Designing 2D and 3D Non-Orthogonal Frame Fields Article - Juillet 2021

David Desobry, Yoann Coudert-Osmont, Etienne Corman, Nicolas Ray, Dmitry Sokolov

David Desobry, Yoann Coudert-Osmont, Etienne Corman, Nicolas Ray, Dmitry Sokolov, « Designing 2D and 3D Non-Orthogonal Frame Fields  », Computer-Aided Design, juillet 2021, pp. 1-9. ISSN 0010-4485

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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