#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)
+
+/*---------- 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;
}
-/*---------- main energy computation and subroutines ----------*/
+/*---------- 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; ci<NPRECOMPS; ci++) {
+ precomps[ci](vs->a, section);
+ inparallel_barrier();
+ }
+ for (ci=0; ci<NCOSTS; ci++)
+ energies[ci]= costs[ci].fn(vs->a, 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; ci<NCOSTS; ci++)
+ totals[ci] += energies[ci];
+}
double compute_energy(const struct Vertices *vs) {
static int bests_unprinted;
-
- double energy;
- int printing;
- compute_edge_lengths(vs->a);
- compute_vertex_areas(vs->a);
- energy= 0;
+ double totals[NCOSTS], energy;
+ int ci, printing;
printing= printing_check(pr_cost,0);
if (printing) printf("%15lld c>e |", evaluations);
- if (XBITS==3) {
- COST( 3e2, line_bending_cost(vs->a));
- COST( 1e3, edge_length_variation_cost(vs->a));
- COST( 0.4e3, rim_proximity_cost(vs->a));
- COST( 1e6, edge_angle_cost(vs->a));
-// COST( 1e1, small_triangles_cost(vs->a));
- COST( 1e12, noncircular_rim_cost(vs->a));
- stop_epsilon= 1e-6;
- } else if (XBITS==4) {
- COST( 3e2, line_bending_cost(vs->a));
- COST( 3e3, edge_length_variation_cost(vs->a));
- COST( 9.0e1, rim_proximity_cost(vs->a)); // 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(vs->a));
- COST( 1e12, noncircular_rim_cost(vs->a));
- stop_epsilon= 1e-5;
- } else {
- abort();
- }
+ for (ci=0; ci<NCOSTS; ci++)
+ totals[ci]= 0;
+
+ inparallel(vs,
+ compute_energy_separately,
+ compute_energy_combine,
+ sizeof(totals) /* really, size of energies */,
+ totals);
+
+ energy= 0;
+ for (ci=0; ci<NCOSTS; ci++)
+ addcost(&energy, costs[ci].weight, totals[ci], printing);
if (printing) printf("| total %# e |", energy);
static void addcost(double *energy, double tweight, double tcost, int pr) {
double tenergy= tweight * tcost;
- if (pr) printf(" %# e x %g > %# 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;
}
}
-/*---------- 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:
* Q,e
*/
-double line_bending_cost(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];
double delta= atan2(magnD(axb) + axb_epsilon, dotprod(a,b));
double cost= pow(delta,exponent_r);
- if (!e && !(qi & ~XMASK))
- cost *= 10;
-
total_cost += cost;
}
return total_cost;
* Q,e
*/
-double edge_length_variation_cost(const Vertices vertices) {
+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 += 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]) {
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;
/*---------- 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);
return cost;
}
-/*---------- triangle bad normals 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 `-_
- * / | `-_
- * / | `-.
- * / | S
- * / | _,-'
- * / | _,-'
- * / , P '
- * / ,-'
- * /,-'
+ * / | `-_ P'Q' ------ S'
+ * / | `-. _,' `. .
+ * / | S _,' : .
+ * / | _,-' _,' :r .r
+ * / | _,-' R' ' `. .
+ * / , P ' ` . r : .
+ * / ,-' ` . :
+ * /,-' ` C'
* /'
* R
*
+ *
+ *
* Let delta = angle between two triangles' normals
*
* Giving energy contribution:
* vd, edge PQ vd
*/
-double edge_angle_cost(const Vertices vertices) {
- double sq[D3], pq[D3], qr[D3], sqp[D3], pqr[D3], rs[D3];
- double x[D3], y[D3];
+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) {
+
+ 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 {
- sq[k]= vertices[si][k] - vertices[qi][k];
- pq[k]= vertices[pi][k] - vertices[qi][k];
- qr[k]= vertices[qi][k] - vertices[ri][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];
}
- xprod(sqp, pq,sq);
- xprod(pqr, pq,qr);
-
- double dot= dotprod(sqp,pqr);
- xprod(x,sqp,pqr);
-
- K rs[k]= -vertices[ri][k] + vertices[si][k];
- xprod(y, pq,rs);
- double delta=
- pow(atan2(magnD(x), dot), 2.0) * pow(magnD2(pq), 2.0) /
- (pow(magnD(y), 0.3) + 1e-6);
- double cost= pow(delta, 2.0);
+ 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;
-//double cost= pow(magnD(spqxpqr), 3);
-//assert(dot>=-1 && dot <=1);
-//double cost= 1-dot;
total_cost += cost;
}
-
+
return total_cost;
}
/*---------- 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) {
+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) {
+
+ 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;
//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;
}
~ian / moebius2.git / blobdiff