Algorithm to Calculate the Minkowski Sums of 3-polytopes: Application to Tolerance Analysis

In tolerance analysis, it is necessary to check that the cumulative defect limits specified for the component parts of a product are compliant with the functional requirements expected of the product. Cumulative defect limits can be modelled using a calculated polytope, the result of a set of intersections and Minkowski sums of polytopes. This article presents a method to be used to determine from which vertices of the operands the vertices of the Minkowski sum derive and to which facets of the operands each facet of the Minkowski sum is oriented.