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Article: Spectral Quadrangulation with Feature Curve Alignment and Element Size Control

TitleSpectral Quadrangulation with Feature Curve Alignment and Element Size Control
Authors
Issue Date2014
PublisherAssociation for Computing Machinery, Inc. The Journal's web site is located at http://tog.acm.org
Citation
ACM Transactions on Graphics, 2014, v. 34 n. 1, article no.11 How to Cite?
AbstractExisting methods for surface quadrangulation cannot ensure accurate alignment with feature or boundary curves and tight control of local element size, which are important requirements in many numerical applications (e.g., FEA). Some methods rely on a prescribed direction field to guide quadrangulation for feature alignment, but such a direction field may conflict with a desired density field, thus making it difficult to control the element size. We propose a new spectral method that achieves both accurate feature curve alignment and tight control of local element size according to a given density field. Specifically, the following three technical contributions are made. First, to make the quadrangulation align accurately with feature curves or surface boundary curves, we introduce novel boundary conditions for wave-like functions that satisfy the Helmholtz equation approximately in the least squares sense. Such functions, called quasi-eigenfunctions, are computed efficiently as the solutions to a variational problem. Second, the mesh element size is effectively controlled by locally modulating the Laplace operator in the Helmholtz equation according to a given density field. Third, to improve robustness, we propose a novel scheme to minimize the vibration difference of the quasi-eigenfunction in two orthogonal directions. It is demonstrated by extensive experiments that our method outperforms previous methods in generating feature-aligned quadrilateral meshes with tight control of local elememt size. We further present some preliminary results to show that our method can be extended to generating hex-dominant volume meshes.
Persistent Identifierhttp://hdl.handle.net/10722/191790
ISSN
2015 Impact Factor: 4.218
2015 SCImago Journal Rankings: 2.552

 

DC FieldValueLanguage
dc.contributor.authorLing, Ren_US
dc.contributor.authorHuang, Jen_US
dc.contributor.authorJuettler, Ben_US
dc.contributor.authorSun, Fen_US
dc.contributor.authorBao, HJen_US
dc.contributor.authorWang, WPen_US
dc.date.accessioned2013-10-15T07:23:25Z-
dc.date.available2013-10-15T07:23:25Z-
dc.date.issued2014-
dc.identifier.citationACM Transactions on Graphics, 2014, v. 34 n. 1, article no.11en_US
dc.identifier.issn0730-0301-
dc.identifier.urihttp://hdl.handle.net/10722/191790-
dc.description.abstractExisting methods for surface quadrangulation cannot ensure accurate alignment with feature or boundary curves and tight control of local element size, which are important requirements in many numerical applications (e.g., FEA). Some methods rely on a prescribed direction field to guide quadrangulation for feature alignment, but such a direction field may conflict with a desired density field, thus making it difficult to control the element size. We propose a new spectral method that achieves both accurate feature curve alignment and tight control of local element size according to a given density field. Specifically, the following three technical contributions are made. First, to make the quadrangulation align accurately with feature curves or surface boundary curves, we introduce novel boundary conditions for wave-like functions that satisfy the Helmholtz equation approximately in the least squares sense. Such functions, called quasi-eigenfunctions, are computed efficiently as the solutions to a variational problem. Second, the mesh element size is effectively controlled by locally modulating the Laplace operator in the Helmholtz equation according to a given density field. Third, to improve robustness, we propose a novel scheme to minimize the vibration difference of the quasi-eigenfunction in two orthogonal directions. It is demonstrated by extensive experiments that our method outperforms previous methods in generating feature-aligned quadrilateral meshes with tight control of local elememt size. We further present some preliminary results to show that our method can be extended to generating hex-dominant volume meshes.-
dc.languageengen_US
dc.publisherAssociation for Computing Machinery, Inc. The Journal's web site is located at http://tog.acm.org-
dc.relation.ispartofACM Transactions on Graphicsen_US
dc.rightsACM Transactions on Graphics. Copyright © Association for Computing Machinery, Inc.-
dc.titleSpectral Quadrangulation with Feature Curve Alignment and Element Size Controlen_US
dc.typeArticleen_US
dc.identifier.emailLing, R: rtling@cs.hku.hken_US
dc.identifier.emailHuang, J: hjwdzh00@hku.hken_US
dc.identifier.emailSun, F: fengsun@hku.hken_US
dc.identifier.emailWang, WP: wenping@cs.hku.hk-
dc.identifier.authorityWang, WP=rp00186en_US
dc.identifier.doi10.1145/2653476-
dc.identifier.hkuros225503en_US
dc.identifier.hkuros256022-
dc.identifier.volume34-
dc.identifier.issue1-
dc.identifier.spagearticle no.11-
dc.identifier.epagearticle no.11-
dc.publisher.placeUnited States-

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