Geometric tolerance evaluation: A discussion on minimum zone fitting algorithms

Estimating any geometric tolerance requires to sample a cloud of points on the feature to check, and then to fit an ideal substitute geometry respect to which to evaluate errors. Usually, points will be sampled by means of a CMM, and then a suitable software algorithm will be applied to them. Algorithms that can be found in literature show some limitations: they may be very slow, the solution they propose is just an approximated one, or some degenerate situations cannot be managed. We will propose a categorization of algorithms found in literature, highlighting merits and defects for them. Moreover, a new algorithm will be proposed. This algorithm will be tested against classical algorithms to show its advantages.