Published in

Springer, Discrete & Computational Geometry, 3(62), p. 700-742, 2019

DOI: 10.1007/s00454-019-00095-w

Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, p. 161-173

DOI: 10.1137/1.9781611973402.12

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Implicit manifold reconstruction

Journal article published in 2013 by Siu-Wing Cheng ORCID, Man-Kwun Chiu
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

Let P be a dense set of points sampled from an Tridimensional compact smooth manifold ∑ in Rd. We show how to construct an implicit function φ : Rd→Rd-m from P so that the zero-set Sφ of φ contains a homeomorphic approximation of ∑. The Hausdorff distance between ∑ and this homeomorphic approximation is at most ετfor any fixed τ