带有切线多边形的一类有理样条的扩展曲线  

Extension of a Class of Rational Spline Curve with Given Tangent Polygon

作　　者：王成伟[1] 

机构地区：[1]北京服装学院基础教学部,北京100029

出　　处：《北京服装学院学报（自然科学版）》2011年第1期5-12,共8页Journal of Beijing Institute of Fashion Technology：Natural Science Edition

基　　金：北京市教育委员会科技发展计划面上项目(KM201010012010)

摘　　要：利用一个对称的调配函数,结合NURBS曲线中权的思想,在曲线控制顶点处引进调配参数,将一类有理样条曲线进行扩展,得到的新曲线比原来的曲线有更强的描述能力,并且包含了原曲线形式.描述了一种与给定多边形相切的一类有理样条扩展曲线的算法.在算法中,所有的有理样条扩展曲线的控制点可以通过对多边形的顶点简单计算产生.所构造的曲线对多边形具有保形性,曲线可以局部修改,最后给出了2个算例.调配参数可以用来控制曲线的局部形状,特别适用于自由曲线曲面的设计,在CAD/CAM中具有很好的应用前景.By introducing the concept of weights in NURBS curve into a blending technique,we extend the representation of the rational spline curve.Shape-control capability of the extension curve is shown to be much better than that of the rational spline curve.An algorithm for constructing extension of the rational spline which is tangent to the given polygon is described.The control points of the extension of the rational spline curve to be constructed are computed simply by the vertices of the given polygon.The constructed curve is shape-preserving to the polygon.The local modification to the extension of the rational spline curve can be completed by simply adjusting the corresponding control parameters.Two examples are given.The curve is easy to reshape by varying the parameters;so it is useful in the applications of CAD/CAM.

关 键 词：有理样条曲线 曲线设计 形状参数 多边形 

分 类 号：TP391[自动化与计算机技术—计算机应用技术] O241.3[自动化与计算机技术—计算机科学与技术]