Fast C<sup>1</sup> proximity queries using support mapping of sphere-torus-patches bounding volumes

Abstract

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 C1 property of the distance function -and hence, its gradient continuity. STP-BV 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] and its EPA extension to penetration cases [3]. Implementation and experiments of the proposed method and its performance are demonstrated with potential applications to robotics and computer graphics.