A note on measuring the volume of space-time prisms and the area of their spatial projections

Abstract

Space-time prisms are often used to model the uncertainty of space-time locations of moving objects between measured sample points. The volume of such prisms and the area of their spatial projections are frequently used as measures for spatio-temporal and spatial accessibility. The aim of this article is to provide correct expressions for this volume and area, both for prisms with and without stationary activity time, and to provide proofs, based on elementary geometry, of their correctness. In this way we provide a better understanding and a clarification of the historical (and difficult to find) references, Lenntorp (1976) and Burns (1979), that are usually used.