From: Ian Jackson Date: Wed, 9 Jan 2008 18:34:59 +0000 (+0000) Subject: tidy up and normalise line bending cost X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=moebius2.git;a=commitdiff_plain;h=23c346bb18366c8e9509743aacc5d777bd7f85cb tidy up and normalise line bending cost --- diff --git a/energy.c b/energy.c index e9b93fd..db13fbf 100644 --- a/energy.c +++ b/energy.c @@ -13,6 +13,12 @@ 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) { @@ -27,7 +33,7 @@ double compute_energy(const struct Vertices *vs) { if (printing) printf("cost > energy |"); - COST(3e2, edgewise_vertex_displacement_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)); @@ -58,7 +64,7 @@ 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; } @@ -66,7 +72,7 @@ static void addcost(double *energy, double tweight, double tcost, int pr) { 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]); } @@ -93,7 +99,7 @@ void compute_vertex_areas(const Vertices vertices) { // } // xprod(av, e1v, e2v); // total += magnD(av); - + count++; } vertex_areas[v0]= total / count; @@ -104,69 +110,78 @@ void compute_vertex_areas(const Vertices vertices) { /*---------- 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 * - * Let delta = 180deg - angle RMS + * Calculation: * - * Let l = |PQ| - * d = |RS| + * Let vector A = PQ + * B = QR * - * Giving energy contribution: + * -1 A . B + * delta = tan ------- + * | A x B | * - * 3 - * l delta - * E = F . -------- - * vd, edge PQ vd d + * which is always in the range 0..pi because the denominator + * is nonnegative. We add epsilon to |AxB| to avoid division + * by zero. * + * Normalisation: * - * (The dimensions of this are those of F_vd.) + * 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 + * + * , -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 ----------*/ @@ -181,7 +196,7 @@ double edge_length_variation_cost(const Vertices vertices) { cost += diff*diff; } return cost; -} +} /*---------- rim proximity cost ----------*/ @@ -224,7 +239,7 @@ double noncircular_rim_cost(const Vertices vertices) { FOR_RIM_VERTEX(vy,vx,v) { find_nearest_oncircle(oncircle, vertices[v]); - + double d2= hypotD2(vertices[v], oncircle); cost += d2*d2; } diff --git a/minimise.c b/minimise.c index 51114a6..e5bbc87 100644 --- a/minimise.c +++ b/minimise.c @@ -73,6 +73,7 @@ int main(int argc, const char *const *argv) { graph_layout_prepare(); printing_init(); + energy_init(); printf("X=%d=0x%x Y=%d=0x%x DIM=%d\n",X,X,Y,Y,DIM); diff --git a/minimise.h b/minimise.h index f1da76f..b0d285d 100644 --- a/minimise.h +++ b/minimise.h @@ -8,6 +8,7 @@ #include "mgraph.h" double compute_energy(const struct Vertices *vs); +void energy_init(void); double graph_layout_cost(const Vertices v); void graph_layout_prepare(); @@ -16,8 +17,10 @@ void compute_vertex_areas(const Vertices vertices); void compute_edge_lengths(const Vertices vertices); extern double vertex_areas[N], vertex_mean_edge_lengths[N], edge_lengths[N][V6]; +extern double density; + +double line_bending_adjcost(const Vertices vertices); double noncircular_rim_cost(const Vertices vertices); -double edgewise_vertex_displacement_cost(const Vertices vertices); double edge_length_variation_cost(const Vertices vertices); double rim_proximity_cost(const Vertices vertices);