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COMPGEOM
2004
ACM

The number of lines tangent to arbitrary convex polyhedra in 3D

10 years 12 days ago
The number of lines tangent to arbitrary convex polyhedra in 3D
We prove that the lines tangent to four possibly intersecting convex polyhedra in   3 with n edges in total form Θ(n2 ) connected components in the worst case. In the generic case, each connected component is a single line, but our result still holds for arbitrary degenerate scenes. More generally, we show that a set of k convex polyhedra with a total of n edges admits, in the worst case, Θ(n2 k2 ) connected components of (possibly occluded) lines tangent to any four of these polyhedra. We also show a lower bound of Ω(n2 k2 ) on the number of non-occluded maximal line segments tangent to any four of these k convex polyhedra. Categories and Subject Descriptors F.2.2 [Nonnumerical Algorithms and Problems]: Geometrical problems and computations; G.2.1 [Combinatorics]: Counting problems; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling; I.3.7 [ThreeDimensional Graphics and Realism]: Visible line/surface algorithms General Terms Algorithms, Theory. Keywords Comput...
Hervé Brönnimann, Olivier Devillers, V
Added 30 Jun 2010
Updated 30 Jun 2010
Type Conference
Year 2004
Where COMPGEOM
Authors Hervé Brönnimann, Olivier Devillers, Vida Dujmovic, Hazel Everett, Marc Glisse, Xavier Goaoc, Sylvain Lazard, Hyeon-Suk Na, Sue Whitesides
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