Kinetic prisms: incorporating acceleration limits into space–time prisms

Abstract

Presently, data concerning moving objects abound. These data mainly consist of time-stamped geographical locations, which are collected by location aware devices, such as Global Positioning System receivers. Space–time prisms are used to model the spatio-temporal space of potential movement in between measured locations (called anchors). They rely on the knowledge of the maximal speed of travel of an object and they capture all space–time paths that respect this speed limit. However, the classic space–time path and prism model is not physically realistic, in the sense that it contains spatio-temporal paths of moving objects can alter their direction and speed instantaneously. Since this is physically impossible, the classical model is not acceptable in applications where mechanics and kinetics are vital. We propose a more realistic version of space–time prisms, in which not only speed but also acceleration is bounded. This additional bound results in a physically realistic model, which we refer to as kinetic prisms. Furthermore, we study how imposing constraints on the speed and heading at anchor points affects the geometry of kinetic prisms. In this paper, we give analytical descriptions of kinetic prisms and algorithms for their construction for movement in one- and two-dimensional space.