Efficient piecewise higher-order parametrization of discrete surfaces with local and global injectivity

Autor(en): Mandad, Manish
Campen, Marcel 
Stichwörter: 3D; ALGORITHM; Bezier triangles; BOUNDARY; Computer Science; Computer Science, Software Engineering; CONSTRUCTION; CURVED MESHES; Hessian majorization; MAPPINGS; MESH GENERATION; PARAMETERIZATION; QUALITY; SYMMETRIC QUADRATURE-RULES
Erscheinungsdatum: 2020
Herausgeber: ELSEVIER SCI LTD
Journal: COMPUTER-AIDED DESIGN
Volumen: 127
Zusammenfassung: 
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. (C) 2020 Elsevier Ltd. All rights reserved.
Beschreibung: 
Symposium on Solid and Physical Modeling (SPM) collocated with the Shape Modeling International Conference (SMI), ELECTR NETWORK, JUN 02-04, 2020
ISSN: 00104485
DOI: 10.1016/j.cad.2020.102862

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