基于牛顿插值的多项式参数曲线隐式化  

Implicitization of polynomial parametric curves by means of Newton interpolation

作　　者：赵若晨[1] 于建平[2] 孙永利[1] 

机构地区：[1]北京化工大学理学院,北京100029 [2]北京科技大学数理学院,北京100083

出　　处：《北京化工大学学报（自然科学版）》2011年第4期140-143,共4页Journal of Beijing University of Chemical Technology(Natural Science Edition)

基　　金：中央高校基本科研业务费(00621605)

摘　　要：利用Bezout矩阵与牛顿插值多项式的基本理论,给出了多项式参数曲线隐式化的一种方法。与基于拉格朗日插值多项式的参数曲线隐式化相比,该方法节省了时间和空间,从而极大地提高了隐式化的运算速度。通过隐式化的例子,验证了本文算法的准确性和有效性。A method of implicitization of polynomial parametric curves, which is based on a Bezout matrix and Newton interpolation, is given in this paper. Compared to the implicitization of polynomial parametric curves via Lagrange interpolation, the new method saves both time and space and therefore greatly improves the operation speed. Finally, some examples are given which prove the effectiveness and accuracy of this method.

关 键 词：多项式参数曲线 BEZOUT矩阵 牛顿插值 

分 类 号：O187.1[理学—数学]