Abstract We select the sample points of the construction polynomial based on the dynamic circle radius selection method, and select three weight functions, including the local distance ratio, the inverse distance weighted, and weighted iteration method. We compare and analyze the accuracy and reliability of the local polynomial interpolation results. It is shown that the results of three methods are similar without gross error. When the gross error is added, the results of the first two methods deviate from the interpolated surface without gross error, and the undulation of weighted iteration method is consistent with previous result.