约束5点决定二次曲线的研究及其在参数插值中的应用  

Study of Determining a Conic with Five Constrained Points and Its Application in Parametric Interpolation

作　　者：刘毅[1] 张彩明[1] 

机构地区：[1]山东大学计算机科学与技术学院,济南250061

出　　处：《计算机研究与发展》2005年第12期2161-2168,共8页Journal of Computer Research and Development

基　　金：国家自然科学基金项目(60173052)

摘　　要：讨论了约束4点决定一条抛物线、5个点的几何分布对二次曲线形状的影响,提出了用有序5点确定一条二次曲线的计算方法·给出了隐式二次曲线和有理二次B啨zier曲线相互转化的计算公式,其转化过程可用来计算插值点的参数,并提出了对此参数进行重新参数化的计算方法·计算实例表明,新的参数化计算方法可提高节点的精度,从而使构造的插值曲线具有更高的插值精度·还以实例对两种新参数化方法和其他方法的精度进行了比较·Discussed in this paper the problem of determining a parabola with four orderly points and the effect of the geometric distributing of constrained orderly five points in respect to the shape of conics. A computing method of determining a conic uniquely with five distinct planar points is introduced. The computing translation formulas between implicit conics and rational quadratic Bézier curves are proposed too, and then it is expedient to figure out the parameters of the interpolation knots. Based on this study, a new computational technique of rational re-parameterizations of the constructed knots＇ parameters is presented. Experiment results show that the error is amended considerably and the interpolating precision is higher with respect to the constructed quadratic curve. Experiments for comparing the efficiency of the two new methods with that of other methods are also included.

关 键 词：二次曲线 有理二次Bézier曲线 插值 参数化 单位速率 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]