Heat method extensions for distance function estimation in planar and space domains

Alexander Belyaev; Pierre-Alain Fayolle

doi:10.1016/j.cad.2025.103968

Heat method extensions for distance function estimation in planar and space domains

Alexander Belyaev, Pierre-Alain Fayolle

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Abstract

Given a bounded domain, we deal with the problem of estimating the distance function from the internal points of the domain to the boundary of the domain. Two simple extensions of the heat method for distance computation are introduced and evaluated. The extensions are based on first- and second-order Taylor series extrapolations. Numerical experiments demonstrate that the extensions deliver more accurate and robust estimates of the distance function.

Original language	English
Article number	103968
Journal	Computer-Aided Design
Volume	190
Early online date	15 Sept 2025
DOIs	https://doi.org/10.1016/j.cad.2025.103968
Publication status	E-pub ahead of print - 15 Sept 2025

Keywords

Distance function
Heat method
Taylor series extrapolation

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title = "Heat method extensions for distance function estimation in planar and space domains",

abstract = "Given a bounded domain, we deal with the problem of estimating the distance function from the internal points of the domain to the boundary of the domain. Two simple extensions of the heat method for distance computation are introduced and evaluated. The extensions are based on first- and second-order Taylor series extrapolations. Numerical experiments demonstrate that the extensions deliver more accurate and robust estimates of the distance function.",

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AU - Belyaev, Alexander

AU - Fayolle, Pierre-Alain

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N2 - Given a bounded domain, we deal with the problem of estimating the distance function from the internal points of the domain to the boundary of the domain. Two simple extensions of the heat method for distance computation are introduced and evaluated. The extensions are based on first- and second-order Taylor series extrapolations. Numerical experiments demonstrate that the extensions deliver more accurate and robust estimates of the distance function.

AB - Given a bounded domain, we deal with the problem of estimating the distance function from the internal points of the domain to the boundary of the domain. Two simple extensions of the heat method for distance computation are introduced and evaluated. The extensions are based on first- and second-order Taylor series extrapolations. Numerical experiments demonstrate that the extensions deliver more accurate and robust estimates of the distance function.

KW - Distance function

KW - Heat method

KW - Taylor series extrapolation

UR - https://www.scopus.com/pages/publications/105016304622

U2 - 10.1016/j.cad.2025.103968

DO - 10.1016/j.cad.2025.103968

M3 - Article

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VL - 190

JO - Computer-Aided Design

JF - Computer-Aided Design

M1 - 103968

ER -

Heat method extensions for distance function estimation in planar and space domains

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