基于拉格朗日插值的参数曲面隐式化

Implicitization of parametric surfaces by means of Lagrange interpolation

首先给出了Dixon矩阵的算法,并以此为基础,利用Dixon矩阵以及拉格朗日插值的基本理论,给出了参数曲面隐式化的一种方法。该方法有效克服了用经典结式方法求参数曲面隐式方程的中间膨胀问题。既减少了计算量,又节省了时间和空间,提高了参数曲面隐式化的速度。最后,通过实例,证明了本文算法的准确性和有效性。

The algorithm of Dixon’s matrix is first derived and then a method of the implicitization of parametric surfaces,which is based on Dixon matrix and Lagrange interpolation,is given.This method not only reduces the computational cost,but also saves the time and space cost.Further,it speeds up the implicitization of the parametric surfaces.Finally,some examples are provided to prove the accuracy and efficiency of the algorithm.