过测地线的B样条曲面优化设计  

Optimization Design of B-Spline Surfaces through Geodesics

作　　者：杨火根[1,2] 汪国昭[1] 

机构地区：[1]浙江大学数学系,杭州310027 [2]江西理工大学理学院,赣州341000

出　　处：《计算机辅助设计与图形学学报》2013年第10期1433-1438,共6页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(61272300);国家自然科学基金重点项目(60933008)

摘　　要：给定一组不相交B样条曲线或满足一定约束的相交B样条曲线,提出了插值已知B样条曲线且以这组曲线为等参测地线的B样条曲面构造方法.插值曲面上的控制顶点分2步确定:首先利用B样条乘积和升阶理论显式计算曲面上与插值条件相关的控制顶点,其次由极小化Dirichlet能量确定曲面上其他自由控制顶点.采用文中方法构造的插值测地线曲面具有次数低、形状易控制等优点,并通过计算实例验证了该方法的正确性和有效性.Given a set of non-intersecting B-spline curves or intersecting B-spline curves which satisfy certain constraints, the B-spline surfaces are constructed to interpolate these curves, such that they are the boundary geodesics of the constructed surfaces. The control points of interpolating surfaces are determined in two steps. Firstly, based on the theory of products and degree raising of B-spline, the control points related with interpolation conditions are computed explicitly. Secondly, other free control points of the surfaces are determined by minimizing the Dirichlet energy. The constructed surfaces have such advantages as low degrees and easily-controlled shape, and the correctness and validity of the proposed method is demonstrated by the computational examples.

关 键 词：B样条曲面 测地线 优化设计 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]