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Frame Field Operators
Author(s) -
Palmer D.,
Stein O.,
Solomon J.
Publication year - 2021
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.14370
Subject(s) - discretization , quadrilateral , finite element method , interpolation (computer graphics) , mathematics , operator (biology) , laplace operator , operator theory , cotangent bundle , fourier integral operator , differential operator , microlocal analysis , mathematical analysis , computer science , frame (networking) , geometry , trigonometric functions , physics , telecommunications , biochemistry , chemistry , repressor , transcription factor , gene , thermodynamics
Differential operators are widely used in geometry processing for problem domains like spectral shape analysis, data interpolation, parametrization and mapping, and meshing. In addition to the ubiquitous cotangent Laplacian, anisotropic second‐order operators, as well as higher‐order operators such as the Bilaplacian, have been discretized for specialized applications. In this paper, we study a class of operators that generalizes the fourth‐order Bilaplacian to support anisotropic behavior. The anisotropy is parametrized by a symmetric frame field , first studied in connection with quadrilateral and hexahedral meshing, which allows for fine‐grained control of local directions of variation. We discretize these operators using a mixed finite element scheme, verify convergence of the discretization, study the behavior of the operator under pullback, and present potential applications.