#include <CGAL/Regular_triangulation_2.h>

Inherits From

Triangulation_2<Gt,Tds>

The functions insert and remove are overwritten to maintain the regular property and the checking function is_valid() is also overwritten to additionally test the local regular property of any pair of neighboring faces.

Types

Creation

Regular_triangulation_2<Gt, Tds> rt ( Gt gt = Gt());
	Introduces an empty regular triangulation rt.
Regular_triangulation_2<Gt, Tds> rt ( Regular_triangulation_2 rt);
	Copy constructor.

Insertion and Removal

The vertices of the regular triangulation of a set of weighted points $$ PW form only a subset of the set of center points of $$ PW. Therefore the insertion of a weighted point in a regular triangulation does not necessarily imply the creation of a new vertex. If the new inserted point does not appear as a vertex in the regular triangulation, it is said to be hidden by the face in which the corresponding center point is located. Such a weighted point is stored in a list attached to the hiding face, to be used for later tentative of insertions when future removal of some points implies the destruction of the hiding face.

bool	rt.insert ( Weighted_point p, Face_handle f=Face_handle())
		inserts weighted point p. returns true if a new vertex is created. If a weighted point with the same center point but a different weight already exists in the triangulation, it is removed and replaced by the new point.
bool	rt.insert ( Weighted_point p, Locate_type lt, Face_handle loc, int li)
		insert a weighted point p whose bare-point is assumed to be located in lt,loc,li.
Vertex_handle	rt.push_back ( Point p)
		Equivalent to insert(p).
template < class InputIterator >
int	rt.insert ( InputIterator first, InputIterator last)
		inserts the weighted points in the range $$[.first, last$$.). Returns the number of created vertices. Precondition: The value_type of first and last is Weighted_point.
int	rt.remove ( Vertex_handle v)
		removes the vertex from the triangulation and returns the number of new vertices created by the insertion of previously hidden points.

Geometric Predicates

Oriented_side	rt.power_test ( Face_handle f, Weighted_point p)
		Returns the power test of p with respect to the power circle associated with f

Miscellaneous

bool	rt.is_valid ( bool verbose = false, int level = 0)
		Tests the validity of the triangulation as a Triangulation_2 and additionally test the regularity of the triangulation. This method is mainly useful for debugging Delaunay triangulation algorithms designed by the user.