A Mesh-Based Approach for RBF-Based Planar Shape Deformation

Planar shape deformation has wide applications in computer graphics. Traditional mesh-based methods can flexibly control the distortions of the deformation while has the weakness of non-smoothness due to its piece-wise-linear nature. And the mesh-free methods have the feature of smoothness, but most of them are lack of dis-tortion control. Though a few take distortions into consideration, the computation is complicated and time-consuming. To this end, we combine the advantages of both the two kinds of methods and propose a radial basis functions (RBF)-based planar shape deformation combining with mesh-based method. It constructs trian-gle-mesh structure for the rest shape domain and uses RBF to represent the deformation, and then builds the op-timization equations for the deformation with locally injective constraints. To solve the problem efficiently, it borrows the computational framework of the mesh-based methods, which calculates geodesic fields for the radial basis functions and linearly approximates the numerical calculus of deformation energy by using the mesh structure. A large number of comparative experiments show that our deformation results are more smooth, nat-ural and with lower distortions than the traditional mesh-based methods, and it is also more efficient than traditional mesh-free methods with comparative results. Meanwhile, the method has the feature of controllable, simple and extendable. © 2020, Beijing China Science Journal Publishing Co. Ltd. All right reserved.