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NORMAL-MAP BETWEEN NORMAL-COMPATIBLE MANIFOLDS

FREDERIC CHAZAL

Institute of Mathematics of Burgundy, Dijon, France

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ANDRE LIEUTIER

Dassault Systèmes and LMC/IMAG, Grenoble, France

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JAREK ROSSIGNAC

College of Computing, Georgia Institute of Technology, Atlanta, Georgia, USA

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https://doi.org/10.1142/S0218195907002422Cited by:11 (Source: Crossref)

Abstract

Consider two (n−1)-dimensional manifolds, S and S′ in ℝⁿ. We say that they are normal-compatible when the closest projection of each one onto the other is a homeomorphism. We give a tight condition under which S and S′ are normal-compatible. It involves the minimum feature size of S and of S′ and the Hausdorff distance between them. Furthermore, when S and S′ are normal-compatible, their Frechet distance is equal to their Hausdorff distance. Our results hold for arbitrary dimension n.

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