static Cell_handle findBestCell(const Vector_3 &direction,
const Vertex_handle &infinity,
const Cell_handle &startingCell)
{
DEBUG_START;
/* FIXME: Maybe some hint will be useful here */
ASSERT(startingCell->has_vertex(infinity) && "Wrong input");
Cell_handle bestCell = startingCell;
Cell_handle nextCell = bestCell;
double maxProduct = calculateProduct(direction, bestCell, infinity);
unsigned numIterations = 0;
do
{
++numIterations;
bestCell = nextCell;
ASSERT(bestCell->has_vertex(infinity) && "Wrong iteration");
int infinityIndex = bestCell->index(infinity);
for (int i = 0; i < NUM_CELL_VERTICES; ++i)
{
if (i == infinityIndex)
continue;
Cell_handle neighbor = bestCell->neighbor(i);
double product = calculateProduct(direction,
neighbor, infinity);
if (product > maxProduct)
{
nextCell = neighbor;
maxProduct = product;
}
}
} while (nextCell != bestCell);
ASSERT(bestCell->has_vertex(infinity) && "Wrong result");
DEBUG_END;
return bestCell;
}
bool
is_p_outside(const Point& q, const Triangulation& triang,
const Cell_handle& start_cell,
Cell_handle& c, int& u, int& v)
{
Triangulation::Locate_type lt;
u = -1; v = -1;
c = triang.locate(q, lt, u, v, start_cell);
if( lt == Triangulation::OUTSIDE_AFFINE_HULL )
{
cerr << "Point " << q << " is outside the affine hull." << endl;
return true;
}
else if( lt == Triangulation::OUTSIDE_CONVEX_HULL )
return true;
else
{
if( lt == Triangulation::CELL )
{
if( c->outside )
return true;
else
return false;
}
else if( lt == Triangulation::FACET )
{
Cell_handle _c = c->neighbor(u);
if( c->outside && _c->outside )
return true;
else
return false;
}
else if( lt == Triangulation::EDGE )
{
if( is_outside_VF(triang, Edge(c, u, v)) )
return true;
else
return false;
}
else
{
CGAL_assertion( lt == Triangulation::VERTEX );
return false;
}
}
}
AlphaSimplex3D::
AlphaSimplex3D(const Delaunay3D::Facet& f, const SimplexSet& simplices, const Delaunay3D& Dt)
{
Cell_handle c = f.first;
for (int i = 0; i < 4; ++i)
if (i != f.second)
Parent::add(c->vertex(i));
Cell_handle o = c->neighbor(f.second);
int oi = o->index(c);
VertexSet::const_iterator v = static_cast<const Parent*>(this)->vertices().begin();
const DPoint& p1 = (*v++)->point();
const DPoint& p2 = (*v++)->point();
const DPoint& p3 = (*v)->point();
attached_ = false;
if (!Dt.is_infinite(c->vertex(f.second)) &&
CGAL::side_of_bounded_sphere(p1, p2, p3,
c->vertex(f.second)->point()) == CGAL::ON_BOUNDED_SIDE)
attached_ = true;
else if (!Dt.is_infinite(o->vertex(oi)) &&
CGAL::side_of_bounded_sphere(p1, p2, p3,
o->vertex(oi)->point()) == CGAL::ON_BOUNDED_SIDE)
attached_ = true;
else
alpha_ = CGAL::squared_radius(p1, p2, p3);
if (attached_)
{
if (Dt.is_infinite(c))
alpha_ = simplices.find(AlphaSimplex3D(*o))->alpha();
else if (Dt.is_infinite(o))
alpha_ = simplices.find(AlphaSimplex3D(*c))->alpha();
else
alpha_ = std::min(simplices.find(AlphaSimplex3D(*c))->alpha(),
simplices.find(AlphaSimplex3D(*o))->alpha());
}
}
// 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;
}
bool is_degenerate_VF(const Triangulation& triang, const Cell_handle& c, const int& fid, const int& uid, const int& vid, const Point& d, const char* prefix)
{
char degen_op_filename[200];
strcat(strcpy(degen_op_filename, prefix), ".degen_VF");
// an extra check - probably not needed.
if (triang.is_infinite(c) || triang.is_infinite(c->neighbor(fid)) || triang.is_infinite(c->neighbor(6 - fid - uid - vid)))
{
return true;
}
vector<Cell_handle> VF;
Facet_circulator fcirc = triang.incident_facets(Edge(c,uid,vid));
Facet_circulator begin = fcirc;
do
{
if (triang.is_infinite((*fcirc).first))
{
cerr << "< Inf VF >";
return true; // by check-1 it is degenerate.
}
Cell_handle cur_c = (*fcirc).first;
int cur_fid = (*fcirc).second;
// check if cur_c and its cur_fid neighbors are cospherical.
if (is_cospherical_pair(triang, Facet(cur_c,cur_fid)))
{
cerr << "< Cosph VF >";
return true; // by check-2 it is degenerate.
}
fcirc ++;
}
while (fcirc != begin);
// check-3
Point vv[3];
vv[0] = c->voronoi();
vv[1] = c->neighbor(fid)->voronoi();
vv[2] = c->neighbor(6 - fid - uid - vid)->voronoi();
Vector v[3];
v[0] = vv[0] - d;
v[1] = vv[1] - d;
v[2] = vv[2] - d;
Vector v1xv0 = CGAL::cross_product(v[1], v[0]);
Vector v0xv2 = CGAL::cross_product(v[0], v[2]);
if (CGAL::to_double(v1xv0 * v0xv2) < 0)
{
ofstream fout;
fout.open(degen_op_filename, ofstream::app);
fout << "# prob : v1xv0 * v0xv2 = " <<
CGAL::to_double(v1xv0 * v0xv2) << endl;
fout << "{LIST " << endl;
fout << "# VF - color yellow " << endl;
draw_VF(triang, Edge(c, uid, vid), 1, 1, 0, 1, fout);
fout << "# v0 : segment(driver, voronoi(c)) - color red " << endl;
draw_segment(Segment(d, vv[0]), 1, 0, 0, 1, fout);
fout << "# v1 : segment(driver, voronoi(c->neighbor1)) - color green " << endl;
draw_segment(Segment(d, vv[1]), 0, 1, 0, 1, fout);
fout << "# v2 : segment(driver, voronoi(c->neighbor2)) - color blue " << endl;
draw_segment(Segment(d, vv[2]), 0, 0, 1, 1, fout);
fout << "}" << endl;
fout.close();
cerr << "< - v1xv0 * v0xv2 < 0 - >";
return true;
}
return false;
}
float
sdf( const Point& q, const Mesh &mesh, const vector<double>& weights,
KdTree& kd_tree, const Triangulation& triang )
{
VECTOR3 query (CGAL::to_double(q.x()),
CGAL::to_double(q.y()),
CGAL::to_double(q.z()));
kd_tree.queryPosition(query);
// Initialize the search structure, and search all N points
int n_vid = kd_tree.getNeighbourPositionIndex(0);
if(n_vid == -1) throw std::runtime_error("No nearest neighbor. MDS empty?");
CGAL_assertion( ! mesh.vert_list[n_vid].iso());
MVertex nv = mesh.vert_list[n_vid];
double min_sq_d = HUGE;
int n_fid = -1;
for(int i = 0; i < nv.num_inc_face; i ++)
{
MFace f = mesh.face_list[nv.inc_face(i)];
Point p[3] = {mesh.vert_list[f.get_corner(0)].point(),
mesh.vert_list[f.get_corner(1)].point(),
mesh.vert_list[f.get_corner(2)].point()};
Triangle_3 t (p[0], p[1], p[2]);
Plane_3 H (p[0], p[1], p[2]);
Point _q = H.projection(q);
// check if _q is inside t.
if( t.has_on(_q) )
{
double sq_d = CGAL::to_double((q-_q)*(q-_q));
if( sq_d < min_sq_d ) { min_sq_d = sq_d; n_fid = nv.inc_face(i); }
}
else
{
for(int j = 0; j < 3; j ++)
{
double _d = CGAL::to_double(CGAL::squared_distance(_q,Segment(p[j], p[(j+1)%3])));
double sq_d = CGAL::to_double((q-_q)*(q-_q)) + _d;
if( sq_d < min_sq_d ) { min_sq_d = sq_d; n_fid = nv.inc_face(i); }
}
}
}
// locate the query point in the triang which is already tagged
// with in-out flag by the reconstruction.
bool is_q_outside = false;
Triangulation::Locate_type lt;
int u = -1, v = -1;
Cell_handle c = triang.locate(q, lt, u, v);
if( lt == Triangulation::OUTSIDE_AFFINE_HULL )
{
is_q_outside = true;
cerr << "Point " << q << " is outside the affine hull." << endl;
}
else if( lt == Triangulation::OUTSIDE_CONVEX_HULL )
is_q_outside = true;
else
{
if( lt == Triangulation::CELL )
{
if( c->outside )
is_q_outside = true;
else
is_q_outside = false;
}
else if( lt == Triangulation::FACET )
{
Cell_handle _c = c->neighbor(u);
if( c->outside && _c->outside )
is_q_outside = true;
else
is_q_outside = false;
}
else if( lt == Triangulation::EDGE )
{
if( is_outside_VF(triang, Edge(c, u, v)) )
is_q_outside = true;
else
is_q_outside = false;
}
else
{
CGAL_assertion( lt == Triangulation::VERTEX );
is_q_outside = false;
}
}
double w;
if(weights.size() && mesh.face_list[n_fid].label != -1) w = weights[mesh.face_list[n_fid].label];
else w = 1.0;
// double w = mesh.face_list[n_fid].w;
double gen_sdf = 0;
if( is_q_outside ) gen_sdf = w*sqrt(min_sq_d);
else gen_sdf = -w*min_sq_d;
#if 0
double MAX = 10, MIN = -10;
if( gen_sdf > MAX ) gen_sdf = MAX;
if( gen_sdf < MIN ) gen_sdf = MIN;
#endif
return gen_sdf;
}