+/*
+ * Everything that needs the Boost Graph Library and C++ templates etc.
+ * (and what a crazy set of stuff that all is)
+ */
+
+#include <math.h>
+
+#include <iterator>
+
+#include <boost/config.hpp>
+#include <boost/iterator/iterator_facade.hpp>
+#include <boost/graph/graph_traits.hpp>
+#include <boost/graph/graph_concepts.hpp>
+#include <boost/graph/dijkstra_shortest_paths.hpp>
+#include <boost/graph/properties.hpp>
+#include <boost/iterator/counting_iterator.hpp>
+#include <boost/iterator/iterator_categories.hpp>
+
extern "C" {
+#include "bgl.h"
#include "mgraph.h"
}
#define VMASK (YMASK|XMASK)
#define ESHIFT (YBITS|XBITS)
+class Graph { }; // this is a dummy as our graph has no actual representation
+
+struct OutEdgeIncrable {
+ int f;
+ OutEdgeIncrable& operator++() { f += 1<<ESHIFT; return *this; }
+ OutEdgeIncrable(int v, int e) : f(v | (e << ESHIFT)) { }
+};
+
namespace boost {
- // We make Layout a model of various BGL Graph concepts.
- // This mainly means that graph_traits<Layout> has lots of stuff.
+ // We make Graph a model of various BGL Graph concepts.
+ // This mainly means that graph_traits<Graph> has lots of stuff.
// First, some definitions used later:
public virtual vertex_list_graph_tag,
public virtual edge_list_graph_tag { };
- struct OutEdgeIncrable {
- int f;
- OutEdgeIncrable& operator++() { f += 1<<ESHIFT; return self; }
- OutEdgeIncrable(int v, int e) : f(v | (e << ESHIFT)) { }
- };
-
- struct graph_traits<Layout> {
+ struct graph_traits<Graph> {
// Concept Graph:
typedef int vertex_descriptor; /* vertex number, -1 => none */
typedef int edge_descriptor; /* see above */
typedef undirected_tag directed_category;
- typedef disallow_parallel_ege edge_parallel_category;
+ typedef disallow_parallel_edge_tag edge_parallel_category;
typedef layout_graph_traversal_category traversal_category;
inline int null_vertex() { return -1; }
// Concept IncidenceGraph:
typedef counting_iterator<OutEdgeIncrable,
- forward_iterator_tag> out_edge_iterator;
- typedef int degree_size_type;
+ std::forward_iterator_tag> out_edge_iterator;
+ typedef unsigned degree_size_type;
- inline int source(int f, const Layout&) { return f&VMASK; }
- inline int target(int f, const Layout&) { return EDGE_END2(f&VMASK, f>>ESHIFT); }
+ inline int source(int f, const Graph&) { return f&VMASK; }
+ inline int target(int f, const Graph&) { return EDGE_END2(f&VMASK, f>>ESHIFT); }
inline std::pair<out_edge_iterator,out_edge_iterator>
- out_edges(int v, const Layout&) {
+ out_edges(int v, const Graph&) {
return std::make_pair(out_edge_iterator(OutEdgeIncrable(v, VE_MIN(v))),
out_edge_iterator(OutEdgeIncrable(v, VE_MAX(v))));
}
- out_degree(int v, const Layout&) { return VE_MAX(v) - VE_MIN(v); }
+ inline unsigned out_degree(int v, const Graph&) {
+ return VE_MAX(v) - VE_MIN(v);
+ }
// Concept VertexListGraph:
typedef counting_iterator<int> vertex_iterator;
typedef unsigned vertices_size_type;
inline std::pair<vertex_iterator,vertex_iterator>
- vertices(const Layout&) {
+ vertices(const Graph&) {
return std::make_pair(vertex_iterator(0), vertex_iterator(N));
}
- inline unsigned num_vertices(const Layout&) { return N; }
-
-}
+ inline unsigned num_vertices(const Graph&) { return N; }
+ };
+};
static void single_source_shortest_paths(int v1,
const double edge_weights[/*f*/],
double vertex_distances[/*v*/]) {
- boost::dijkstra_shortest_paths
- (g, v1,
+ Graph g;
+
+ boost::dijkstra_shortest_paths(g, v1,
weight_map(edge_weights).
vertex_index_map(identity_property_map()).
distance_map(vertex_distances));
}
-double graph_layout_energy(const Layout *g) {
- /* For each (vi,vj) computes shortest path pij = vi..vj along edges,
- * and actual distance dij = vi-vj.
+double graph_layout_cost(const Vertices v, const double vertex_areas[N]) {
+ /* For each (vi,vj) computes shortest path s_ij = |vi..vj|
+ * along edges, and actual distance d_ij = |vi-vj|.
+ *
+ * We will also use the `vertex areas': for each vertex vi the
+ * vertex area a_vi is the mean area of the incident triangles.
+ * This is computed elsewhere.
*
* Energy contribution is proportional to
*
- * pij - dij
- * --------- . Sigma length
- * 2 e member (edges(vi) union edges(vj) e
- * dij
+ * -4 2
+ * a a . d . [ (s/d) - 1 ]
+ * vi vj
+ *
+ * (In practice we compute d^2+epsilon and use it for the
+ * divisions, to avoid division by zero.)
*/
- double edge_weights[N*V6], vertex_distances[N];
- int v1, e, f;
+ static const d2_epsilon= 1e-6;
+
+ double edge_weights[N*V6], vertex_distances[N], total_cost;
+ int v1,v2,e,f;
- FOR_VEDGE_X(v1,e,
+ FOR_VEDGE_X(v1,e,v2,
f= v1 | e << ESHIFT,
edge_weights[f]= NaN)
- edge_weights[f]= hypotD(g.v[v1], g.v[v2]);
+ edge_weights[f]= hypotD(v[v1], v[v2]);
FOR_VERTEX(v1) {
+ double a1= vertex_areas[v1];
single_source_shortest_paths(v1, edge_weights, vertex_distances);
FOR_VERTEX(v2) {
-
-
-
-
- { ) {
-
-
- 0);
-
- /* weight_map(). ? */
- /*
-
-
- predecessor_map().
- distance_map()
-
-
-
+ double a2= vertex_areas[v2];
+ double d2= hypotD2plus(v[v1],v[v2], d2_epsilon);
+ double sd= vertex_distances[v2] / d2;
+ double sd2= sd*sd;
+ total_cost += a1*a2 * (sd2 - 1) / (d2*d2);
+ }
+ }
+ return total_cost;
+}