Designing 2D and 3D Non-Orthogonal Frame Fields. (October 2021)

• Record Type: Journal Article
• Authors: Desobry, David; Coudert-Osmont, Yoann; Corman, Etienne; Ray, Nicolas; Sokolov, Dmitry
• Is Part Of: Computer aided design. Volume 139(2021)
• Publication Date: 2021-10
• Subjects: Geometry processing -- Vector field design -- Quadrilateral remeshing -- Hexahedral remeshing; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2021.103081
• Languages: English
• ISSNs: 0010-4485

Abstract

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.