  To be suitable for film-quality animation, rigs for character deformation
must fulfill a broad set of requirements. They must be able to create highly
stylized deformation, allow a wide variety of controls to permit artistic
freedom, and accurately reflect the design intent. Facial deformation is
especially challenging due to its nonlinearity with respect to the animation
controls and its additional precision requirements, which often leads to highly
complex face rigs that are not generalizable to other characters. This lack of
generality creates a need for approximation methods that encode the deformation
in simpler structures. We propose a rig approximation method that addresses
these issues by learning localized shape information in differential
coordinates and, separately, a subspace for mesh reconstruction. The use of
differential coordinates produces a smooth distribution of errors in the
resulting deformed surface, while the learned subspace provides constraints
that reduce the low frequency error in the reconstruction. Our method can
reconstruct both face and body deformations with high fidelity and does not
require a set of well-posed animation examples, as we demonstrate with a
variety of production characters.
