The function regular_neighbor_coordinates_2 computes natural neighbor coordinates, also called Sibson's coordinates, for weighted $$2D points provided a two-dimensional regular triangulation and a (weighted) query point inside the convex hull of the vertices of the triangulation. We call these coordinates regular neighbor coordinates.
#include <CGAL/regular_neighbor_coordinates_2.h>
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computes the regular neighbor coordinates for p with respect to the weighted points in the two-dimensional regular triangulation rt. The template class Rt should be of type Regular_triangulation_2<Traits, Tds>. The value type of the OutputIterator is a pair of Rt::Weighted_point and the coordinate value of type Rt::Geom_traits::FT. The sequence of point/coordinate pairs that is computed by the function is placed starting at out. The function returns a triple with an iterator that is placed past-the-end of the resulting sequence of point/coordinate pairs, the normalization factor of the coordinates and a Boolean value which is set to true iff the coordinate computation was successful, i.e. if p lies inside the convex hull of the points in rt. | ||||
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The same as above. hole_begin and hole_end determines the iterator range over the boundary edges of the conflict zone of p in the triangulation rt. hidden_vertices_begin and hidden_vertices_end determines the iterator range over the hidden vertices of the conflict zone of p inrt. It is the result of the function T.get_boundary_of_conflicts(p,std::back_inserter(hole), std::back_inserter(hidden_vertices), start), see Regular_triangulation_2<Traits, Tds>. | ||||
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This function computes the regular neighbor coordinates of the point vh->point() with respect to the vertices of rt excluding vh->point(). The same as above for the remaining parameters. |