摘要
提出一种基于三角和双曲多项式加权的二次混合样条曲线,这种曲线具有二次非均匀B样条曲线相似性质.这里的权系数也是形状参数,称之为权参数,取值范围从区间[0,1]扩大到区间[-2.6482,3.9412].权参数的不同取值可以整体或局部地调整曲线的形状,并且权参数能像开关那样,使得曲线的各段能非常方便地在三角样条、双曲样条之间自由转换.不需要用重节点方法或解方程组,而只要令某个或某些权参数取-2.6482,曲线就能接插值于控制点或控制边.此外,还能精确表示椭圆(圆)和双曲线.
A method of generating quadratic blending spline curves based on weighted trigono- metric and hyperbolic polynomials is presented in this paper, which shares many important properties of quadratic non-uniform B-splines. Here weight coefficients are also shape parameters, which are called weight parameters. The interval [0, 1] of weight parameter values can be extended to [-2.6482, 3.9412]. Taking different values of the weight parameter, one can not only totally or locally adjust the shape of the curves but also change the type of some segments of a curve among trigonometric or hyperbolic polynomials. Without using multiple knots or solving system of equations and letting one or several weight parameter be -2.6482, the curve can interpolate certain control points or control polygon edge directly. Moreover, it can represent ellipse （circle） and hyperbola exactly.
出处
《计算数学》
CSCD
北大核心
2010年第2期147-156,共10页
Mathematica Numerica Sinica
基金
国家自然科学基金资助项目(60773043
60473114)
教育部博士点基金(20070359014)
安徽省教育厅科技创新团队基金资助项目(2005TD03)
安徽省教育厅自然科研基金项目(KJ2008B250)
安徽省教育厅高校青年教师基金资助项目(2008jq1158)
湖南省教育厅自然科研基金项目(06C791)
关键词
三角双曲多项式
非均匀节点
权参数
整体与局部调控
插值
混合曲线段
trigonometric and hyperbolic polynomial
non-uniform knot
weight parameter
totally or locally adjust
interpolation
blending curve segment
