Mesh Deformation for Arbitrary Polygonal Cages Using Generalized Barycentric Coordinates

Mesh deformation is an important task in computer graphics. It is used to dynamically change the shape of an object by changing the position of mesh vertices while preserving its topology. It has a wide range of applications in the fields of animation, game development and virtual reality. Traditional cage-based mean value coordinates mesh deformation methods are only applicable to control cages composed of triangular meshes or quadrilateral meshes. To address this problem, we propose a cage-based mean value coordinates mesh deformation method, which is applicable to control cages composed of arbitrary polygonal meshes, including non-planar polygons. The proposed method first preprocess planar polygons to obtain subdivided triangular meshes; then polygons of the control cage are interpolated using Wachspress coordinates and the results of the preprocessing, so as to subdivide the control cage composed of arbitrary polygons into triangular mesh; finally, the results of the mesh deformation are obtained by using the GPU-accelerated mean valued coordinates mesh deformation method in the subdivided cage. Compared with traditional method, the proposed method can maintain symmetry of the initial model and can run at a fast speed.