The Free-Form Deformation Technique Base On The Volumetric Subdivision Scheme

These years, with the rapid development of computer and internet technology, the three-dimensional geometric modeling technique plays an increasingly important role in many fields, such as industrial modeling, video processing, game production, film and television special effects and so on. Space deformation is an important tool for shape modification in geometric modeling field.The traditional free-form deformation algorithms are not flexible enough, and it is hard to carry out intuitively and effectively. As to the initial control mesh, the necessary precondition of the Free-form deformation, there has been some problems such as too much complexness in algorithm, hard to implement, large storage and so on. A new interactive, real-time deformation scheme based on volumetric subdivision is proposed in this paper, which use three-dimensional volumetric meshes of arbitrary topology as a means of control, to edit the model which has a large amount of data.The main work of this paper include:First, a new algorithm of volumetric meshes generation is proposed, which overcomes the problems of hard to express arbitrary shape, and excessive growth of the amount of data of the traditional algorithm. A multi-resolution volumetric meshes, which has a similar shape with the object, will be generated by the new algorithm. Second, a new subdivision scheme for tetrahedral meshes is proposed, which overcomes the existing problems of the directional preferences, or the generated volumetric meshes composed of tetrahedrons and octahedrons of the current algorithm. For the volumetric meshes of tetrahedron, the inners of the meshes are subdivided by using the volumetric subdivision, and the surfaces of the meshes are subdivided by using a quasi-Loop surface subdivision with a parameter to control the shapes of the solids. Finally, a new interactive free-form deformation method is brought out. The existing method is not intuitive enough by using the parallelepiped as control meshes. The new method carries out the deformation by using a multi-resolution volumetric meshes of arbitrary topology. The weighted value is calculated by the distance of the vertex and the tetrahedrons, and all the affects to the vertex coming from the tetrahedrons are weighted averaged to get the new position of the vertex. When the all new positions of the vertexes of the object are calculated, a smooth deformation is performed. Compared with the existing free-form deformation algorithm, the proposed algorithm is flexible, intuitive, and real-time interactive. Both the global deformation, and the local deformation can be carried out.In addition, a modeling system by the platform of VS.NET and OpenGL, is designed to implement all the algorithms in the paper. Experiments show that, the free-form deformation of the three-dimensional model could be achieved with excellent effect.