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Explicit array-based compact data structures for triangulations

Luca Castelli Aleardi 1 Olivier Devillers 2
2 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : We consider the problem of designing space efficient solutions for representing triangle meshes. Our main result is a new explicit data structure for compactly representing planar triangulations: if one is allowed to permute input vertices, then a triangulation with n vertices requires at most 4n references (5n references if vertex permutations are not allowed). Our solution combines existing techniques from mesh encoding with a novel use of minimal Schnyder woods. Our approach extends to higher genus triangulations and could be applied to other families of meshes (such as quadrangular or polygonal meshes). As far as we know, our solution provides the most parsimonious data structures for triangulations, allowing constant time navigation in the worst case. Our data structures require linear construction time, and all space bounds hold in the worst case. We have implemented and tested our results, and experiments confirm the practical interest of compact data structures.
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Submitted on : Tuesday, March 13, 2012 - 2:20:44 PM
Last modification on : Thursday, March 5, 2020 - 6:27:46 PM
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  • HAL Id : hal-00678615, version 1



Luca Castelli Aleardi, Olivier Devillers. Explicit array-based compact data structures for triangulations. 22nd International Symposium on Algorithms and Computation, 2011, Yokohama, Japan. pp.312--322. ⟨hal-00678615⟩



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