Differential Methods in Character Rigging

Abstract

Most 3D animation software comes with various mesh deformers for character rigging, based on long known and widely used algorithms, like skeletal subspace deformation or freeform deformation. We demonstrate how these methods can be improved upon and made more flexible while still working interactively as part of complicated character rigs, using the same workflow as before. We first consider the interpolation of affine transformations, and the solution of differential equations, whose properties will be taken advantage of in the algorithms we implemented. Next we consider the problem of shape interpolation, and discuss a representation for mesh deformations that encodes them in affine transformations per triangle, such that they can be interpolated and edited in ways difficult to achieve otherwise. Then we discuss skeletal subspace deformation and recent methods to get rid of its well known artifacts while still being nearly as efficient. Additionally we demonstrate how to