A linear framework for character animation

There are many areas of computer graphics which have been exhaustively researched in the context of static models, but for which the properties of animated models have been largely ignored. A good example of this is the area of level of detail (LOD). LOD techniques produce low-detail approximations to high-detail models, which may be used to speed up display of distant objects where the loss of detail will not be noticed by the viewer. LOD research is quite mature, and can produce an excellent approximation to any given pose. However, producing a low-detail model that is a faithful approximation in all poses is more challenging, and requires knowledge of the dynamics of the model. There have been a few attempts to address this problem [29, 5, 24], but they all rely on a sampling of the pose space rather than analysis of the space itself. Other areas of computer graphics that can benefit from considering the dynamics of a model include parametrisation, shading and visibility culling. Generic animation is too abstract to perform analysis on. Instead, I propose to study skeletally-driven character animation as a concrete instance of animation. Most existing character animation schemes have non-linearities that frustrate analysis; I am developing a character animation framework that expresses the animation as a linear operator. This framework facilitates various kinds of analysis: in particular, it supports the computation of two distance metrics given information about the skeleton and range of motion of bones without resorting to sampling.