# Delaunay Triangulation Based Surface Reconstruction: Ideas and Algorithms

1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : Given a finite sampling $P\subset\mathbbR^d$ of an unknown surface $S$, surface reconstruction is concerned with the calculation of a model of $S$ from $P$. The model can be represented as a smooth or a triangulated surface, and is expected to match $S$ from a topological and geometric standpoints. In this survey, we focus on the recent developments of Delaunay based surface reconstruction methods, which were the first methods (and in a sense still the only ones) for which one can precisely state properties of the reconstructed surface. We outline the foundations of these methods from a geometric and algorithmic standpoints. In particular, a careful presentation of the hypothesis used by these algorithms sheds light on the intrinsic difficulties of the surface reconstruction problem faced by any method, Delaunay based or not.
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Cited literature [1 references]

https://hal.inria.fr/inria-00070610
Contributor : Rapport de Recherche Inria <>
Submitted on : Friday, May 19, 2006 - 9:00:40 PM
Last modification on : Saturday, January 27, 2018 - 1:30:59 AM
Long-term archiving on: : Sunday, April 4, 2010 - 9:34:30 PM

### Identifiers

• HAL Id : inria-00070610, version 1

### Citation

Frédéric Cazals, Joachim Giesen. Delaunay Triangulation Based Surface Reconstruction: Ideas and Algorithms. RR-5393, INRIA. 2004, pp.42. ⟨inria-00070610⟩

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