Discrete & Computational Geometry

, Volume 40, Issue 3, pp 325–356 | Cite as

Reconstruction Using Witness Complexes

Article

Abstract

We present a novel reconstruction algorithm that, given an input point set sampled from an object S, builds a one-parameter family of complexes that approximate S at different scales. At a high level, our method is very similar in spirit to Chew’s surface meshing algorithm, with one notable difference though: the restricted Delaunay triangulation is replaced by the witness complex, which makes our algorithm applicable in any metric space. To prove its correctness on curves and surfaces, we highlight the relationship between the witness complex and the restricted Delaunay triangulation in 2d and in 3d. Specifically, we prove that both complexes are equal in 2d and closely related in 3d, under some mild sampling assumptions.

Keywords

Sampling Reconstruction Delaunay triangulation Witness complex 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Dept. Computer ScienceStanford UniversityStanfordUSA

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