It is important to clarify the difference between the true shape of the workpiece and the shape estimated from the chain of measured points, in the three-coordinate measuring machines. In this paper, the roundness was dealt, first of all. Using "min-max method", the evaluation program was made based on the minimum zone conception. Then the roundness was numerically calculated changing the phase of the starting point of the measurementand the sampling interval (number of measured points). As a result, some remarkable facts have been clarified as follows. The decrease of the uncertainty of the calculated roundness, according to the number of measured points. The lower uncertainty less than intended value, as selection of the number of measured points, in the case where the shape was made only from the highest order of frequency component. Namely, the number of measured points N is given as N=2.2M/√G, where M is the highest order of frequency component, and G is the uncertainty.
