  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.
