参数曲线的隐式化

Implicitization of parametric curves

给出了多项式参数方程定义的参数曲线的有效隐式化算法,此算法主要是基于矩阵理论。首先,给出的是所求隐式方程次数的上界及其隐式方程的一般表示,并由构造的隐式矩阵的零向量,进一步得到了所求隐式方程的所有系数,从而得到了参数曲线的隐式方程。文中给出的一些例子详细证明了该算法的准确性和有效性。

This paper presents an efficient algorithm for the implicitization of parametric curves defined by polynomial parametric equations, which is mainly based on the theory of matrices. Initially, the upper bound of the degree of the desired implicit equation and its general representation are given, and then all of its coefficients can be obtained by the construction of null vectors of the corresponding implicit matrix. Furthermore, the desired implicit equation of the parametric curve can be obtained. Examples given in the paper demonstrate the correcthess and efficiency of the method in detail.