Interpolation over arbitrary topology meshes using Doo-Sabin surfaces
Interpolating an arbitrary topology mesh by a smooth surface plays an important role in geometric modeling and computer graphics. In this paper we present an efficient new algorithm for constructing a Doo-Sabin subdivision surface that interpolates a given mesh. By introducing additional degrees of freedom, the control vertices of the Doo- Sabin subdivision surface can be obtained directly with no need to solve any initial or intermediate large systems. The control points are computed by modifying the geometric rules of the first step of Doo- Sabin subdivision scheme and the resulting surface interpolates given vertices and optionally normal vectors at the vertices. The method has several merits for surface modeling purposes: (1) Efficiency: we obtain a generalized quadratic B-spline surface to interpolate a given mesh in a robust and simple manner. (2) Simplicity: we use only simple geometric rules to construct a smooth surface interpolating given data. (3) Locality: the perturbation of a given vertex only influences the surface shape near this vertex. (4) Freedom: for each vertex, there is one degree of freedom to adjust the shape of the interpolation surface. These features make surface interpolation using Doo-Sabin surface very simple and thus make the method itself suitable for interactive free-form shape design.
Subdivision surfaces Interpolation Doo-Sabin subdivision
Chongyang Deng Xunnian Yang
Institute of Applied Mathematics and Engineering Computations, Hangzhou Dianzi University, Hangzhou3 Department of Mathematics, Zhejiang University, Hangzhou 310027, P.R.China
国际会议
IEEE International Conference on Shape Modeling and Applications (SMI)(2009年形状建模国际会议)
北京
英文
52-57
2009-06-26（万方平台首次上网日期，不代表论文的发表时间）