On Variational and PDE-Based Distance Function Approximations

Alexander G. Belyaev, Pierre-Alain Fayolle

Research output: Contribution to journalArticle

18 Citations (Scopus)
69 Downloads (Pure)

Abstract

In this paper, we deal with the problem of computing the distance to a surface (a curve in two dimensional) and consider several distance function approximation methods which are based on solving partial differential equations (PDEs) and finding solutions to variational problems. In particular, we deal with distance function estimation methods related to the Poisson-like equations and generalized double-layer potentials. Our numerical experiments are backed by novel theoretical results and demonstrate efficiency of the considered PDE-based distance function approximations. In this paper, we deal with the problem of computing the distance to a surface (a curve in two dimensional) and consider several distance function approximation methods which are based on solving partial differential equations (PDEs) and finding solutions to variational problems. In particular, we deal with distance function estimation methods related to the Poisson-like equations and generalized double-layer potentials. Our numerical experiments are backed by novel theoretical results and demonstrate efficiency of the considered PDE-based distance function approximations.

Original languageEnglish
Pages (from-to)104-118
Number of pages15
JournalComputer Graphics Forum
Volume34
Issue number8
Early online date5 Jun 2015
DOIs
Publication statusPublished - Dec 2015

Keywords

  • Distance function approximations
  • Iterative optimization
  • Variational methods

ASJC Scopus subject areas

  • Computer Networks and Communications

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