Frame Field Operators

Differential operators are widely used in geometry processing for problem domains like spectral shape analysis, data interpolation, parametrization and mapping, meshing. In addition to the ubiquitous cotangent Laplacian, anisotropic second-order operators, as well higher-order such Bilaplacian, have been discretized specialized applications. this paper, we study a class of that generalizes fourth-order Bilaplacian support behavior. The anisotropy is parametrized by symmetric frame field, first studied connection with quadrilateral hexahedral meshing, which allows fine-grained control local directions variation. We discretize these using mixed finite element scheme, verify convergence discretization, behavior operator under pullback, present potential