std::pair<Point_3, Dart_handle> operator () (Vertex & v) const
{
Dart_handle d = v.dart ();
int degree = 0;
bool open = false;
LCC::One_dart_per_incident_cell_range<1,0>::iterator it (mlcc, d),
itend(mlcc.one_dart_per_incident_cell<1,0>(d).end());
for (; it != itend; ++it)
{
++degree;
if (mlcc.is_free(it, 2)) open = true;
}
if (open)
return make_pair(v.point(), d);
LCC::FT alpha = (4.0f - 2.0f *
(LCC::FT) cos (2.0f * PI / (LCC::FT) degree)) / 9.0f;
LCC::Vector vec =
LCC::Traits::Construct_scaled_vector()
( LCC::Traits::Construct_vector() (CGAL::ORIGIN, v.point()), (1.0f - alpha));
for (it.rewind (); it != itend; ++it)
{
CGAL_assertion (!mlcc.is_free(it,2));
vec = vec + (mlcc.point(mlcc.beta(it,2)) - CGAL::ORIGIN)
* alpha / degree;
}
std::pair<Point_3, Dart_handle> res=std::make_pair
(LCC::Traits::Construct_translated_point() (CGAL::ORIGIN, vec), d);
return res;
}
Vertex operator () (Vertex & v) const
{
Dart_handle d = v.dart ();
// Old points aren't concerned.
if (mlcc.is_marked(d, old))
{
return v;
}
std::vector<LCC::Point> facetsPoints;
facetsPoints.resize(0);
// We search barycenter point of incidents facets.
for (LCC::One_dart_per_incident_cell_range<1,0>::iterator it =
mlcc.one_dart_per_incident_cell<1,0>(d).begin();
it != mlcc.one_dart_per_incident_cell<1,0>(d).end(); ++it)
{
// If the vertex is on a border.
if (mlcc.is_free(it,2))
{
return v;
}
// If we found barycenter of a facet.
if (!mlcc.is_marked(mlcc.opposite(it), old))
{
facetsPoints.push_back(mlcc.point(mlcc.opposite(it)));
}
}
// If we found more than two points we are on a vertice barycenter of a facet.
// They aren't concerned.
if (facetsPoints.size() > 2 || facetsPoints.size() < 2)
{
return v;
}
// Average.
LCC::Vector averageFacetsV = LCC::Traits::Construct_vector()
( CGAL::ORIGIN, LCC::Point(0,0,0) );
for (unsigned int i=0; i < facetsPoints.size(); i++)
{
averageFacetsV = LCC::Traits::Construct_sum_of_vectors()
(averageFacetsV,
LCC::Traits::Construct_vector() (CGAL::ORIGIN, facetsPoints[i]));
}
averageFacetsV = LCC::Traits::Construct_scaled_vector()
( averageFacetsV, (1.0f/facetsPoints.size()) );
// Barycenter point.
LCC::Vector barycenterV = LCC::Traits::Construct_sum_of_vectors()
( LCC::Traits::Construct_vector() (CGAL::ORIGIN, v.point()), averageFacetsV );
barycenterV = LCC::Traits::Construct_scaled_vector()
( barycenterV, (1.0f/2.0f) );
Vertex res = LCC::Traits::Construct_translated_point() (CGAL::ORIGIN, barycenterV);
res.set_dart (d);
return res;
}
Vertex operator () (Vertex & v) const
{
Dart_handle d = v.dart ();
// Just old points are concerned.
if (!mlcc.is_marked(d, old))
{
return v;
}
unsigned int degree = 0;
std::vector<LCC::Point> edgesPoints;
edgesPoints.resize(0);
std::vector<LCC::Point> facetsPoints;
facetsPoints.resize(0);
// We search barycenter point of incidents facets, and incidents edges points.
for (LCC::One_dart_per_incident_cell_range<1,0>::iterator it =
mlcc.one_dart_per_incident_cell<1,0>(d).begin();
it != mlcc.one_dart_per_incident_cell<1,0>(d).end(); ++it)
{
// If the vertex is on a border
if (mlcc.is_free(it,2))
{
return v;
}
// If incident isn't an old point, it's an edge point.
if (!mlcc.is_marked(mlcc.opposite(it), old))
{
edgesPoints.push_back (mlcc.point(mlcc.opposite(it)));
}
// We go find the "facet point" of incidents facet (barycenter of a facet).
facetsPoints.push_back (mlcc.point(mlcc.beta(mlcc.opposite(it), 0)));
++degree;
}
CGAL_assertion (facetsPoints.size() != 0 && edgesPoints.size() != 0);
if (facetsPoints.size() < 3 || edgesPoints.size() < 3 )
{
return v;
}
// Average of incidents "edge points".
LCC::Vector averageEdgesV = LCC::Traits::Construct_vector()
(CGAL::ORIGIN, LCC::Point(0,0,0));
for (unsigned int i=0; i < edgesPoints.size(); i++)
{
averageEdgesV = LCC::Traits::Construct_sum_of_vectors()
( averageEdgesV,
LCC::Traits::Construct_vector() (CGAL::ORIGIN, edgesPoints[i]));
}
averageEdgesV = LCC::Traits::Construct_scaled_vector()
( averageEdgesV, 1.0f/ (LCC::FT) edgesPoints.size() );
// Average of incidents "facet points".
LCC::Vector averageFacetsV = LCC::Traits::Construct_vector()
(CGAL::ORIGIN, LCC::Point(0,0,0));
for (unsigned int i=0; i < facetsPoints.size(); i++)
{
averageFacetsV = LCC::Traits::Construct_sum_of_vectors()
( averageFacetsV,
LCC::Traits::Construct_vector() (CGAL::ORIGIN, facetsPoints[i]));
}
averageFacetsV = LCC::Traits::Construct_scaled_vector()
( averageFacetsV, (1.0f/ (LCC::FT) facetsPoints.size()) );
// COEFFICIENTS of PQQ - Catmull–Clark subdivision :
// point = ( averageFacets + 2*averageEdges + point*(degree-3) )/degree
averageFacetsV = LCC::Traits::Construct_scaled_vector()
( averageFacetsV, 1.0f/ (LCC::FT) degree);
averageEdgesV = LCC::Traits::Construct_scaled_vector()
( averageEdgesV, 2.0f/ (LCC::FT) degree);
LCC::Vector pointV = LCC::Traits::Construct_scaled_vector()
( LCC::Traits::Construct_vector() (CGAL::ORIGIN, v.point() ),
(LCC::FT) (degree-3)/ (LCC::FT) degree );
// New position of the old point.
LCC::Vector newPosition = LCC::Traits::Construct_sum_of_vectors()
( averageFacetsV, averageEdgesV);
newPosition = LCC::Traits::Construct_sum_of_vectors()
( newPosition, pointV);
Vertex res = LCC::Traits::Construct_translated_point() (CGAL::ORIGIN, newPosition);
res.set_dart (d);
return res;
}
