Signed Lp-distance fields

Alexander Belyaev, Pierre-Alain Fayolle, Alexander Pasko

Research output: Contribution to journalArticle

Abstract

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 high practical potential of our approach.
Original languageEnglish
Pages (from-to)523-528
Number of pages6
JournalComputer-Aided Design
Volume45
Issue number2
DOIs
Publication statusPublished - 2012

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Signed
Double Layer Potential
Power Mean
Distance Function
Numerical Experiment
Angle
Approximation
Estimate

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Belyaev, Alexander ; Fayolle, Pierre-Alain ; Pasko, Alexander. / Signed Lp-distance fields. In: Computer-Aided Design. 2012 ; Vol. 45, No. 2. pp. 523-528.
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Belyaev, A, Fayolle, P-A & Pasko, A 2012, 'Signed Lp-distance fields', Computer-Aided Design, vol. 45, no. 2, pp. 523-528. https://doi.org/10.1016/j.cad.2012.10.035

Signed Lp-distance fields. / Belyaev, Alexander; Fayolle, Pierre-Alain; Pasko, Alexander.

In: Computer-Aided Design, Vol. 45, No. 2, 2012, p. 523-528.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Signed Lp-distance fields

AU - Belyaev, Alexander

AU - Fayolle, Pierre-Alain

AU - Pasko, Alexander

PY - 2012

Y1 - 2012

N2 - 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 high practical potential of our approach.

AB - 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 high practical potential of our approach.

U2 - 10.1016/j.cad.2012.10.035

DO - 10.1016/j.cad.2012.10.035

M3 - Article

VL - 45

SP - 523

EP - 528

JO - Computer-Aided Design

JF - Computer-Aided Design

SN - 0010-4485

IS - 2

ER -