X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=moebius2.git;a=blobdiff_plain;f=energy.c;h=3c1731a8e971c304c2d40bf222b741ad89011b4a;hp=f6a4c290c5883d2c04ef0b9150717cc991f409b6;hb=HEAD;hpb=c3fc916a828edf56f715a88e6a20f450c8b40fbd diff --git a/energy.c b/energy.c index f6a4c29..3c1731a 100644 --- a/energy.c +++ b/energy.c @@ -7,7 +7,11 @@ #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; @@ -29,23 +33,62 @@ typedef struct { static PreComputation *const precomps[]= { compute_edge_lengths, - compute_vertex_areas + compute_vertex_areas, + compute_rim_twist_angles }; static const CostContribution costs[]= { #if XBITS==3 #define STOP_EPSILON 1e-6 - COST( 3e3, line_bending_cost) - COST( 3e3, edge_length_variation_cost) + COST( 3e3, vertex_displacement_cost) COST( 0.4e3, rim_proximity_cost) - COST( 1e6, edge_angle_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 1e-4 + COST( 3e5, vertex_displacement_cost) + COST( 3e5, 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==4 +#if XBITS>=7 /* nonsense follows but never mind */ #define STOP_EPSILON 1e-6 COST( 3e5, line_bending_cost) COST( 10e2, edge_length_variation_cost) @@ -75,7 +118,7 @@ void compute_energy_separately(const struct Vertices *vs, int ci; for (ci=0; cia, section); + precomps[ci](vs->a, section); inparallel_barrier(); } for (ci=0; ci %# e* |", tcost, tweight, tenergy); + if (pr) printf(/*" %# e >"*/ " %# e* |", /*tcost,*/ tenergy); *energy += tenergy; } @@ -190,7 +233,118 @@ void compute_vertex_areas(const Vertices vertices, int section) { } } -/*---------- 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: @@ -275,6 +429,34 @@ double edge_length_variation_cost(const Vertices vertices, int section) { 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]) { @@ -289,7 +471,7 @@ static void find_nearest_oncircle(double oncircle[D3], const double p[D3]) { } double rim_proximity_cost(const Vertices vertices, int section) { - double oncircle[3], cost=0; + double oncircle[D3], cost=0; int v; FOR_VERTEX(v, OUTER) { @@ -323,6 +505,40 @@ double noncircular_rim_cost(const Vertices vertices, int section) { 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 ----------*/ /* @@ -397,26 +613,9 @@ double edge_angle_cost(const Vertices vertices, int section) { /*---------- small triangles cost ----------*/ /* + * Consider a triangle PQS * - * Q `-_ - * / | `-_ - * / | `-. - * / | S - * / | _,-' - * / | _,-' - * / , P ' - * / ,-' - * /,-' - * /' - * R - * - * Let delta = angle between two triangles' normals - * - * Giving energy contribution: - * - * 2 - * E = F . delta - * vd, edge PQ vd + * Cost is 1/( area^2 ) */ double small_triangles_cost(const Vertices vertices, int section) { @@ -447,3 +646,48 @@ double small_triangles_cost(const Vertices vertices, int section) { 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; +}