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Matrix palette skinning (also known as skeletal subspace deformation) is a very popular real-time animation technique. So far, it has only been applied to the class of quasi-articulated objects, such as moving human or animal figures. In this paper, we demonstrate how to automatically construct skinning approximations of arbitrary precomputed animations, such as those of cloth or elastic materials. In contrast to previous approaches, our method is particularly well suited to input animations without rigid components. Our transformation fitting algorithm finds optimal skinning transformations (in a least-squares sense) and therefore achieves considerably higher accuracy for non-quasi-articulated objects than previous methods. This allows the advantages of skinned animations (e.g., efficient rendering, rest-pose editing and fast collision detection) to be exploited for arbitrary deformations.