Provably Good Surface Sampling and Approximation

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dc.contributor.authorBoissonnat, J-D.en_US
dc.contributor.authorOudot, S.en_US
dc.contributor.editorLeif Kobbelt and Peter Schroeder and Hugues Hoppeen_US
dc.date.accessioned2014-01-29T08:19:37Z
dc.date.available2014-01-29T08:19:37Z
dc.date.issued2003en_US
dc.description.abstractWe present an algorithm for meshing surfaces that is a simple adaptation of a greedy "farthest point" technique proposed by Chew. Given a surface S, it progressively adds points on S and updates the 3-dimensional Delaunay triangulation of the points. The method is very simple and works in 3d-space without requiring to parameterize the surface. Taking advantage of recent results on the restricted Delaunay triangulation, we prove that the algorithm can generate good samples on S as well as triangulated surfaces that approximate S. More precisely, we show that the restricted Delaunay triangulation Del??S of the points has the same topology type as S, that the Hausdorff distance between Del??S and S can be made arbitrarily small, and that we can bound the aspect ratio of the facets of Del??S. The algorithm has been implemented and we report on experimental results that provide evidence that it is very effective in practice. We present results on implicit surfaces, on CSG models and on polyhedra. Although most of our theoretical results are given for smooth closed surfaces, the method is quite robust in handling smooth surfaces with boundaries, and even non-smooth surfaces.en_US
dc.description.seriesinformationEurographics Symposium on Geometry Processingen_US
dc.identifier.isbn3-905673-06-1en_US
dc.identifier.issn1727-8384en_US
dc.identifier.urihttps://doi.org/10.2312/SGP/SGP03/009-019en_US
dc.publisherThe Eurographics Associationen_US
dc.subjectCategories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Boundary representations.en_US
dc.titleProvably Good Surface Sampling and Approximationen_US
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SGP03: Eurographics Symposium on Geometry Processing