Abstract: 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.