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Curved optimal delaunay triangulation

Feng, Leman and Alliez, Pierre and Busé, Laurent and Delingette, Hervé and Desbrun, Mathieu (2018) Curved optimal delaunay triangulation. ACM Transactions on Graphics, 37 (4). Art. No. 61. ISSN 0730-0301. https://resolver.caltech.edu/CaltechAUTHORS:20180731-144255627

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Abstract

Meshes with curvilinear elements hold the appealing promise of enhanced geometric flexibility and higher-order numerical accuracy compared to their commonly-used straight-edge counterparts. However, the generation of curved meshes remains a computationally expensive endeavor with current meshing approaches: high-order parametric elements are notoriously difficult to conform to a given boundary geometry, and enforcing a smooth and non-degenerate Jacobian everywhere brings additional numerical difficulties to the meshing of complex domains. In this paper, we propose an extension of Optimal Delaunay Triangulations (ODT) to curved and graded isotropic meshes. By exploiting a continuum mechanics interpretation of ODT instead of the usual approximation theoretical foundations, we formulate a very robust geometry and topology optimization of Bézier meshes based on a new simple functional promoting isotropic and uniform Jacobians throughout the domain. We demonstrate that our resulting curved meshes can adapt to complex domains with high precision even for a small count of elements thanks to the added flexibility afforded by more control points and higher order basis functions.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1145/3197517.3201358DOIArticle
ORCID:
AuthorORCID
Desbrun, Mathieu0000-0003-3424-6079
Additional Information:© 2018 held by the owner/author(s). Publication rights licensed to ACM. All meshes in this paper are courtesy of AIM@SHAPE and Luxology/ Foundry. This work was supported by the European Union under grant 675789 (ITN ARCADES), and by the French government through the UCAJEDI Investments managed by the National Research Agency (ANR-15-IDEX-01). MD gratefully acknowledges the INRIA International Chair program, and Zhejiang University for hosting him superbly well during the final editing of this work.
Funders:
Funding AgencyGrant Number
European Research Council (ERC)675789
Agence Nationale pour la Recherche (ANR)ANR-15-IDEX-01
Institut national de recherche en informatique et en automatique (INRIA)UNSPECIFIED
Zhejiang UniversityUNSPECIFIED
Subject Keywords:Higher-order meshing, Optimal Delaunay Triangulations, higher order finite elements, Bézier elements
Issue or Number:4
Record Number:CaltechAUTHORS:20180731-144255627
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180731-144255627
Official Citation:Leman Feng, Pierre Alliez, Laurent Busé, Hervé Delingette, and Mathieu Desbrun. 2018. Curved Optimal Delaunay Triangulation. ACM Trans. Graph. 37, 4, Article 61 (August 2018), 16 pages. https://doi.org/10.1145/3197517. 3201358
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:88395
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:31 Jul 2018 22:00
Last Modified:03 Mar 2020 13:01

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