The creation of character animation of humans, animals, or plants plays one of the most important roles in computer graphics, with tremendous applications on creating motion pictures, video games, and virtual worlds. To this day, one of the most popular character animation techniques is skinning, where a set of low-dimensional control parameters is mapped to the high-dimensional geometric shape of the character model. Once the skinning model is setup, a manipulation on control parameters is propagated to the surface of the model accordingly, generating articulations and deformations of the character model. Skinning techniques allow effective controls of animation from different sources, such as artist input or motion capture data. In addition, skinning techniques can be used to accelerate the animation rendering or compress the motion data. This dissertation explores fundamental problems in the skinning pipeline including the model set up and the hardware accelerated rendering of animation. The scope of this dissertation only focuses on linear skinning models with using bone transformations as the controller. To setup the skinning model, I propose example-based rigging techniques to extract the linear blend skinning (LBS) model from mesh sequence of the character model in different poses. The output LBS model consists of sparse, convex, and smooth skinning weights and rigid (orthogonal) bone transformations with or without a skeletal structure. The key contributions of my rigging technique are: (1) a fast iterative linear solver to optimize the orthogonal bone transformations, (2) a problem formulation and an optimization method to accurately constraint bone rotations around skeletal joints, (3) a rigidness Laplacian regularizer to constraint the smoothness of skinning weights, and (4) a robust method to extract the skeletal structure from an over-completed initialization. To accelerate the rendering of the LBS model during animation, I introduce a two-layer linear blend skinning model which can substantially reduce the computational cost of a dense-weight LBS model with insignificant loss of its visual quality. This two-layer model allows fast skinning animation without requiring the sparseness constraint on the skinning weights (dense-weight), which offers more flexibility on applications of the LBS model. The two-layer model is constructed by the sparse coding technique with directly using dense skinning weights or with using additional example poses to further improve its accuracy. ; Computer Science, Department of