CGAL::Triangulation_conformer_2<CDT>
The class Triangulation_conformer_2<CDT> 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.
#include <CGAL/Triangulation_conformer_2.h>
Parameters
The template parameter CDT should be a model of the concept
ConstrainedDelaunayTriangulation_2.
The geometric traits class of the instance of CDT has to be
a model of the concept ConformingDelaunayTriangulationTraits_2.
Using this class
The constructor of the class Triangulation_conformer_2<CDT> 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<CDT> 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<CDT> 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
CGAL::Constrained_triangulation_plus_2<CDT>.
Creation
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Triangulation_conformer_2<CDT> m ( CDT& t);
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Create a new conforming maker, working on t.
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Operations
Conforming methods
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void
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m.make_conforming_Delaunay ()
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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.
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void
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m.make_conforming_Gabriel ()
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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.
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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.
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bool
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m.is_conforming_Delaunay ()
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Returns true iff all triangles fulfill the Delaunay property.
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bool
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m.is_conforming_Gabriel ()
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Returns true iff all constrained edges have the Gabriel property:
their circumsphere is empty.
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Step by step operations
The Triangulation_conformer_2<CDT> 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.
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void
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m.init_Delaunay ()
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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.
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bool
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m.step_by_step_conforming_Delaunay ()
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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.
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void
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m.init_Gabriel ()
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Analog to
init_Delaunay for Gabriel conforming.
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bool
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m.step_by_step_conforming_Gabriel ()
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Analog to
step_by_step_conforming_Delaunay() for Gabriel conforming.
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bool
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m.is_conforming_done ()
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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.
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