int main()
{
// generate points on a 3D grid
std::vector<Weighted_point> P;
int number_of_points = 0;
for (int z=0 ; z<5 ; z++)
for (int y=0 ; y<5 ; y++)
for (int x=0 ; x<5 ; x++) {
Point p(x, y, z);
Weight w = (x+y-z*y*x)*2.0; // let's say this is the weight.
P.push_back(Weighted_point(p, w));
++number_of_points;
}
Rt T;
// insert all points in a row (this is faster than one insert() at a time).
T.insert (P.begin(), P.end());
assert( T.is_valid() );
assert( T.dimension() == 3 );
std::cout << "Number of vertices : " << T.number_of_vertices() << std::endl;
// removal of all vertices
int count = 0;
while (T.number_of_vertices() > 0) {
T.remove (T.finite_vertices_begin());
++count;
}
assert( count == number_of_points );
return 0;
}
// Constructs regular triangulation of weighted points.
// Builds graph of cells with voids. Finds connected components of this graph (voids as clusters of cells).
// For each component calculates total void volume and area.
// Excludes roughs on the surface (components, connected to the infinite cell).
bool regular_triangulation_voids(const Wpi_container& points, Voids_result &res)
{
typedef typename boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS, Cell_handle> CellGraph;
typedef typename boost::graph_traits<CellGraph>::vertex_descriptor GVertex;
typedef typename boost::graph_traits<CellGraph>::vertex_iterator GVertex_iterator;
Rt T; // regular triangulation
CellGraph G; // Voronoi subgraph where cells_sqr_r > 0 and edges_sqr_r > 0 (cells and edges with voids)
GVertex_iterator vi, vi_end;
res.out_log << "Number of input points for RT : " << points.size() << std::endl;
T.insert(points.begin(), points.end()); // insert all points in a row (this is faster than one insert() at a time).
T.infinite_vertex()->info().atom_id = -1; // set special atom_id for dummy infinite triangulation vertex
assert(T.dimension() == 3);
/*res.out_log << "Is valid : " << T.is_valid() << std::endl;*/
res.out_log << "Number of vertices in RT : " << T.number_of_vertices() << std::endl;
res.out_log << "Number of cells : " << T.number_of_cells() << std::endl;
res.out_log << "Number of finite cells : " << T.number_of_finite_cells() << std::endl;
/*res.out_log << "Inf. vert. atom id : " << T.infinite_vertex()->info().atom_id << std::endl;*/
// Add finite cells having sqr_r > 0 as graph verticies
Finite_cells_iterator cit, cit_end = T.finite_cells_end();
for (cit = T.finite_cells_begin(); cit != cit_end; cit++) {
if (cit->weighted_circumcenter().weight() > 0) // cached weighted circumcenter computation
cit->id() = add_vertex(Cell_handle(cit), G); // store corresponding graph vertex descriptor in cell's id()
}
// store one of infinite cells in graph: it will represent all of them. It should be the last vertex in graph with maximal vertex_descriptor.
const GVertex inf_graph_v = add_vertex(T.infinite_cell(), G);
res.out_log << "inf_graph_v descriptor : " << inf_graph_v << std::endl;
// Add graph edges connecting cells with void
for (boost::tie(vi, vi_end) = vertices(G); vi != vi_end; ++vi) {
const GVertex v1 = *vi; // current graph vertex
if (v1 != inf_graph_v) { // check edges only from finite cells
const Cell_handle c1 = G[v1]; // current cell
for (int i = 0; i < 4; i++) { // for each of four neighbor cells
const Cell_handle c2 = c1->neighbor(i);
bool ends_in_void = false; // do both corresponding Voronoi verticies lie in void space?
bool on_same_side = false; // do both ends lie on the same side of corresponding cell facet?
const Weighted_point &p1 = c1->vertex((i+1)&3)->point(); // weighted points of common facet between c and c2 cells
const Weighted_point &p2 = c1->vertex((i+2)&3)->point();
const Weighted_point &p3 = c1->vertex((i+3)&3)->point();
const Point &wcc = c1->weighted_circumcenter().point();
GVertex v2; // neighbor vertex in graph to construct edge to
if (c2->id() != -1) { // neighbor cell is finite and in graph: id()=vertex_descriptor
v2 = c2->id();
ends_in_void = true;
on_same_side = (orientation(p1.point(), p2.point(), p3.point(), wcc) ==
orientation(p1.point(), p2.point(), p3.point(), c2->weighted_circumcenter().point()));
} else if (T.is_infinite(c2)) {
v2 = inf_graph_v; // use our infinite graph vertex as destination if neighbor cell is infinite
ends_in_void = true;
on_same_side = (orientation(p1.point(), p2.point(), p3.point(), wcc) !=
orientation(p1.point(), p2.point(), p3.point(), c1->vertex(i)->point().point())); // same side with infinite vertex = different sides with cell vertex
}
typename K::Compute_squared_radius_smallest_orthogonal_sphere_3 r_mouth; // facet bottleneck squared radius (facet closed if < 0)
if (ends_in_void && (v2 > v1) && (on_same_side || r_mouth(p1, p2, p3) > 0))
add_edge(v1, v2, G); // use ordering v2>v1 to rule out most of the parallel edges: rely on v_inf>v1 for all finite vertices
}
}
}
res.out_log << "Number of vertices in G : " << num_vertices(G) << std::endl;
res.out_log << "Number of edges in G : " << num_edges(G) << std::endl;
// Find connected components on this Voronoi subnetwork
std::vector<int> component(num_vertices(G));
int num_components = boost::connected_components(G, &component[0]);
const int inf_comp_id = component[inf_graph_v]; // component of infinite vertex
res.out_log << "Number of connected components : " << num_components << std::endl;
res.out_log << "Component id of infinite vertex : " << inf_comp_id << std::endl;
// Reserve storage for results
res.voids.resize(num_components);
std::fill(res.atom_surf.begin(), res.atom_surf.end(), 0.0L);
// Calculate total volume of each finite component
for (boost::tie(vi, vi_end) = vertices(G); vi != vi_end; ++vi) {
const int comp_id = component[*vi];
if (comp_id != inf_comp_id) { // skip infinite component
Cell_handle cell = G[*vi]; // current cell
double Vc, Sc; // cell volume and surface
Array_double_4 Sa; // per atom surface in cell
Vc = cell_void_volume(cell, Sc, Sa); // void volume of cell and its surface area
res.voids[comp_id].volume += Vc; // add to volume of component
res.voids[comp_id].surface += Sc;
for (int k = 0; k < 4; k++) { // process four cell atoms
int atom_id = cell->vertex(k)->info().atom_id;
res.atom_surf[atom_id] += Sa[k]; // atom exposed surface
res.voids[comp_id].atoms.insert(atom_id); // add to set of cavity atoms
}
}
}
// Remove skipped infinite component with zero values
res.voids.erase(res.voids.begin() + inf_comp_id);
// Sort cavities by volume
std::sort(res.voids.begin(), res.voids.end(), void_greater);
return true;
}