Approximate merging of B-spline curves and surfaces  

作　　者：CHEN Jun： WANG Guo-jin 

机构地区：[1]Department of Mathematics, Zhejiang University, Hangzhou 310027, China [2]Ningbo University of Technology, Ningbo 315016, China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2010年第4期429-436,共8页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China (60873111, 60933007)

摘　　要：Applying the distance function between two B-spline curves with respect to the L2 norm as the approximate error, we investigate the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. Then this method can be easily extended to the approximate merging problem of multiple B-spline curves and of two adjacent surfaces. After minimizing the approximate error between curves or surfaces, the approximate merging problem can be transformed into equations solving. We express both the new control points and the precise error of approximation explicitly in matrix form. Based on homogeneous coordinates and quadratic programming, we also introduce a new framework for approximate merging of two adjacent NURBS curves. Finally, several numerical examples demonstrate the effectiveness and validity of the algorithm.Applying the distance function between two B-spline curves with respect to the L2 norm as the approximate error, we investigate the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. Then this method can be easily extended to the approximate merging problem of multiple B-spline curves and of two adjacent surfaces. After minimizing the approximate error between curves or surfaces, the approximate merging problem can be transformed into equations solving. We express both the new control points and the precise error of approximation explicitly in matrix form. Based on homogeneous coordinates and quadratic programming, we also introduce a new framework for approximate merging of two adjacent NURBS curves. Finally, several numerical examples demonstrate the effectiveness and validity of the algorithm.

关 键 词：Computer aided geometric design approximate merging B-spline curves and surfaces. 

分 类 号：O175.7[理学—数学] TP391.72[理学—基础数学]