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Reports Year : 2004

Delaunay Triangulation Based Surface Reconstruction: Ideas and Algorithms

Frédéric Cazals
Joachim Giesen
  • Function : Author

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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Dates and versions

inria-00070610 , version 1 (19-05-2006)

Identifiers

  • HAL Id : inria-00070610 , version 1

Cite

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