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 language | English |
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Pages (from-to) | 104-118 |
Number of pages | 15 |
Journal | Computer Graphics Forum |
Volume | 34 |
Issue number | 8 |
Early online date | 5 Jun 2015 |
DOIs | |
Publication status | Published - Dec 2015 |
Keywords
- Distance function approximations
- Iterative optimization
- Variational methods
ASJC Scopus subject areas
- Computer Networks and Communications
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Alexander Belyaev
- School of Engineering & Physical Sciences - Associate Professor
- School of Engineering & Physical Sciences, Institute of Sensors, Signals & Systems - Associate Professor
Person: Academic (Research & Teaching)