The traditional way of representing motion in 3D space-time uses a trajectory, i.e. a sequence of (x,y,t) points. Such a trajectory may be produced by periodic sampling of a Global Positioning System (GPS) receiver. The are two problems with this representation of motion. First, imprecision due to errors (e.g. GPS receivers often produce off-the-road locations), and second, space complexity due to a large number of samplings. We examine an alternative representation, called a nonmaterialized trajectory, which addresses both problems by taking advantage of the a priori knowledge that the motion occurs on a transport network.