Minimal Exhaustive Search Heuristics (MESH) of point clouds for form tolerances: The minimum zone roundness

Abstract

MESH is an ɛ-approximate algorithm to find the minimum zone center of a given roundness profile, with ɛ=10−d, where d is the number of required decimal digits.The proposed MESH algorithm is able to provide only the accuracy that is necessary to find the minimum zone error roundness (circularity). The basic principle is to exhaustively assess all MZR center candidates located at the cross points of a mesh, with spacing directly related to the target accuracy. Criteria for the selection of the required manufacturing (designer's) target accuracy (product specifications) are discussed. This result has been made possible by previous work on the limit search space to be searched. The algorithm effectiveness has been shown by computation experiments up to 16,384 cloud datapoints and by comparison with genetic algorithms and an exact method from the literature. The MESH algorithm can also serve for benchmarking purposes to assess the performance of other algorithms in terms of both accuracy and speed. The extension to other form tolerances of the exhaustive mesh based approach is discussed.