Transfinite Barycentric Interpolation via Dirichlet Energy Minimization for Conical Surfaces

Alexander Belyaev; Pierre-Alain Fayolle

doi:10.1134/S0965542522080036

Transfinite Barycentric Interpolation via Dirichlet Energy Minimization for Conical Surfaces

Alexander Belyaev
, Pierre-Alain Fayolle

Research output: Contribution to journal › Article › peer-review

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Abstract

In this theoretical work, we analyze general constructions for transfinite (also known as continuous and integral-based) barycentric coordinates and consider a simple variational principle to arrive at a transfinite version of the Laplace barycentric coordinates. We demonstrate how our approach leads to a general description of the transfinite barycentric coordinates and establish links with Dirichlet energy minimization problems for conical surfaces. Both the 2D and 3D cases are studied. Links with the Minkowski and Christoffel inverse problem in differential geometry are discussed.

Original language	English
Pages (from-to)	1234-1251
Number of pages	18
Journal	Computational Mathematics and Mathematical Physics
Volume	62
Issue number	8
DOIs	https://doi.org/10.1134/S0965542522080036
Publication status	Published - Aug 2022

Keywords

Dirichlet energy minimization
generalized barycentric coordinates
transfinite (integral-based, continuous) barycentric coordinates
transfinite Laplace coordinates

ASJC Scopus subject areas

Computational Mathematics

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10.1134/S0965542522080036

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© 2022 Springer Nature Switzerland AG. Comput. Math. and Math. Phys. 62, 1234–1251 (2022). https://doi.org/10.1134/S0965542522080036
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abstract = "In this theoretical work, we analyze general constructions for transfinite (also known as continuous and integral-based) barycentric coordinates and consider a simple variational principle to arrive at a transfinite version of the Laplace barycentric coordinates. We demonstrate how our approach leads to a general description of the transfinite barycentric coordinates and establish links with Dirichlet energy minimization problems for conical surfaces. Both the 2D and 3D cases are studied. Links with the Minkowski and Christoffel inverse problem in differential geometry are discussed.",

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KW - transfinite (integral-based, continuous) barycentric coordinates

KW - transfinite Laplace coordinates

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Transfinite Barycentric Interpolation via Dirichlet Energy Minimization for Conical Surfaces

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Keywords

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