# On the Number of Lines Tangent to Four Convex Polyhedra

1 PRISME - Geometry, Algorithms and Robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
3 ISA - Models, algorithms and geometry for computer graphics and vision
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We prove that, under a certain general position assumption, the number of lines tangent to four bounded disjoint convex polyhedra in $\Real^3$ with a total of $n$ edges is $O(n^2)$. Under the same assumption, we show that a set of $k$ bounded disjoint convex polyhedra has at most $O(n^2k^2)$ lines, possibly occluded, that are tangent to four of these polyhedra.
Mots-clés :
Type de document :
Communication dans un congrès
14th Canadian Conference on Computational Geometry - CCCG'02, 2002, Lethbridge, Canada, 2002
Domaine :

https://hal.inria.fr/inria-00099449
Contributeur : Sylvain Lazard <>
Soumis le : mardi 15 décembre 2009 - 15:18:19
Dernière modification le : samedi 27 janvier 2018 - 01:31:34
Document(s) archivé(s) le : mardi 6 avril 2010 - 01:11:52

### Identifiants

• HAL Id : inria-00099449, version 1

### Citation

Hervé Brönnimann, Olivier Devillers, Vida Dujmovic, Hazel Everett, Marc Glisse, et al.. On the Number of Lines Tangent to Four Convex Polyhedra. 14th Canadian Conference on Computational Geometry - CCCG'02, 2002, Lethbridge, Canada, 2002. 〈inria-00099449〉

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