陈青;潘日晶;黄丽琴;林传銮;

• 1:福建师范大学数学与计算机科学学院

摘要(Abstract)：

提出一种基于渐进迭代逼近的等距曲线改进算法.该改进算法利用曲线段的高控制采样误差,在充分反映基曲线的形状特征的前提下尽可能地减少采样点数量.在采样点中选取等距曲线上的特征点作为主控制点,利用渐进迭代逼近方法插值所选取的主控制点,迭代过程中综合考虑法矢和参数化一致性两个因素以更好地控制等距逼近曲线的形状.最后,同样利用曲线段的高控制逼近误差,以避免误差过估,对得到的逼近等距曲线的B样条曲线实现更精确的全局误差控制.给出一些实例来验证该改进算法在采样点数量、所需控制顶点个数、迭代次数、误差控制、等距逼近曲线的形状控制等方面实现了性能的提高.

关键词(KeyWords)： 切矢;等距线;B样条曲线;法矢

Abstract:

Keywords:

基金项目(Foundation): 福建省自然科学基金资助项目(2010J01318)

作者(Authors): 陈青;潘日晶;黄丽琴;林传銮;

参考文献(References)：

• [1]Cobb E S.Design of sculptured surfaces using the B-spline representation[D].Salt Lake City:Univesity of Utah,1984.
• [2]Coquillart S.Computing offsets of B-spline curves[J].Computer Aided Design,1987,19(6):305-309.
• [3]Tiller W,Hanson E G.Offsets of two-dimensional profiles[J].IEEE Computer Graphics And Application,1984,4(9):36-46.
• [4]Elber G,Cohen E.Offset approximation improvement by control points perturbation[C]//Mathematical Methods in CAGD and Image Processing.New York:Academic Press,1992:229-237.
• [5]刘利刚,王国瑾.基于控制顶点偏移的等距曲线最优逼近[J].软件学报,2002,13(3):398-403.
• [6]Klass R.An offset spline approximation for plane cubic splines[J].Computer Aided Design,1983,15(4):297-299.
• [7]Hoschek J.Spline approximation of offset curves[J].Computer Aided Geometric Design,1988,20(1):33-40.
• [8]Pham B.Offset approximation of uniform B-splines[J].Computer Aided Design,1988,20(8):471-474.
• [9]Hoschek J,Wissel N.Optimal approximate conversion of spline curves and spline approximation of offset curves[J].Computer Aided Design,1988,20(8):475-483.
• [10]Li Y M,Hsu V Y.Curve offsetting based on Legendre series[J].Computer Aided Geometric Design,1998,15(7):711-720.
• [11]Piegl L A,Tiller W.Computing offsets of NURBS curves and surfaces[J].Computer Aided Design,1999,31(2):147-156.
• [12]Bezier D K N,Sian C N.Approximating offset curves by rational Bezier cubics and quartics[J].Sains Malaysiana,2008,37(4):421-427.
• [13]Maqsood A Khan,Chen Z C.Approximation of planar offset curves with globally bounded error for B-spline NC tool paths[J].International Journal of Production Research,2012,50(23):6811-6825.
• [14]Lee I K,Kim.M S,Elber G.Planar curve offset based on circle approximation[J].Computer Aided Design,1996,28(8):617-630.
• [15]Shih J L,Chuang S H F,One-sided offset approximation of freeform curves for interference-free NURBS machining[J].Computer Aided Design,2008,40(9):931-937.