ECG IST-2000-26473 Effective Computational Geometry for Curves and Surfaces

نویسندگان

  • Steve Oudot
  • Jean-Daniel Boissonnat
چکیده

We 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 3dimensional 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. Partially supported by the IST Programme of the EU as a Shared-cost RTD (FET Open) Project under Contract No IST-2000-26473 (ECG Effective Computational Geometry for Curves and Surfaces)

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ECG IST-2000-26473 Effective Computational Geometry for Curves and Surfaces

Project funded by the European Community under the " Information Society Technologies " Programme (1998–2002)

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تاریخ انتشار 2003