Benefits of applicability constraints in decomposition-free interference detection between nonconvex polyhedral models

Nonconvex polyhedral models of workpieces or robot parts can be directly tested for interference, without resorting to a previous decomposition into convex entities. We show that this interference detection, based on the elemental edge face intersection test, can be performed efficiently: a strategy based on applicability constraints reduces drastically the set of edge - face pairings that have to be considered for intersection. This is accomplished by using an appropriate representation, the spherical face orientation graph, developed by the authors, as well as feature pairing algorithms based on the plane sweep paradigm that have been adapted to work on that representation. Furthermore, the benefits of such a strategy extend to the computation of a lower distance bound between the polyhedra, both lowering the computational effort and improving the quality of the bound. Experimental results confirm the expected advantages of this strategy.