compute_energy(const struct Vertices *vs) { static void addcost(double *energy, double tweight, double tcost, int pr) { double tenergy= tweight * tcost; - if (pr) printf(" %# e > %# e |", tcost, tenergy); + if (pr) printf(" %# e x %# e > %# e* |", tcost, tweight, tenergy); *energy += tenergy; } -static void compute_vertex_areas(const Vertices vertices, double areas[N]) { - int v0,v1,v2, e1,e2, k; +/*---------- Precomputations ----------*/ + +void compute_edge_lengths(const Vertices vertices) { + int v1,e,v2; + + FOR_EDGE(v1,e,v2) + edge_lengths[v1][e]= hypotD(vertices[v1],vertices[v2]); +} + +void compute_vertex_areas(const Vertices vertices) { + int v0,v1,v2, e1,e2; +// int k; FOR_VERTEX(v0) { - double total= 0.0; + double total= 0.0, edges_total=0; int count= 0; FOR_VEDGE(v0,e1,v1) { @@ -70,85 +90,144 @@ static void compute_vertex_areas(const Vertices vertices, double areas[N]) { 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; } } /*---------- Edgewise vertex displacement ----------*/ /* + * Definition: + * + * At each vertex Q, in each direction e: + * + * e + * Q ----->----- R + * _,-'\__/ + * _,-' delta + * P ' * + * r + * cost = delta (we use r=3) + * Q,e * * - * Q `-_ - * / | `-_ - * / | `-. - * / M - - - - - S - * / ' | _,-' - * / ' | _,-' - * / ' , P ' - * / ',-' - * /,-' - * /' - * R + * Calculation: * - * Let delta = 180deg - angle RMS + * Let vector A = PQ + * B = QR * - * Let l = |PQ| - * d = |RS| + * -1 A . B + * delta = tan ------- + * | A x B | * - * Giving energy contribution: + * which is always in the range 0..pi because the denominator + * is nonnegative. We add epsilon to |AxB| to avoid division + * by zero. * - * 3 - * l delta - * E = F . -------- - * vd, edge PQ vd d + * Normalisation: * + * We want the answer to remain unchanged when the vertices lie + * on circles. Interposing M and N so that we have P-M-Q-N-R + * generates half as much delta for each vertex. So * - * (The dimensions of this are those of F_vd.) + * , -1 + * cost = D . cost + * Q,e Q,e + * + * where D is the linear density. + * + * , -1 + * Sigma cost = N . D . Sigma cost + * Q,e Q,e Q,e Q,e * - * We calculate delta as atan2(|AxB|, A.B) - * where A = PQ, B = QR * - * 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. */ -double edgewise_vertex_displacement_cost(const Vertices vertices) { +double line_bending_adjcost(const Vertices vertices) { static const double axb_epsilon= 1e-6; + static const double exponent_r= 3; - int pi,e,qi,ri, k; //,si - double a[D3], b[D3], axb[D3]; //m[D3], + int pi,e,qi,ri, k; + double a[D3], b[D3], axb[D3]; double total_cost= 0; FOR_EDGE(qi,e,ri) { pi= EDGE_END2(qi,(e+3)%V6); if (pi<0) continue; -// K m[k]= (vertices[pi][k] + vertices[qi][k]) * 0.5; 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,3); + double cost= pow(delta,exponent_r); if (!e && !(qi & YMASK)) cost *= 10; total_cost += cost; } - return total_cost; + return total_cost / (N / density); +} + +/*---------- edge length variation ----------*/ + +double edge_length_variation_cost(const Vertices vertices) { + double diff, cost= 0; + int v0, efwd,vfwd, eback; + + FOR_EDGE(v0,efwd,vfwd) { + eback= edge_reverse(v0,efwd); + diff= edge_lengths[v0][efwd] - edge_lengths[v0][eback]; + cost += diff*diff; + } + 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) { + double oncircle[3], cost=0; + int v; + + FOR_VERTEX(v) { + 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 cost; } /*---------- noncircular rim cost ----------*/ @@ -156,17 +235,11 @@ double edgewise_vertex_displacement_cost(const Vertices vertices) { double noncircular_rim_cost(const Vertices vertices) { int vy,vx,v; double cost= 0.0; + double oncircle[3]; 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; + find_nearest_oncircle(oncircle, vertices[v]); + double d2= hypotD2(vertices[v], oncircle); cost += d2*d2; }