On Integral-Based (Transfinite) Laplace Coordinates

Alexander G. Belyaev, Pierre-Alain Fayolle

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this theoretical work, we analyze general constructions for integral-based (transfinite, continuous) barycentric coordinates and consider a simple variational principle to arrive at a continuous version of the Laplace barycentric coordinates. We demonstrate how our approach leads to a general description of the integral-based barycentric coordinates and establish links with Dirichlet energy minimization problems for conical surfaces. Both the 2D and 3D cases are studied. An application to a surface generation problem is briefly considered.

Original languageEnglish
Title of host publicationNumerical Geometry, Grid Generation and Scientific Computing
EditorsVladimir A. Garanzha, Lennard Kamenski, Hang Si
PublisherSpringer
Pages341-357
Number of pages17
ISBN (Electronic)9783030767983
ISBN (Print)9783030767976
DOIs
Publication statusPublished - 7 May 2021
Event10th International Conference on Numerical Geometry, Grid Generation, and Scientific Computing celebrating the 130th anniversary of B. N. Delaunay - Moscow, Russian Federation
Duration: 25 Nov 202027 Nov 2020

Publication series

NameLecture Notes in Computational Science and Engineering
Volume143
ISSN (Print)1439-7358
ISSN (Electronic)2197-7100

Conference

Conference10th International Conference on Numerical Geometry, Grid Generation, and Scientific Computing celebrating the 130th anniversary of B. N. Delaunay
Abbreviated titleNUMGRID 2020
Country/TerritoryRussian Federation
CityMoscow
Period25/11/2027/11/20

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering(all)
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Mathematics

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