二次有理B样条G^2连续插值  

INTERPOLATION OF RATIONAL QUADRATIC B-SPLINE G^2 CONTINUITY

作　　者：杨文颖[1] 宋来忠[1] 彭刚[2] 

机构地区：[1]三峡大学理学院,湖北宜昌443002 [2]三峡大学土木水电学院,湖北宜昌443002

出　　处：《计算机应用与软件》2009年第12期264-267,277,共5页Computer Applications and Software

摘　　要：给出二次有理B样条G2连续拼接的条件,提出一种二次有理B样条G2连续插值曲线的构造方法。首先给定某段曲线的首端相对曲率和该段曲线的首端切矢量的方向角以及插值曲线的权因子,然后利用G2连续条件求出其余控制顶点,并给出了构造过渡曲线的方法,得到了G2连续的闭插值曲线。该方法可以通过简单地调整某段曲线的首端曲率或该段曲线的首端切矢量的方向角或该段曲线的权因子对曲线进行调节。最后给出了曲线插值的一些实例以检验方法的有效性。The stitching conditions of rational quadratic B-spline G^2 continuity are introduced. A method to construct an interpolation curve of rational quadratic B-spline G^2 continuity is given. First, the relative curvature of a certain curve at its first end and the directional angle of the first port tangent vector of that curve as well as the weight factor of the interpolation curve are given, then all the other control vertexes can be gotten by using the conditions of G^2 continuity, and a method to construct transitional curves is also introduced so that we can get the closed interpolation curve which achieves G^2 continuity globally. The shape of curve could be modified to satisfy the demand simply through the amendment of the first end curvature or the directional angle of the first port tangent vector or the weight factor of a certain curve. At last some examples of curve＇ s interpolation are given to verify the effectiveness of the method.

关 键 词：二次有理B样条 型值点 控制顶点 相对曲率 权因子 插值 过渡曲线 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术] O157[自动化与计算机技术—计算机科学与技术]