Abstract: Traditional 2D shape deformation algorithms classify shapes into man-made shapes or organic shapes for deformation. Different types of shapes require different deformation effects, lacking a unified deformation framework. Therefore, a 2D shapes deformation algorithm based on controllable deformation effect properties is proposed. This work performs deformation based on polygon meshes, introducing a rotation matrix at the vertices of the polygon mesh. By changing the magnitude of the rotation matrix, the deformation effect properties can be altered to achieve the desired deformation effect on the shapes. After the user sets the deformation effect information, this method first analyzes and calculates the deformation effect information for each vertex, and then solves the vertex coordinates using the deformation effect information and geometric information, achieving controllable shape deformation. Experimental results on a large number of 2D shapes and user surveys indicate that the proposed method produces better deformation effects compared to existing methods and better meets user expectations.