Abstract: Quasi-incremental algorithm is proposed to evaluate roundness error by minimum circumscribed circle (MCC) and minimum radius separation (MRS) methods. The measured profile is regarded as an ordered set of points. Several points in the set are picked as initial subset to construct a circle. Each time, one new point out of the current circle is added into the subset and a new circle is constructed , also a point which not reside on the border of the circle is removed. The previous step repeats until the circle covers all the points and follows corresponding rule, and then the roundness error can be calculated. This algorithm is proved to be ccorrect and convergent in monotonous. And a new method using the four points for the minimum circumscribed circle methods as initial points for minimum zone method is proposed. The algorithm is well defined, with simple model, and very easy to be applied by computer. Some practical examples show that the algorithm is correct, accurate and efficient.

Key words: Computational geometry, Minimum circumscribed circle method, Minimum zone method, Quasi-incremental algorithm, Roundness error, Tolerance evaluation