Kinetic prisms: incorporating acceleration limits into space-time prisms

Abstract

Presently, a flood of data concerning moving objects is available. These data mainly consist of time-stamped geographical locations, which are collected by location aware devices, such as GPS. Linear interpolation between sampled locations gives a space-time path, that can be used to estimate the location of a moving object over time. Space-time prisms are used to model the space-time 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 since it relies on the assumption that 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 think of the scientific understanding of animal migration, vehicles moving through water or air, human-powered mobility and environmental applications of transportation. The goal of this paper is to propose a more realistic version of spacetime prisms, in which not only the speed, but also the 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 visualisation, for movement in one- and two-dimensional space.