Efficient piecewise higher-order parametrization of discrete surfaces with local and global injectivity. (October 2020)

• Record Type: Journal Article
• Authors: Mandad, Manish; Campen, Marcel
• Is Part Of: Computer aided design. Volume 127(2020)
• Publication Date: 2020-10
• Subjects: Bézier triangles -- Curved meshes -- Hessian majorization; 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.2020.102862
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: The parametrization of triangle meshes, in particular by means of computing a map onto the plane, is a key operation in computer graphics. Typically, a piecewise linear setting is assumed, i.e., the map is linear per triangle. We present a method for the efficient computation and optimization of piecewise nonlinear parametrizations, with higher-order polynomial maps per triangle. We describe how recent advances in piecewise linear parametrization, in particular efficient second-order optimization based on majorization, as well as practically important constraints, such as local injectivity, global injectivity, and seamlessness, can be generalized to this higher-order regime. Not surprisingly, parametrizations of higher quality, i.e., lower distortion, can be obtained that way, as we demonstrate on a variety of examples.