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Title: Frame Field Operators
Abstract

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 asymmetric 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.

 
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Award ID(s):
1838071
NSF-PAR ID:
10447961
Author(s) / Creator(s):
 ;  ;  
Publisher / Repository:
Wiley-Blackwell
Date Published:
Journal Name:
Computer Graphics Forum
Volume:
40
Issue:
5
ISSN:
0167-7055
Page Range / eLocation ID:
p. 231-245
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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