多项式参数曲线隐式化的新方法  

A new method for the implicitization of polynomial parametric curves

作　　者：于建平[1] 孙永利[2] 

机构地区：[1]北京科技大学应用科学学院,北京100083 [2]北京化工大学理学院,北京100029

出　　处：《北京化工大学学报（自然科学版）》2008年第3期108-111,共4页Journal of Beijing University of Chemical Technology(Natural Science Edition)

摘　　要：给出了多项式参数曲线隐式化的一种新方法。此方法主要是利用了Bezout矩阵与拉格朗日插值的相关理论,首先给出了参数曲线隐式化的一般描述,给出了多项式参数曲线隐式化的一般算法。通过相应的例子,证明了本文方法的准确性和有效性。本方法在很大程度上减少了计算量,节约了计算所需要的空间,从而在很大程度上提高了多项式参数曲线隐式化的效率。This paper presents a new method for the implicitization of polynomial parametric curves. The new method is predominantly based on the theories and computations of the Bezout matrix and Lagrange interpolation. A general description of the implicitization of the parametric curves is first presented, the important results needed in this paper are then constructed and proved and, based on them, the general algorithm for the implicitization of the polynomial parametric curves is given. The correctness and efficiency of the new method are demonstrated by use of appropriate examples. Finally, a comparison with other methods shows that the new method is much more efficient, greatly reduces the amount of computation required, and requires less space; these factors result in a significant increase in the efficiency of implicitization of polynomial parametric curves.

关 键 词：多项式参数曲线 BEZOUT矩阵 拉格朗日插值 

分 类 号：O187.1[理学—数学]