Visibility, occlusion, and the aspect graph
International Journal of Computer Vision
The visibility skeleton: a powerful and efficient multi-purpose global visibility tool
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Fast and accurate hierarchical radiosity using global visibility
ACM Transactions on Graphics (TOG)
ACM Transactions on Graphics (TOG)
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
The Expected Number of 3D Visibility Events Is Linear
SIAM Journal on Computing
Towards an implementation of the 3D visibility skeleton
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
On incremental rendering of silhouette maps of a polyhedral scene
Computational Geometry: Theory and Applications
Lines and Free Line Segments Tangent to Arbitrary Three-Dimensional Convex Polyhedra
SIAM Journal on Computing
An Upper Bound on the Average Size of Silhouettes
Discrete & Computational Geometry
On the degree of standard geometric predicates for line transversals in 3D
Computational Geometry: Theory and Applications
On the computation of 3D visibility skeletons
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Lines through segments in 3d space
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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The 3D visibility skeleton is a data structure used to encode global visibility information about a set of objects. Previous theoretical results have shown that for kconvex polytopes with nedges in total, the worst case size complexity of this data structure is 茂戮驴(n2k2) [Brönnimann et al. 07]; whereas for kuniformly distributed unit spheres, the expected size is 茂戮驴(k) [Devillers et al. 03].In this paper, we study the size of the visibility skeleton experimentally. Our results indicate that the size of the 3D visibility skeleton, in our setting, is $ C\,k\sqrt{n\,k}$, where Cvaries with the scene density but remains small. This is the first experimentally determined asymptotic estimate of the size of the 3D visibility skeleton for reasonably large nand expressed in terms of both nand k. We suggest theoretical explanations for the experimental results we obtained. Our experiments also indicate that the running time of our implementation is O(n3/2klogk), while its worst-case running time complexity is O(n2k2logk).