A general characterisation of space-time prisms with spatial anchor uncertainty

Abstract

We investigate the geometry of space-time prisms and their associated potential path areas (for movement that takes place in the plane) in the setting where the prism anchors have a spatial uncertainty area attached to them. Our main result is a characterisation of such space-time prisms and their potential path areas in terms of a generalised distance function between closed subsets of the ambient space. Since the case where this spatial anchor uncertainty takes the form of a closed disk has already been addressed by Kuijpers and Othman (2017), we focus on the more realistic case where the uncertainty areas are ellipses and we apply our general characterisation to this example to obtain explicit descriptions of the uncertain prisms and their potential path areas.