Signed Lp-distance fields

Alexander Belyaev

doi:10.1016/j.cad.2012.10.035

Signed Lp-distance fields

2013-02-01

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DOI：10.1016/j.cad.2012.10.035

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Abstract

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We introduce and study a family of generalized double-layer potentials which are used to build smooth and accurate approximants for the signed distance function. Given a surface, the value of an approximant at a given point is a power mean of distances from the point to the surface points parameterized by the angle they are viewed from the given point. We analyze mathematical properties of the potentials and corresponding approximants. In particular, approximation accuracy estimates are derived. Our theoretical results are supported by numerical experiments which reveal the high practical potential of our approach. (C) 2012 Elsevier Ltd. All rights reserved.

Keywords:

Approximate distance functions

Singular integrals

Generalized double potentials

Signed Lp-distance fields

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