\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.14 - 2D Conforming Triangulations and Meshes
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CGAL::Triangulation_conformer_2< CDT > Class Template Reference
2D Conforming Triangulations and Meshes Reference

#include <CGAL/Triangulation_conformer_2.h>

Definition

The class Triangulation_conformer_2 is an auxiliary class of Delaunay_mesher_2<CDT>.

It permits to refine a constrained Delaunay triangulation into a conforming Delaunay or conforming Gabriel triangulation. For standard needs, consider using the global functions make_conforming_Gabriel_2() and make_conforming_Delaunay_2().

Template Parameters
CDTmust be a 2D constrained Delaunay triangulation and its geometric traits class must be a model of the concept ConformingDelaunayTriangulationTraits_2.

Using This Class

The constructor of the class Triangulation_conformer_2 takes a reference to a CDT as an argument. A call to the method make_conforming_Delaunay() or make_conforming_Gabriel() will refine this constrained Delaunay triangulation into a conforming Delaunay or conforming Gabriel triangulation. Note that if, during the life time of the Triangulation_conformer_2 object, the triangulation is externally modified, any further call to its member methods may lead to undefined behavior. Consider reconstructing a new Triangulation_conformer_2 object if the triangulation has been modified.

The conforming methods insert points into constrained edges, thereby splitting them into several sub-constraints. You have access to the initial inserted constraints if you instantiate the template parameter by a Constrained_triangulation_plus_2<CDT>.

Creation

 Triangulation_conformer_2 (CDT &t)
 Create a new conforming maker, working on t.
 

Conforming methods

void make_conforming_Delaunay ()
 Refines the triangulation into a conforming Delaunay triangulation. More...
 
void make_conforming_Gabriel ()
 Refines the triangulation into a conforming Gabriel triangulation. More...
 

Checking

The following methods verify that the constrained triangulation is conforming Delaunay or conforming Gabriel.

These methods scan the whole triangulation and their complexity is proportional to the number of edges.

bool is_conforming_Delaunay ()
 Returns true iff all triangles fulfill the Delaunay property.
 
bool is_conforming_Gabriel ()
 Returns true iff all constrained edges have the Gabriel property: their circumsphere is empty.
 

Step by Step Operations

The Triangulation_conformer_2 class allows, for debugging or demos, to play the conforming algorithm step by step, using the following methods.

They exist in two versions, depending on whether you want the triangulation to be conforming Delaunay or conforming Gabriel, respectively. Any call to a step_by_step_conforming_XX function requires a previous call to the corresponding function init_XX and Gabriel and Delaunay methods can not be mixed between two calls of init_XX.

void init_Delaunay ()
 The method must be called after all points and constrained segments are inserted and before any call to the following methods. More...
 
bool step_by_step_conforming_Delaunay ()
 Applies one step of the algorithm, by inserting one point, if the algorithm is not done. More...
 
void init_Gabriel ()
 Analog to init_Delaunay for Gabriel conforming.
 
bool step_by_step_conforming_Gabriel ()
 Analog to step_by_step_conforming_Delaunay() for Gabriel conforming.
 
bool is_conforming_done ()
 Tests if the step by step conforming algorithm is done. More...
 

Member Function Documentation

◆ init_Delaunay()

template<typename CDT >
void CGAL::Triangulation_conformer_2< CDT >::init_Delaunay ( )

The method must be called after all points and constrained segments are inserted and before any call to the following methods.

If some points or segments are then inserted in the triangulation, this method must be called again.

◆ is_conforming_done()

template<typename CDT >
bool CGAL::Triangulation_conformer_2< CDT >::is_conforming_done ( )

Tests if the step by step conforming algorithm is done.

If it returns true, the following calls to step_by_step_conforming_XX will not insert any points, until some new constrained segments or points are inserted in the triangulation and init_XX is called again.

◆ make_conforming_Delaunay()

template<typename CDT >
void CGAL::Triangulation_conformer_2< CDT >::make_conforming_Delaunay ( )

Refines the triangulation into a conforming Delaunay triangulation.

After a call to this method, all triangles fulfill the Delaunay property, that is the empty circle property.

◆ make_conforming_Gabriel()

template<typename CDT >
void CGAL::Triangulation_conformer_2< CDT >::make_conforming_Gabriel ( )

Refines the triangulation into a conforming Gabriel triangulation.

After a call to this method, all constrained edges \( e\) have the Gabriel property: the circle with diameter \( e\) does not contain any vertex of the triangulation.

◆ step_by_step_conforming_Delaunay()

template<typename CDT >
bool CGAL::Triangulation_conformer_2< CDT >::step_by_step_conforming_Delaunay ( )

Applies one step of the algorithm, by inserting one point, if the algorithm is not done.

Returns false iff no point has been inserted because the algorithm is done.