Abstract: The 2-d shape interpolation or shape morphing which involves the creation of a smooth transition from a source planar polygon to a target one, has gained widespread application in recent years. In this study, we implemented an interpolation framework. As for an interpolating key issue which is correspondence between the source and target shape, we proposed a scheme for corresponding and improving the interpolation. We only triangulate the source shape and find the position of vertex in target shape by the technology of deformation with constraints. Our method avoids the shape remeshing for correspondence. As for large rotation and small strain problem, our method can work well. This method is easy to implement in the exiting FEM code. Experiments show that the proposed framework is effective for as-rigid-as-possible interpolation.