Vertex location optimisation for improved remeshing

Lai, Yukun ORCID: https://orcid.org/0000-0002-2094-5680 and Martin, Ralph Robert 2012. Vertex location optimisation for improved remeshing. Graphical Models 74 (4) , pp. 233-243. 10.1016/j.gmod.2012.04.011

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Abstract

Remeshing aims to produce a more regular mesh from a given input mesh, while representing the original geometry as accurately as possible. Many existing remeshing methods focus on where to place new mesh vertices; these samples are placed exactly on the input mesh. However, considering the output mesh as a piecewise linear approximation of some geometry, this simple scheme leads to significant systematic error in non-planar regions. Here, we use parameterised meshes and the recent mathematical development of orthogonal approximation using Sobolev-type inner products to develop a novel sampling scheme which allows vertices to lie in space near the input surface, rather than exactly on it. The algorithm requires little extra computational effort and can be readily incorporated into many remeshing approaches. Experimental results show that on average, approximation error can be reduced by 40% with the same number of vertices.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Computer Science & Informatics
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Uncontrolled Keywords:	Piecewise linear approximation; Remeshing; Optimisation; Sobolev inner products
Additional Information:	PDF uploaded in accordance with publisher's policy http://www.elsevier.com/about/open-access/open-access-policies/article-posting-policy [accessed 16/04/2015] NOTICE: this is the author’s version of a work that was accepted for publication in Graphical Models. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Graphical Models, [VOL 74, ISSUE 4, 2012 DOI 10.1016/j.gmod.2012.04.011
Publisher:	Academic Press
ISSN:	1524-0703
Funders:	EPSRC
Last Modified:	01 Dec 2024 09:30
URI:	https://orca.cardiff.ac.uk/id/eprint/29980

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