隐式代数曲线的有理参数化(Ⅰ)

Parameterization of Implicit Curve (Ⅰ)

曲线和曲面的隐式表示和参数表示各有其优点.为了能够利用两种表示方法的优点,必须能够有效地进行曲线曲面的两种表达形式的相互转换.研究隐式代数曲线的有理参数化问题.根据平面二次曲线有理参数化的有关理论,给出并讨论了二次曲线有理参数化的几何和代数算法,研制了相应的软件.所给出的实例,证明了此算法的有效性.

The implicit and parametric forms for curves and surfaces have their advantages. Efficient transformation of the expressions from one form to another is needed in order to make best use of the advantages. Rational parameterization of curves is discussed, and the theory and algorithm for rational parameterization of algebra plane curves are presented with some samples which prove the effectiveness of the parameterization.