To evaluate the flatness errors of mechanical parts accurately and rapidly

an algorithm using geometry searching approximation to evaluate the flatness error minimum zone was presented. The principle and steps of the algorithm to solve the flatness error was described in detail and the mathematical formulas were given. First

the three edge points of the measured plane were selected as reference points

and the auxiliary points

reference plane and auxiliary planes were constructed based on the reference points. Then

the distance differences of all measurement points to the supposed ideal planes were calculated by taking the reference plane and auxiliary planes as supposed ideal planes. The reference points

auxiliary points

reference plane and auxiliary planes were reconstructed by comparing the distance differences. Finally

by repeating this processes

the minimum zone evaluation for flatness error was implemented. The method was used to process a group of metrical data

and the results indicate that the flatness error value from this algorithm can be reduced by 17.1

7.3

18.03

6.13 and 0.3 m respectively as compared with those from the convex hull method

computational geometric method

least square method

genetic algorithm and the evolutionary strategy when the criteria of stop searching is 0.000 01 mm

The results demonstrate that the algorithm can get not only the minimum zone solution accurately but also has good stability. It is suited for the evaluation of flatness error measuring instruments and Coordinate Measuring Machines(CMMs)．