An Experimental Assessment of the 2D Visibility Complex

Hazel Everett 1 Sylvain Lazard 1 Sylvain Petitjean 1 Linqiao Zhang 1
1 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We make an experimental assessment of the size of the 2D visibility complex of disjoint unit discs randomly distributed in the plane with density $\mu$. We observe that the number of free bitangents is asymptotically linear in the number of discs and we study the dependence of the linear asymptote in terms of the density of the scene. Specifically, for a particular range of scene densities $\mu$, we exhibit an approximation of the number of free bitangents in terms of $\mu$ and the number $n$ of discs, for $n$ larger than some function of $\mu$. We also notice how our approximation gained for rather large densities can be used to guess the onset of the linear behavior for small densities.
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https://hal.inria.fr/inria-00000373
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Submitted on : Tuesday, October 4, 2005 - 12:12:25 PM
Last modification on : Thursday, January 11, 2018 - 6:20:14 AM
Long-term archiving on : Monday, September 20, 2010 - 11:39:23 AM

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Hazel Everett, Sylvain Lazard, Sylvain Petitjean, Linqiao Zhang. An Experimental Assessment of the 2D Visibility Complex. 17th Canadian Conference on Computational Geometry - CCCG'2005, Aug 2005, Windsor, Canada. ⟨inria-00000373v2⟩

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