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.
Document type :
Conference papers
Complete list of metadatas

Cited literature [25 references]  Display  Hide  Download


https://hal.inria.fr/hal-00678615
Contributor : Olivier Devillers <>
Submitted on : Tuesday, March 13, 2012 - 2:20:44 PM
Last modification on : Wednesday, March 27, 2019 - 4:41:27 PM
Long-term archiving on : Thursday, June 14, 2012 - 5:54:51 PM

Files

CompactTriangleMeshes.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00678615, version 1

Collections

Citation

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⟩

Share

Metrics

Record views

710

Files downloads

646