Kinetic space-time prisms

Abstract

The space-time path and prism demarcate the estimated and potential locations (respectively) of a moving object with respect to time. The path is typically formed through linear interpolation between sampled locations of a moving object, while the prism is the envelope of all possible paths between two locations given the maximum speed of travel. The classic path and prism, however, are not physically realistic since they imply the ability of the object to make instantaneous changes in direction and speed without acceleration and deceleration. This is not acceptable in applications where kinetics is vital for scientific understanding such as animal ecology, vehicles moving through media such as ships through water and planes through air, human-powered movement such as bicycling and walking and environmental applications of transportation such as energy consumption and emissions modeling. In this paper we demonstrate how imposing an upper bound on acceleration, as well as information such as the initial speed and heading, affects the geometry of the space-time prism. We discuss how to calculate kinetic paths and prisms in one-dimensional and two dimensional space, and provide examples comparing the kinetic prisms and classical prisms.