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Laurent Rineau 2025-06-26 10:28:30 +02:00
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Constrained_triangulation_3/doc/Constrained_triangulation_3/Constrained_triangulation_3.txt
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@ -175,22 +175,23 @@ of a `CGAL::Conforming_constrained_Delaunay_triangulation_3` object from either
\subsection CT_3_geomtraits Traits and Kernel Choice
The requirements on geometric objects and operations are described in the traits class concept
The requirements for geometric objects and operations are specified by the traits class concept
`ConformingConstrainedDelaunayTriangulationTraits_3`. Any CGAL kernel is a model of this concept.
However, since this package is based on the 3D Triangulation package we inherit the requirement that
a traits class providing exact predicates is needed.
However, because this package builds upon the 3D Triangulation package, it inherits the requirement
that the traits class must provide exact predicates.
One important new part of this algorithm is the creation of new points that are not part of the input.
Those points are the Steiner points that are constructed on segments and polygons of the input PLC.
If a traits with inexact constructions is used, it is not possible to guarantee that the points are
exactly on segments/polygons. As a consequence, when using inexact constructions, the output will
only be an approximation of the input (up to the rounding of the computed Steiner points).
Also in such a case, it will not always be possible to get a result if the input PLC features
too close non-adjacent simplices. The algorithm will abort the triangulation if the distance between
simplices goes below a threshold internally computed. In such a case, an error message with
the involved simplices will be displayed on the standard output. In case the issue is coming from badly
shaped triangles, methods such as `CGAL::Polygon_mesh_processing::remove_almost_degenerate_faces()`
might be useful to overcome this limitation.
A key aspect of this algorithm is the creation of new points, known as Steiner points, which are
inserted on the segments and polygons of the input PLC. If a traits class with inexact constructions
is used, it cannot be guaranteed that these points will lie exactly on the intended segments or polygons.
As a result, the output will only approximate the input, with the accuracy limited by the rounding
of the computed Steiner points.
Furthermore, when using inexact constructions, the algorithm may fail if the input PLC contains
non-adjacent simplices that are too close to each other. In such cases, the triangulation process
will emit an error if the distance between simplices falls below an internally computed threshold.
An error message describing the involved simplices will be displayed on the standard output.
If the issue is caused by poorly shaped triangles, functions such as
`CGAL::Polygon_mesh_processing::remove_almost_degenerate_faces()` may help resolve the problem.
\section CT_3_examples Examples