隐式多项式曲线数据拟合的稳定性分析

对数据点集合轮廓进行隐式多项式曲线或者曲面建模需要分析隐式多项式曲线的稳定性，因为这直接关系到隐式多项式曲线或者曲面建模是否有效。通过对隐式多项式曲线上点和系数关系的分析，从理论上得出了隐式多项式曲线上点的变动对其最高次齐次项影响很小，而数据点距离原点越远则隐式多项式曲线建模的有效性越差。文章的实验显示了隐式多项式曲线建模的数据点预处理方法和应用依据。

Analysis of stability of data fitting by implicit polynomial curve

Analysis of stability is necessary to model the data set point contour with implicit polynomial curve,which determines whether the model is successful.The relation is analyzed between the points in implicit polynomial curve and coefficients of them and then it is proved that the variation of points in implicit polynomial curve has little effect on the first homogeneous item of it,and far away from coordinate origin,the implicit polynomial curve model becomes more invalid.The experiments illustrate the basis of data point preprocess and application.