How to trace the significant information in tolerance analysis with polytopes

Manufacturing a mechanical system is tightly related to geometric tolerancing. In this field, verifying the respect of the functional conditions relies on a way to model both the contacts and the manufacturing defects. Polytopes have proven to be a powerful tool to fulfill such objectives. However they've been used so far as restrictions of underlying polyhedra, with the aim of handling bounded bodies to fit with algorithmic requirements. This approach has reached its limit in terms of complexity. The method presented here allows us to treat polytopes, as if they were polyhedra, separating the facets holding the relevant physical information from the bounding facets. Separating the facets not only saves computation time but also memory space in a very significant way. The second part of the paper is dedicated to running the algorithm on a mechanical example to prove its efficiency