Approximating, editing, and processing free -form motion

Motion is an important part of computer graphics. Skeletal motion, in particular, has been the focus of a great deal of research. Today, there exists a large body of techniques for processing and editing skeletal motion, increasing the versatility of each animation clip. However, analogous techniques have not yet been developed for deforming surface animations, where the surface geometry undergoes completely free-form motion.;Likewise, polygonal meshes are a central part of computer graphics, and have also been the focus of much research. Many techniques have been developed for editing and approximating meshes with static geometry. However, these techniques do not generally carry over to deforming surfaces.;This is unfortunate, as free-form deforming surfaces are becoming increasingly common in movies, games, and scientific applications. Moreover, these surfaces are frequently quite time-consuming to generate. It is therefore important to develop ways to increase the versatility of each generated motion clip. This dissertation presents the methods I have developed to do just that, allowing motion clips to be edited and processed in ways analogous to existing static mesh and skeletal motion methods.;Also, deforming surfaces are frequently generated with entirely too many vertices for any given frame. This is especially true of physically generated animations (such as cloth), since the surface must be subdivided enough to accommodate any possible deformation. After generation, however, this extra detail is not needed for tasks such as rendering and playback. This dissertation presents my deforming surface approximation method, which yields a temporally coherent sequence of multiresolution meshes that approximate the surface at multiple levels of detail.;I have also developed a simple but powerful rotation-invariant differential mesh representation that can easily accommodate any connected triangle mesh (including non-manifold and non-orientable surfaces). This representation is useful not only for free-form motion processing but also for general geometric mesh editing.