Particle-based Anisotropic Surface Meshing
Identifieur interne : 003B10 ( Hal/Curation ); précédent : 003B09; suivant : 003B11Particle-based Anisotropic Surface Meshing
Auteurs : Zichun Zhong [États-Unis] ; Xiaohu Guo [États-Unis] ; Wenping Wang [République populaire de Chine] ; Bruno Lévy [France] ; Feng Sun [République populaire de Chine] ; Yang Liu [États-Unis] ; Weihua Mao [États-Unis]Source :
- ACM Transactions on Graphics [ 0730-0301 ] ; 2013.
English descriptors
Abstract
This paper introduces a particle-based approach for anisotropic surface meshing. Given an input polygonal mesh endowed with a Riemannian metric and a specified number of vertices, the method generates a metric-adapted mesh. The main idea consists of mapping the anisotropic space into a higher dimensional isotropic one, called "embedding space". The vertices of the mesh are generated by uniformly sampling the surface in this higher dimensional embedding space, and the sampling is further regularized by optimizing an energy function with a quasi-Newton algorithm. All the computations can be re-expressed in terms of the dot product in the embedding space, and the Jacobian matrices of the mappings that connect different spaces. This transform makes it unnecessary to explicitly represent the coordinates in the embedding space, and also provides all necessary expressions of energy and forces for efficient computations. Through energy optimization, it naturally leads to the desired anisotropic particle distributions in the original space. The triangles are then generated by computing the Restricted Anisotropic Voronoi Diagram and its dual Delaunay triangulation. We compare our results qualitatively and quantitatively with the state-of-the-art in anisotropic surface meshing on several examples, using the standard measurement criteria.
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DOI: 10.1145/2461912.2461946
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Given an input polygonal mesh endowed with a Riemannian metric and a specified number of vertices, the method generates a metric-adapted mesh. The main idea consists of mapping the anisotropic space into a higher dimensional isotropic one, called "embedding space". The vertices of the mesh are generated by uniformly sampling the surface in this higher dimensional embedding space, and the sampling is further regularized by optimizing an energy function with a quasi-Newton algorithm. All the computations can be re-expressed in terms of the dot product in the embedding space, and the Jacobian matrices of the mappings that connect different spaces. This transform makes it unnecessary to explicitly represent the coordinates in the embedding space, and also provides all necessary expressions of energy and forces for efficient computations. Through energy optimization, it naturally leads to the desired anisotropic particle distributions in the original space. The triangles are then generated by computing the Restricted Anisotropic Voronoi Diagram and its dual Delaunay triangulation. We compare our results qualitatively and quantitatively with the state-of-the-art in anisotropic surface meshing on several examples, using the standard measurement criteria.</div></front></TEI><hal api="V3"><titleStmt><title xml:lang="en">Particle-based Anisotropic Surface Meshing</title><author role="aut"><persName><forename type="first">Zichun</forename><surname>Zhong</surname></persName><email></email><idno type="halauthor">968472</idno><affiliation ref="#struct-109343"></affiliation></author><author role="aut"><persName><forename type="first">Xiaohu</forename><surname>Guo</surname></persName><email></email><idno type="halauthor">619879</idno><affiliation ref="#struct-109343"></affiliation></author><author role="aut"><persName><forename type="first">Wenping</forename><surname>Wang</surname></persName><email></email><idno type="halauthor">156291</idno><affiliation ref="#struct-99478"></affiliation></author><author role="aut"><persName><forename type="first">Bruno</forename><surname>Lévy</surname></persName><email></email><idno type="idhal">bruno-levy</idno><idno type="halauthor">136961</idno><idno type="arXiv">http://arxiv.org/a/brlevy</idno><affiliation ref="#struct-205118"></affiliation></author><author role="aut"><persName><forename type="first">Feng</forename><surname>Sun</surname></persName><email></email><idno type="halauthor">558485</idno><affiliation ref="#struct-99478"></affiliation></author><author role="aut"><persName><forename type="first">Yang</forename><surname>Liu</surname></persName><email></email><idno type="halauthor">417225</idno><affiliation ref="#struct-12319"></affiliation></author><author role="aut"><persName><forename type="first">Weihua</forename><surname>Mao</surname></persName><email></email><idno type="halauthor">968473</idno><affiliation ref="#struct-241508"></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 13:28:31</date><date type="whenModified">2015-12-16 01:10:32</date><date type="whenReleased">2014-01-14 13:28:31</date><date type="whenProduced">2013</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-00930147</idno><idno type="halUri">https://hal.inria.fr/hal-00930147</idno><idno type="halBibtex">zhong:hal-00930147</idno><idno type="halRefHtml">ACM Transactions on Graphics, Association for Computing Machinery, 2013, 32 (4), pp.99:1--99:14. <10.1145/2461912.2461946></idno><idno type="halRef">ACM Transactions on Graphics, Association for Computing Machinery, 2013, 32 (4), pp.99:1--99:14. <10.1145/2461912.2461946></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="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">Particle-based Anisotropic Surface Meshing</title><author role="aut"><persName><forename type="first">Zichun</forename><surname>Zhong</surname></persName><idno type="halAuthorId">968472</idno><affiliation ref="#struct-109343"></affiliation></author><author role="aut"><persName><forename type="first">Xiaohu</forename><surname>Guo</surname></persName><idno type="halAuthorId">619879</idno><affiliation ref="#struct-109343"></affiliation></author><author role="aut"><persName><forename type="first">Wenping</forename><surname>Wang</surname></persName><idno type="halAuthorId">156291</idno><affiliation ref="#struct-99478"></affiliation></author><author role="aut"><persName><forename type="first">Bruno</forename><surname>Lévy</surname></persName><idno type="idHal">bruno-levy</idno><idno type="halAuthorId">136961</idno><idno type="arXiv">http://arxiv.org/a/brlevy</idno><affiliation ref="#struct-205118"></affiliation></author><author role="aut"><persName><forename type="first">Feng</forename><surname>Sun</surname></persName><idno type="halAuthorId">558485</idno><affiliation ref="#struct-99478"></affiliation></author><author role="aut"><persName><forename type="first">Yang</forename><surname>Liu</surname></persName><idno type="halAuthorId">417225</idno><affiliation ref="#struct-12319"></affiliation></author><author role="aut"><persName><forename type="first">Weihua</forename><surname>Mao</surname></persName><idno type="halAuthorId">968473</idno><affiliation ref="#struct-241508"></affiliation></author></analytic><monogr><idno type="localRef">4</idno><idno type="halJournalId" status="VALID">2596</idno><idno type="issn">0730-0301</idno><title level="j">ACM Transactions on Graphics</title><imprint><publisher>Association for Computing Machinery</publisher><biblScope unit="volume">32</biblScope><biblScope unit="issue">4</biblScope><biblScope unit="pp">99:1--99:14</biblScope><date type="datePub">2013</date></imprint></monogr><idno type="doi">10.1145/2461912.2461946</idno></biblStruct></sourceDesc><profileDesc><langUsage><language ident="en">English</language></langUsage><textClass><keywords scheme="author"><term xml:lang="en">anisotropic meshing</term><term xml:lang="en">gaussian kernel</term><term xml:lang="en">particle</term></keywords><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">This paper introduces a particle-based approach for anisotropic surface meshing. Given an input polygonal mesh endowed with a Riemannian metric and a specified number of vertices, the method generates a metric-adapted mesh. The main idea consists of mapping the anisotropic space into a higher dimensional isotropic one, called "embedding space". The vertices of the mesh are generated by uniformly sampling the surface in this higher dimensional embedding space, and the sampling is further regularized by optimizing an energy function with a quasi-Newton algorithm. All the computations can be re-expressed in terms of the dot product in the embedding space, and the Jacobian matrices of the mappings that connect different spaces. This transform makes it unnecessary to explicitly represent the coordinates in the embedding space, and also provides all necessary expressions of energy and forces for efficient computations. Through energy optimization, it naturally leads to the desired anisotropic particle distributions in the original space. The triangles are then generated by computing the Restricted Anisotropic Voronoi Diagram and its dual Delaunay triangulation. We compare our results qualitatively and quantitatively with the state-of-the-art in anisotropic surface meshing on several examples, using the standard measurement criteria.</abstract></profileDesc></hal></record>Pour manipuler ce document sous Unix (Dilib)
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