Delaunay triangulations of closed Euclidean d-orbifolds
Identifieur interne : 000124 ( Main/Exploration ); précédent : 000123; suivant : 000125Delaunay triangulations of closed Euclidean d-orbifolds
Auteurs : Manuel Caroli [France] ; Monique Teillaud [France]Source :
- Discrete and Computational Geometry [ 0179-5376 ] ; 2016.
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Abstract
We give a definition of the Delaunay triangulation of a point set in a closed Euclidean d-manifold, i.e. a compact quotient space of the Euclidean space for a discrete group of isometries (a so-called Bieberbach group or crystallographic group). We describe a geometric criterion to check whether a partition of the manifold actually forms a triangulation (which subsumes that it is a simplicial complex). We provide an incremental algorithm to compute the Delaunay triangulation of the manifold defined by a given set of input points, if it exists. Otherwise, the algorithm returns the Delaunay triangulation of a finite-sheeted covering space of the manifold. The algorithm has optimal randomized worst-case time and space complexity. It extends to closed Euclidean orbifolds. An implementation for the special case of the 3D flat torus has been released in Cgal 3.5. To the best of our knowledge, this is the first general result on this topic.
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DOI: 10.1007/s00454-016-9782-6
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We describe a geometric criterion to check whether a partition of the manifold actually forms a triangulation (which subsumes that it is a simplicial complex). We provide an incremental algorithm to compute the Delaunay triangulation of the manifold defined by a given set of input points, if it exists. Otherwise, the algorithm returns the Delaunay triangulation of a finite-sheeted covering space of the manifold. The algorithm has optimal randomized worst-case time and space complexity. It extends to closed Euclidean orbifolds. An implementation for the special case of the 3D flat torus has been released in Cgal 3.5. To the best of our knowledge, this is the first general result on this topic.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Metz</li><li>Nancy</li></settlement><orgName><li>Université de Lorraine</li></orgName></list><tree><country name="France"><noRegion><name sortKey="Caroli, Manuel" sort="Caroli, Manuel" uniqKey="Caroli M" first="Manuel" last="Caroli">Manuel Caroli</name></noRegion><name sortKey="Teillaud, Monique" sort="Teillaud, Monique" uniqKey="Teillaud M" first="Monique" last="Teillaud">Monique Teillaud</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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