Curved Optimal Delaunay Triangulation - Inria - Institut national de recherche en sciences et technologies du numérique
Journal Articles ACM Transactions on Graphics Year : 2018

Curved Optimal Delaunay Triangulation

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.
Fichier principal
Vignette du fichier
CODT-preprint-final.pdf (5.32 Mo) Télécharger le fichier
Origin Files produced by the author(s)
Loading...

Dates and versions

hal-01826055 , version 1 (18-10-2018)

Identifiers

Cite

Leman Feng, Pierre Alliez, Laurent Busé, Hervé Delingette, Mathieu Desbrun. Curved Optimal Delaunay Triangulation. ACM Transactions on Graphics, 2018, Proceedings of SIGGRAPH 2018, 37 (4), pp.16. ⟨10.1145/3197517.3201358⟩. ⟨hal-01826055⟩
920 View
1025 Download

Altmetric

Share

More