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Frame Field Operators
arXiv - CS - Graphics Pub Date : 2021-06-28 , DOI: arxiv-2106.14360
David R. PalmerMassachusetts Institute of Technology, Oded SteinMassachusetts Institute of Technology, Justin SolomonMassachusetts Institute of Technology

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.

中文翻译:

帧场运算符

微分算子广泛用于问题域的几何处理,如光谱形状分析、数据插值、参数化和映射以及网格划分。除了无处不在的余切拉普拉斯算子外,各向异性二阶算子以及高阶算子(如双拉普拉斯算子)已被离散化以用于特殊应用。在本文中,我们研究了一类可以推广四阶双拉普拉斯算子以支持各向异性行为的算子。各向异性由对称框架场参数化,首先结合四边形和六面体网格进行研究,这允许对局部变化方向进行细粒度控制。我们使用混合有限元方案对这些算子进行离散化,验证离散化的收敛性,研究在回调下的算子行为,
更新日期:2021-06-29
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