Surface Feature Interpolation on Two-Dimensional Time-Space Maps

Abstract

A procedure is described for interpolating surface features on a map based on a two-dimensional time-space configuration of points. Initially an objective procedure is used to give a best fit of a previously obtained time-space configuration of points to the physical configuration of the same points. The resultant set of vectors, each of which shows the residual displacement between a point in time space and physical space, is used as the basis of a fast, objective procedure for interpolating any other points or lines in the time space. This enables such things to be shown as the time-space distortion of an urban street network or of a square graticule from physical space. The process can also be reversed so that, for example, the solution points of a facility location problem solved in time space can be converted to their equivalent locations in physical space.