2D Shape Deformation And Controllable Interpolation Using Moving Least Squares

Computer animation takes advantage of human eye’s visual staying phenomenon, that the continuous playing of static pictures can make human feel like seeing moving scenes. Computer animation technology combines computer graphics and art, which has been widely used in various fields, such as film and television special effects production, construction and interior design, commercial advertising, and so on.Shape deformation and shape interpolation are key computer animation techniques. Deformation using moving least squares (MLS) allows the user to manipulate2D characters via control points or control line segments. The traditional MLS spreads the deformation of the controls with respect to the spatial distance, but oblivious to the shape topology, and thus possibly leads to distortion. As rigid as possible shape interpolation method can produce more natural intermediate frame sequences. However, these methods, the intermediate frame sequences of shape interpolation which are completely determined by the source and the target shape.Lack of effective ways allow the user to control the intermediate frame sequences of shape interpolation. To solve the above problems, we present a topology-aware MLS deformation approach for2D characters and a controllable interpolation using moving least squares method.(1) we present a topology-aware MLS deformation approach for2D characters. First, a Laplace equation is solved to obtain a set of weights, which are called as harmonic weights. Then, the MLS deformation is performed by using the harmonic weights as the deformation influence of the user-specified controls. Consequently, the possible distortion in the traditional MLS can be effectively avoided, since the harmonic weights spread the deformation of the controls in a local and topology-aware way. In addition, an area-preserving variant of MLS deformation is proposed, which is suitable for the editing of incompressible objects.(2) we propose a controllable interpolation using moving least squares method. This method allows the user to control the interpolation frame sequence of the shape by a set of control points. First, we utilize as rigid as shape interpolation algorithm, an initial frame sequence which is generated between the source and the target shapes. Then, in order to control the frame sequence of the shape interpolation, the user will pre-place some control points on the source shape according to the requirement. Finally, after the user edits these control points on the selected intermediate frame, deformation algorithm using the moving least squares can automatically and smoothly propagate user control to the entire shape and the adjacent frames which ultimately implements user controlled shape interpolation intermediate frame sequences. The experiment results show that the new method allows the user to obtain vision natural interpolation intermediate frame sequences by simple and intuitive interactions.