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# Dynamic updates of succinct triangulations

2 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : In a recent article, we presented a succinct representation of triangulations that supports efficient navigation operations. Here this representation is improved to allow for efficient local updates of the triangulations. Precisely, we show how a succinct representation of a triangulation with $m$ triangles can be maintained under vertex insertions in $O(1)$ amortized time and under vertex deletions/edge flips in $O(\lg^{2} m)$ amortized time. Our structure achieves the information theory bound for the storage for the class of triangulations with a boundary, requiring asymptotically $2.17m+o(m)$ bits, and supports adjacency queries between triangles in $O(1)$ time (an extra amount of $O(g\lg m)$ bits are needed for representing triangulations of genus $g$ surfaces).
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Conference papers
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Cited literature [8 references]

https://hal.inria.fr/inria-00001187
Contributor : Olivier Devillers <>
Submitted on : Wednesday, April 12, 2006 - 2:55:22 PM
Last modification on : Tuesday, December 29, 2020 - 7:04:02 AM
Long-term archiving on: : Saturday, April 3, 2010 - 10:10:15 PM

### Identifiers

• HAL Id : inria-00001187, version 1

### Citation

Luca Castelli Aleardi, Olivier Devillers, Gilles Schaeffer. Dynamic updates of succinct triangulations. 18th Canadian Conference on Computational Geometry, 2005, Windsor, Canada, France. ⟨inria-00001187⟩

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