Fast C1 proximity queries using support mapping of sphere-torus-patches bounding volumes

STP-BV is a bounding volume made of patches of spheres and toruses. These patches are assembled so that a convex polyhedral hull is bulged, in a tunable way, into a strictly convex form. Strict convexity ensures at least C property of the distance function –and hence, its gradient continuity. STPBV were introduced in our previous work [1], but proximity distance queries were limited to pairs of STP-BV covered objects. In this work we present an alternative to achieve fast proximity distance queries between a STP-BV object and any other convex shape. This is simply made by proposing a support mapping for STP-BV to be used with GJK algorithm [2]. Implementation and experiments of the proposed method and its performance are demonstrated with potential applications to robotics and computer graphics.