高阶C-B样条曲线曲面的显式形式  

AN EXPLICIT FORM FOR HIGHER-ORDER C-B SPLINE CURVES AND SURFACES

作　　者：蒋春娟[1] 唐月红[1] 

机构地区：[1]南京航空航天大学数学系,南京210016

出　　处：《高等学校计算数学学报》2008年第1期26-39,共14页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(No.60472117);南京航空航天大学创新基金(No.Y0607-082)资助项目.

摘　　要：1引言基于多项式空间span{1,t,t^2,…,t^k}的B样条和Bézier曲线（面）是构造自由曲线、曲面强有力的工具,但是它们不能精确表示圆弧、椭圆等,也不能精确地表示正弦曲线和二次曲面,于是文献[1 提出了一种新的三次曲线（面）模型,称为C曲线（面）,它们是低次多项式样条曲线（面）的拓广,具有很多B样条的良好性质,如对称性、保凸性等,不仅能精确表示二次曲线和曲面和某些超越曲线,而且克服了NURBS求导求积复杂的困难,因此引起了国内外广泛的关注,近年来涌现了大量的文献.C-B spline curves and surfaces based on the space spanned by {sint, cost,, 1, t,…, t^k-3, } are new tools for surface modeling . In this paper a new explicit form for C-B spline curves and surfaces is proposed, which is represented as a linear combination of {sint, cos t,, 1, t,…, t^k-3} . And the explicit expression for its important subclass C-Bezier curves and surfaces is derived as well. Then the explicit form is used for the approximate degree reduction of C- Bezier curves and surfaces. The degenerate conditions for them are obtained. And from the new form a set of generated Hermite basis of order n can be expressed as a linear combination of C-Bezier basis of the same order. It is easy to see from the applications above that the use of this new different representation for C-B spline curves and surfaces in this paper is more convenient and effective in some cases. Finally, we give an example of C-Bezier curves of order 5 in the explicit representation.

关 键 词：C-B样条 曲线曲面 显式形式 BÉZIER曲线 多项式空间 高阶 NURBS 自由曲线 

分 类 号：TP391[自动化与计算机技术—计算机应用技术] TP391.72[自动化与计算机技术—计算机科学与技术]