Designing 2D and 3D Non-Orthogonal Frame Fields. (October 2021) - Desobry, David; Coudert-Osmont, Yoann; Corman, Etienne; Ray, Nicolas; Sokolov, Dmitry
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. Graphical abstract: Highlights: Method for direction field design on meshes, supporting non-orthogonality. This method offers a geometrically meaningful notion of smoothness. Non orthogonal frame field is necessary to fit a sharp corner metric. Quad and hex-meshes can be generated from hard surface and volume metric.