Mesh-Free Discrete Laplace-Beltrami Operator

Autor:	Elias S. Helou, Luis Gustavo Nonato, Afonso Paiva, Fabiano Petronetto, D. E. Stewart
Rok vydání:	2013
Předmět:	Surface (mathematics) Smoothed-particle hydrodynamics Operator (computer programming) Discretization Laplace–Beltrami operator Triangle mesh Applied mathematics Point (geometry) Segmentation Topology Computer Graphics and Computer-Aided Design ComputingMethodologies_COMPUTERGRAPHICS Mathematics
Zdroj:	Computer Graphics Forum. 32:214-226
ISSN:	0167-7055
DOI:	10.1111/cgf.12086
Popis:	In this work we propose a new discretization method for the Laplace-Beltrami operator defined on point-based surfaces. In contrast to the existing point-based discretization techniques, our approach does not rely on any triangle mesh structure, turning out truly mesh-free. Based on a combination of Smoothed Particle Hydrodynamics and an optimization procedure to estimate area elements, our discretization method results in accurate solutions while still being robust when facing abrupt changes in the density of points. Moreover, the proposed scheme results in numerically stable discrete operators. The effectiveness of the proposed technique is brought to bear in many practical applications. In particular, we use the eigenstructure of the discrete operator for filtering and shape segmentation. Point-based surface deformation is another application that can be easily carried out from the proposed discretization method.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::4b1e7d785ad1554afc78d62edbf2525d https://doi.org/10.1111/cgf.12086 Zobrazit plný text záznamu Plný text ve formátu PDF Plný text ve formátu HTML
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