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Merge branch 'Triangulation_3-CDT_3-lrineau' of https://github.com/lrineau/cgal into Triangulation_3-CDT_3-lrineau

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Jane Tournois 2025-06-23 16:20:30 +02:00
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4
Constrained_triangulation_3/doc/Constrained_triangulation_3/Constrained_triangulation_3.txt
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@ -46,7 +46,7 @@ that satisfy the following properties:
shared vertex. shared vertex.
- The boundary of each polygonal face in the PLC is an ordered list of vertices from the PLC, forming - The boundary of each polygonal face in the PLC is an ordered list of vertices from the PLC, forming
one closed loop. one closed loop.
- Each polygonal face must be a simple polygon, i.e. its edges don't intersect, - Each polygonal face must be a simple polygon, i.e., its edges don't intersect,
except consecutive edges, which intersect at their common vertex. except consecutive edges, which intersect at their common vertex.
- Each polygonal face may have one or more holes, each of them also represented by an ordered list of vertices - Each polygonal face may have one or more holes, each of them also represented by an ordered list of vertices
from the PLC, forming a closed loop. from the PLC, forming a closed loop.
@ -82,7 +82,7 @@ joining them does not intersect any polygonal face of the PLC, except for polygo
the segment. the segment.
In 3D, constrained triangulations do not always exist. This can be demonstrated using the example of In 3D, constrained triangulations do not always exist. This can be demonstrated using the example of
Schönhardt polyhedra \cgalCite{schonhardt1928zerlegung} (see \cgalFigureRef{CT_3_schonhardt_fig}), Schönhardt polyhedra \cgalCite{s-udzvd-28} (see \cgalFigureRef{CT_3_schonhardt_fig}),
\cgalCite{b-ip-48a}. Shewchuk \cgalCite{cgal:shewchuk1998condition} demonstrated that for any PLC, \cgalCite{b-ip-48a}. Shewchuk \cgalCite{cgal:shewchuk1998condition} demonstrated that for any PLC,
there exists a refined there exists a refined
version of the original PLC that admits a constrained Delaunay triangulation. This refinement is version of the original PLC that admits a constrained Delaunay triangulation. This refinement is

10
Documentation/doc/biblio/geom.bib
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@ -152087,16 +152087,6 @@ keywords = {polygonal surface mesh, Surface reconstruction, kinetic framework, s
publisher={Elsevier} publisher={Elsevier}
} }
@article{schonhardt1928zerlegung,
title={{\"U}ber die Zerlegung von Dreieckspolyedern in Tetraeder},
author={Sch{\"o}nhardt, Erich},
journal={Mathematische Annalen},
volume={98},
number={1},
pages={309--312},
year={1928},
publisher={Springer}
}
@inproceedings{si2005meshing, @inproceedings{si2005meshing,
title={Meshing piecewise linear complexes by constrained {Delaunay} tetrahedralizations}, title={Meshing piecewise linear complexes by constrained {Delaunay} tetrahedralizations},