Abstract: The establishment of a good correspondence mapping is a key issue in planar animations such as image morphing and deformation. In this paper, we present a novel mapping framework for animation of complex shapes. We firstly let the user extract the outlines of the interested object and target interested area from the input images and specify some optional feature lines, and then we generate a sparse delaunay triangulation mesh taking the outlines and the feature lines of the source shape as constraints. Then we copy the topology from the source shape to the target shape to construct a valid triangulation in the target shape. After that, each triangle of this triangular mesh is further segmented into a dense mesh patch. Each mesh patch is parameterized onto a unit circle domain. With such parameterization, we can easily construct a correspondence mapping between the source patches and the corresponding target patches. Our framework can work well for various applications such as shape deformation and morphing. Pleasing results generated by our framework show that the framework works well.