Abstract: This paper discusses the number of sampling points necessary for representing the roundness error of a closed curve without distortion. Through mathematical deduction by the authors, the relationship between the center coordinates of a least square circle of a curve with statistical roundness error and its Fourier coefficients is obtained. Then the sampling rule which must be obeyed is acquired, and the verification results of the test problem and practical periphery are given.

Key words: roundness error, reference center, sampling rule