Automatic computation of range of motion for coherent contact maintenance/transition of moving scaled convex polyhedra

Appropriate application of spatial coherence can speed up the collision detection of moving objects without sacrificing accuracy. This paper presents an automatic method applicable to convex polyhedral objects that can undergo both uniform scaling transformation and any type of relative motion for computing the range of motion for spatial coherence, i.e. that can keep the scaled contact features after motion unchanged as original undeformed configuration. Within the range, the contact maintenance/transition relation between the scaling pairs, contact features and intended relative motion conditions(type, direction, amount) is very similar before and after relative motion. These families of decision curves can be constructed efficiently by taking advantage of the a priori information provided by the decision curve before motion. We illustrate usage of the family of decision curves after motion within coherent ranges for designing the dimensions, contact features and relative contact configuration of a pair of convex polyhedral objects to mate precisely in assembly.