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Designing 2D and 3D Non-Orthogonal Frame Fields

David Desobry 1 Yoann Coudert-Osmont 1 Etienne Corman 1 Nicolas Ray 1 Dmitry Sokolov 1 
1 PIXEL - Structurer des formes géométriques
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : We present a method for direction field design on surface and volumetric meshes supporting non-orthogonality. Our approach is a generalization of the representation of 3D cross fields in spherical harmonic basis. As such it induces a geometrically meaningful measure of smoothness, allows orthogonality control by a simple parameter and enables orientation constraints of a single direction. To the best of our knowledge this is the first work to propose non-orthogonal 3D frame field design. We demonstrate the applicability of our method to generate anisotropic quadrangular and hexahedral meshes which are particularly useful for remeshing CAD models.
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https://hal.inria.fr/hal-03287233
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Submitted on : Thursday, July 22, 2021 - 10:48:35 AM
Last modification on : Friday, July 8, 2022 - 10:04:48 AM
Long-term archiving on: : Saturday, October 23, 2021 - 6:03:44 PM

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David Desobry, Yoann Coudert-Osmont, Etienne Corman, Nicolas Ray, Dmitry Sokolov. Designing 2D and 3D Non-Orthogonal Frame Fields. Computer-Aided Design, 2021, 139, pp.1-9. ⟨10.1016/j.cad.2021.103081⟩. ⟨hal-03287233⟩

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