Transfinite Barycentric Interpolation via Dirichlet Energy Minimization for Conical Surfaces View Full Text


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Article Info

DATE

2022-08

AUTHORS

A. G. Belyaev, P.-A. Fayolle

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. More... »

PAGES

1234-1251

References to SciGraph publications

  • 1996-12. Barycentric coordinates for convex polytopes in ADVANCES IN COMPUTATIONAL MATHEMATICS
  • 2006. Issues and Implementation of C1 and C2 Natural Neighbor Interpolation in ADVANCES IN VISUAL COMPUTING
  • 2021-05-07. On Integral-Based (Transfinite) Laplace Coordinates in NUMERICAL GEOMETRY, GRID GENERATION AND SCIENTIFIC COMPUTING
  • 1903-12. Volumen und Oberfl√§che in MATHEMATISCHE ANNALEN
  • 2006-12-20. Barycentric coordinates for convex sets in ADVANCES IN COMPUTATIONAL MATHEMATICS
  • 2019-12-02. Transfinite mean value interpolation over polygons in NUMERICAL ALGORITHMS
  • 2006-01. A general construction of barycentric coordinates over convex polygons in ADVANCES IN COMPUTATIONAL MATHEMATICS
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    http://scigraph.springernature.com/pub.10.1134/s0965542522080036

    DOI

    http://dx.doi.org/10.1134/s0965542522080036

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