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Conference Papers Year : 2002

## On the Number of Lines Tangent to Four Convex Polyhedra

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Hervé Brönnimann
• Function : Author
Olivier Devillers
Vida Dujmovic
• Function : Author
Hazel Everett
• Function : Author
• PersonId : 830545
Marc Glisse
Xavier Goaoc
Sylvain Lazard
Hyeon-Suk Na
• Function : Author
Sue Whitesides
• Function : Author

#### 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.

#### Domains

Computer Science [cs] Other [cs.OH]

### Dates and versions

inria-00099449 , version 1 (15-12-2009)

### Identifiers

• HAL Id : inria-00099449 , version 1

### Cite

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. ⟨inria-00099449⟩

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