Fitting Polynomial Volumes to Surface Meshes with Voronoï Squared Distance Minimization
Identifieur interne : 000F97 ( Hal/Checkpoint ); précédent : 000F96; suivant : 000F98Fitting Polynomial Volumes to Surface Meshes with Voronoï Squared Distance Minimization
Auteurs : Gilles-Philippe Paillé [Canada] ; Pierre Poulain [Canada] ; Bruno Lévy [France]Source :
- Computer Graphics Forum [ 0167-7055 ] ; 2013-08.
Abstract
We propose a method for mapping polynomial volumes. Given a closed surface and an initial template volume grid, our method deforms the template grid by fitting its boundary to the input surface while minimizing a vol- ume distortion criterion. The result is a point-to-point map distorting linear cells into curved ones. Our method is based on several extensions of Voronoi Squared Distance Minimization (VSDM) combined with a higher-order finite element formulation of the deformation energy. This allows us to globally optimize the mapping without prior parameterization. The anisotropic VSDM formulation allows for sharp and semi-sharp features to be im- plicitly preserved without tagging. We use a hierarchical finite element function basis that selectively adapts to the geometric details. This makes both the method more efficient and the representation more compact. We ap- ply our method to geometric modeling applications in computer-aided design and computer graphics, including mixed-element meshing, mesh optimization, subdivision volume fitting, and shell meshing.
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DOI: 10.1111/cgf.12177
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Given a closed surface and an initial template volume grid, our method deforms the template grid by fitting its boundary to the input surface while minimizing a vol- ume distortion criterion. The result is a point-to-point map distorting linear cells into curved ones. Our method is based on several extensions of Voronoi Squared Distance Minimization (VSDM) combined with a higher-order finite element formulation of the deformation energy. This allows us to globally optimize the mapping without prior parameterization. The anisotropic VSDM formulation allows for sharp and semi-sharp features to be im- plicitly preserved without tagging. We use a hierarchical finite element function basis that selectively adapts to the geometric details. This makes both the method more efficient and the representation more compact. We ap- ply our method to geometric modeling applications in computer-aided design and computer graphics, including mixed-element meshing, mesh optimization, subdivision volume fitting, and shell meshing.</div></front></TEI><hal api="V3"><titleStmt><title xml:lang="en">Fitting Polynomial Volumes to Surface Meshes with Voronoï Squared Distance Minimization</title><author role="aut"><persName><forename type="first">Gilles-Philippe</forename><surname>Paillé</surname></persName><email></email><idno type="halauthor">968351</idno><orgName ref="#struct-300447"></orgName><affiliation ref="#struct-25645"></affiliation></author><author role="aut"><persName><forename type="first">Pierre</forename><surname>Poulain</surname></persName><email></email><idno type="halauthor">968352</idno><orgName ref="#struct-300447"></orgName><affiliation ref="#struct-25645"></affiliation></author><author role="aut"><persName><forename type="first">Bruno</forename><surname>Lévy</surname></persName><email>Bruno.Levy@inria.fr</email><idno type="idhal">bruno-levy</idno><idno type="halauthor">136280</idno><idno type="arXiv">http://arxiv.org/a/brlevy</idno><orgName ref="#struct-300009"></orgName><affiliation ref="#struct-205118"></affiliation></author><editor role="depositor"><persName><forename>Samuel</forename><surname>Hornus</surname></persName><email>Samuel.Hornus@inria.fr</email></editor><funder ref="#projeurop-16585"></funder></titleStmt><editionStmt><edition n="v1" type="current"><date type="whenSubmitted">2014-01-14 11:19:06</date><date type="whenModified">2015-12-16 01:10:32</date><date type="whenReleased">2014-01-14 11:19:06</date><date type="whenProduced">2013-08</date></edition><respStmt><resp>contributor</resp><name key="134463"><persName><forename>Samuel</forename><surname>Hornus</surname></persName><email>Samuel.Hornus@inria.fr</email></name></respStmt></editionStmt><publicationStmt><distributor>CCSD</distributor><idno type="halId">hal-00930030</idno><idno type="halUri">https://hal.inria.fr/hal-00930030</idno><idno type="halBibtex">paille:hal-00930030</idno><idno type="halRefHtml">Computer Graphics Forum, Wiley, 2013, 32 (5), pp.103-112. <10.1111/cgf.12177></idno><idno type="halRef">Computer Graphics Forum, Wiley, 2013, 32 (5), pp.103-112. <10.1111/cgf.12177></idno></publicationStmt><seriesStmt><idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno><idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno><idno type="stamp" n="OPENAIRE">OpenAIRE</idno><idno type="stamp" n="INRIA-LORRAINE">INRIA Nancy - Grand Est</idno><idno type="stamp" n="LORIA2">Publications du LORIA</idno><idno type="stamp" n="INRIA-NANCY-GRAND-EST">INRIA Nancy - Grand Est</idno><idno type="stamp" n="LORIA-ACGI" p="LORIA">Algorithmique, calcul, image et géométrie</idno><idno type="stamp" n="LORIA">LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications</idno><idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno><idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno><idno type="stamp" n="LORIA-ALGO-TEST5">LORIA-ALGO-TEST5 </idno><idno type="stamp" n="INRIA2">INRIA 2</idno></seriesStmt><notesStmt><note type="commentary">Also Proceedings of the Annual Symposium on Geometry Processing</note><note type="audience" n="2">International</note><note type="popular" n="0">No</note><note type="peer" n="1">Yes</note></notesStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Fitting Polynomial Volumes to Surface Meshes with Voronoï Squared Distance Minimization</title><author role="aut"><persName><forename type="first">Gilles-Philippe</forename><surname>Paillé</surname></persName><idno type="halAuthorId">968351</idno><orgName ref="#struct-300447"></orgName><affiliation ref="#struct-25645"></affiliation></author><author role="aut"><persName><forename type="first">Pierre</forename><surname>Poulain</surname></persName><idno type="halAuthorId">968352</idno><orgName ref="#struct-300447"></orgName><affiliation ref="#struct-25645"></affiliation></author><author role="aut"><persName><forename type="first">Bruno</forename><surname>Lévy</surname></persName><email>Bruno.Levy@inria.fr</email><idno type="idHal">bruno-levy</idno><idno type="halAuthorId">136280</idno><idno type="arXiv">http://arxiv.org/a/brlevy</idno><orgName ref="#struct-300009"></orgName><affiliation ref="#struct-205118"></affiliation></author></analytic><monogr><idno type="halJournalId" status="VALID">12023</idno><idno type="issn">0167-7055</idno><idno type="eissn">1467-8659</idno><title level="j">Computer Graphics Forum</title><imprint><publisher>Wiley</publisher><biblScope unit="volume">32</biblScope><biblScope unit="issue">5</biblScope><biblScope unit="pp">103-112</biblScope><date type="datePub">2013-08</date></imprint></monogr><idno type="doi">10.1111/cgf.12177</idno></biblStruct></sourceDesc><profileDesc><langUsage><language ident="en">English</language></langUsage><textClass><classCode scheme="halDomain" n="info.info-cg">Computer Science [cs]/Computational Geometry [cs.CG]</classCode><classCode scheme="halDomain" n="info.info-gr">Computer Science [cs]/Graphics [cs.GR]</classCode><classCode scheme="halTypology" n="ART">Journal articles</classCode></textClass><abstract xml:lang="en">We propose a method for mapping polynomial volumes. Given a closed surface and an initial template volume grid, our method deforms the template grid by fitting its boundary to the input surface while minimizing a vol- ume distortion criterion. The result is a point-to-point map distorting linear cells into curved ones. Our method is based on several extensions of Voronoi Squared Distance Minimization (VSDM) combined with a higher-order finite element formulation of the deformation energy. This allows us to globally optimize the mapping without prior parameterization. The anisotropic VSDM formulation allows for sharp and semi-sharp features to be im- plicitly preserved without tagging. We use a hierarchical finite element function basis that selectively adapts to the geometric details. This makes both the method more efficient and the representation more compact. We ap- ply our method to geometric modeling applications in computer-aided design and computer graphics, including mixed-element meshing, mesh optimization, subdivision volume fitting, and shell meshing.</abstract><particDesc><org type="consortium">Au Québec : FQRNT</org><org type="consortium">NSERC</org><org type="consortium">GRAND</org></particDesc></profileDesc></hal></record>Pour manipuler ce document sous Unix (Dilib)
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