  We propose a method for computing integrable orthogonal frame fields on
planar surfaces. Frames and their symmetries are implicitly represented using
orthogonally decomposable (odeco) tensors. To formulate an integrability
criterion, we express the frame field's Lie bracket solely in terms of the
tensor representation; this is made possible by studying the sensitivity of the
frame with respect to perturbations in the tensor. We construct an energy
formulation that computes smooth and integrable frame fields, in both isotropic
and anisotropic settings. The user can prescribe any size and orientation
constraints in input, and the solver creates and places the singularities
required to fit the constraints with the correct topology. The computed frame
field can be integrated to a seamless parametrization that is aligned with the
frame field.
