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On Variational and PDE‐Based Distance Function Approximations
Author(s) -
Belyaev Alexander G.,
Fayolle PierreAlain
Publication year - 2015
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.12611
Subject(s) - partial differential equation , function (biology) , mathematics , signed distance function , poisson's equation , poisson distribution , mathematical optimization , mathematical analysis , algorithm , evolutionary biology , biology , statistics
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.