二次B样条曲面顶点及法向插值

顶点位置插值是自由曲面造型的基本方法，法向插值在一些CAD／CAM系统中也有重要应用，文中利用子分曲面理论研究双二次B样条曲面的性质，在此基础上利用Doo-Sabin分子模式构造插值顶点位置和法向的双二次B样条曲面控制网络，得到插值曲面的参数表示，为了提高效率，对规模较大的网络数据，先把它成若干片子网格，分别求出满足子网格相关的插值条件的控制网格，最后再反它们整合在一起形成完整的控制网格，使得相应的二次B样条曲面插值所有顶点及法向。

Interpolation of Vertices and Their Normal Vectors with Quadratic B-Spline Surfaces

Interpolation to vertex positions is an essential issue in surface modeling, and interpolation to normal vectors has also important applications in some CAD/CAM areas. Properties of bi quadratic B spline surface are investigated by the subdivision approach, and the control mesh of bi quadratic B spline surface is constructed by employing Doo Sabin subdivision to derive the parametric representation of interpolation surface. For enhancing the efficiency of handling mesh with larger scale data, we first partition the mesh into a number of sub meshes and compute their corresponding control nets satisfying interpolatory conditions, then the sub\|nets are integrated to form a whole net such that its bi quadratic B spline surface interpolates all given vertices and normal vectors.