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Kernel recommandation proposal

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Sébastien Loriot 2025-06-17 17:38:56 +02:00
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Constrained_triangulation_3/doc/Constrained_triangulation_3/Constrained_triangulation_3.txt
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@ -163,12 +163,21 @@ 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
`ConformingConstrainedDelaunayTriangulationTraits_3`. Any CGAL kernel is a model of this concept, but
the package is designed to work with kernels that provide exact predicates.
`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.
As the Steiner points are inserted on the input edges and polygons of the PLC, the coordinates of
those points will be constructed. If the input data set has almost-coplanar input polygons, a kernel
with exact constructions must be used to ensure the correct placement of these points.
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 points 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.
\section CT_3_examples Examples