A hybrid method based on reduced constraint region and convex-hull edge for flatness error evaluation

•Evaluate flatness error by reduced constraint region and convex-hull edge.•Combine nonlinear optimization approach and computational geometry approach.•Rapidly calculate large-sized data sets and obtain the exact minimum zone solution.•Simple and easy to program, and could be evaluating flatness tolerance in real time.

A new hybrid approach is proposed for evaluation of flatness error using the Minimum Zone Method. The reduced constraint region is used to rapidly determine the effective direction of enveloping planes, and the convex-hull edge of that direction is used to obtain the minimum zone solution through iteration. The proposed method is validated through the numerical tests with a number of test data sets including those published in literatures and large new data sets of actual measurements. The computed results indicate that an exact and fast minimum solution can always be obtained using the proposed method. It is therefore concluded that the proposed method is one of the approaches which can be used to further improve the accuracy and efficiency of flatness error evaluation.