Computational geometry: an introduction
Computational geometry: an introduction
New approach for evaluating form errors of engineering surfaces
Computer-Aided Design
IEEE Transactions on Pattern Analysis and Machine Intelligence
The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
Graph theory: An algorithmic approach (Computer science and applied mathematics)
Graph theory: An algorithmic approach (Computer science and applied mathematics)
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Flatness is one of the elementary geometric forms to be tested for ensuring the acceptable quality of machined components. The minimum-zone evaluation problem for flatness is to determine the minimum tolerance zone enclosing all the points measured from a surface of the machined components. Although a variety of attempts has been made for the past two decades to solve the problem, methods guaranteeing an exact minimum-zone solution are very limited. One category of the exact methods is certainly the computational-geometry-based approaches such as the so-called convex-hull edge method. This paper presents a modified convex-hull edge method which significantly enhances its computational efficiency such that large-sized data sets with thousands of points can be solved within a negligible computation time using a personal computer. To test the validity of the method, a number of test data sets including those published in the literature and new large data sets generated in this paper were solved. The obtained solutions were compared with those produced by the existing methods. The results show the effectiveness, efficiency, and robustness of the method in that an exact minimum tolerance is always obtained for each of the test data sets solved in less than tens of CPU milliseconds.