On the three-dimensional visibility skeleton: implementation and analysis

Linqiao Zhang 1, 2
1 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : The visibility skeleton is a data structure that encodes global visibility information of a given scene in either 2D or 3D. While this data structure is in principle very useful in answering global visibility queries, its high order worst-case complexity, especially in 3D scene, appears to be prohibitive. However, previous theoretical research has indicated that the expected size of this data structure can be linear under some restricted conditions. This thesis advances the study of the size of the visibility skeleton, namely, using an experimental approach. We first show that, both theoretically and experimentally, the expected size of the visibility skeleton in 2D is linear, and present a linear asymptote that facilitates estimation of the size of the 2D visibility skeleton. We then study the 3D visibility skeleton defined by visual events, which is a subset of the full skeleton defined by Durand et al.. We first present an implementation to compute the vertices of that skeleton for convex disjoint polytopes in general position. This implementation makes it possible to carry on our empirical study in 3D. We consider input scenes that consist of disjoint convex polytopes that approximate randomly distributed unit spheres. We found that, in our setting, the size of the 3D visibility skeleton is quadratically related to the number of the input polytopes and linearly related to the expected silhouette size of the input polytopes. This estimate is much lower than the worst-case complexity, but higher than the expected linear complexity that we had initially hoped for. We also provide arguments that could explain the obtained complexity. We finally prove that, using the 3D visibility skeleton defined by visual events, we can compute the remaining vertices of the full skeleton in almost linear time in the size of their output.
keyword : visibilite 3D
Document type :
Computer Science [cs]. Université McGill, 2009. English
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Contributor : Sylvain Lazard <>
Submitted on : Thursday, November 12, 2009 - 12:36:39 PM
Last modification on : Tuesday, October 25, 2016 - 5:02:39 PM
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  • HAL Id : tel-00431464, version 1



Linqiao Zhang. On the three-dimensional visibility skeleton: implementation and analysis. Computer Science [cs]. Université McGill, 2009. English. <tel-00431464>



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