Automatic linearization of nonlinear skinning

Linear blending is a very popular skinning technique for virtual characters, even though it does not always generate realistic deformations. Recently, nonlinear blending techniques (such as dual quaternions) have been proposed in order to improve upon the deformation quality of linear skinning. The trade-off consists of the increased vertex deformation time and the necessity to redesign parts of the 3D engine. In this paper, we demonstrate that any nonlinear skinning technique can be approximated to an arbitrary degree of accuracy by linear skinning, using just a few samples of the nonlinear blending function (virtual bones). We propose an algorithm to compute this linear approximation in an automatic fashion, requiring little or no interaction with the user. This enables us to retain linear skinning at the core of our 3D engine without compromising the visual quality or character setup costs.