一种显式Hermite曲线插值方法  

An Explicit Hermite Curve Interpolation

作　　者：陈伟[1] 蔡占川[2] 

机构地区：[1]江南大学数字媒体学院,无锡214122 [2]澳门科技大学资讯科技学院

出　　处：《计算机辅助设计与图形学学报》2016年第8期1326-1332,共7页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家"九七三"重点基础研究发展计划项目(2011CB302400);国家自然科学基金(61170320;61272026;61402201);澳门科技发展基金项目(084/2012/A3;110/2014/A3);浙江大学CAD&CG国家重点实验室开放课题(A1513;A1609);中央高校基本科研业务费专项资金(JUSRP11416)

摘　　要：Hermite曲线插值要求插值曲线不仅严格通过型值点,还要满足型值点处的各阶导数切触条件.针对传统隐式或半显式Hermite曲线插值方法中求解复杂、非严格插值等问题,提出一种显式Hermite曲线插值方法.首先构造了一类基数型Hermite插值基函数,该基函数具有局部支集、对称性、高阶连续等性质;然后将该基函数与给定的Hermite插值条件调配,得到一条严格满足各阶切触条件的k次样条曲线.实验结果表明,利用文中方法得到的插值曲线不仅严格满足插值条件,还具有光滑的曲率与较高的插值精度;与传统方法相比,该方法具有插值过程简单、无需求解方程组的优点.Hermite curve interpolation requires the result curve interpolating the given points as well as various derivatives at these points. The traditional implicit and semi-explicit methods have the problems on difficult solving and inexact interpolation. With respect to these defects, a novel explicit Hermite curve interpolation method is proposed in this paper. Firstly, we constructed a class of cardinal type Hermite basis functions. Then they will be blended with all the given interpolation conditions, and a spline curve of degree k will be obtained directly which satisfies all-order derivatives. The experimental results show that our result curves have smooth curvature and high interpolation precision. Compared with the traditional methods, our method has a simper interpolation process without solving equations.

关 键 词：HERMITE插值 显式基函数 样条曲线 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]