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Triangulation in 2D and 3D space

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Geometry and Robotics (GeoRob 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 391))

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Abstract

This paper is a review of some problems related to the triangulation of polygons or point sets in 2D and 3D space. It includes in particular a proof of the equiangularity properties of the Delaunay triangulation in 2D space and a short review on the different algorithms for the triangulation of polygons. The (still open) question of the intrinsic complexity of the triangulation problem for a simple polygon is also raised. As far as 3D space is concerned, the combinatory relations which provide bounds on the number of tetrahedra which appear in the triangulation of a set of points are given. A divide and conquer algorithm for triangulating arbitrary set of points is also presented. This algorithm is based on a splitting theorem which has been proved independently by Avis and ElGindy on one side and Edelsbrunner, Preparata and West on the other side.

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Authors and Affiliations

  1. Liens _ URA Cnrs 1327 Ecole Normale Supérieure, 45 rue d'Ulm, 75230, Paris, France

    M. Yvinec

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  1. M. Yvinec
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J. -D. Boissonnat J. -P. Laumond

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© 1989 Springer-Verlag Berlin Heidelberg

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Yvinec, M. (1989). Triangulation in 2D and 3D space. In: Boissonnat, J.D., Laumond, J.P. (eds) Geometry and Robotics. GeoRob 1988. Lecture Notes in Computer Science, vol 391. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51683-2_35

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  • DOI: https://doi.org/10.1007/3-540-51683-2_35

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51683-5

  • Online ISBN: 978-3-540-46748-9

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