2D shape deformation based on rigid square matching

In this paper, we propose a fast and stable method for 2D shape deformation based on rigid square matching. Our method utilizes uniform quadrangular control meshes for 2D shapes and tries to maintain the rigidity of each square in the control mesh during user manipulation. A rigid shape matching method is performed to find an optimal pure rotational transformation for each square in the control mesh. An iterative solver is proposed to compute the final deformation result for the entire control mesh by minimizing the difference between the deformed vertices and their counterparts in the neighboring rigid square. The deformation result on the 2D shape is as rigid as possible and the details of the shape are preserved well. As extensions, we present a shape-aware splitting method to improve the deformation effect for coarse meshes and a simple sketch-based clustering method for skeletal deformation. Experiments with various 2D shapes show that our method is efficient and easy to use, and can provide physically plausible result for shapes of objects in real world. Therefore, our shape deformation method is especially suitable for applications in cartoon character animation.