Recent work has shown that it is possible to predict surface parameters measured digitally from a surface profile by means of three points on the autocorrelation function. The weakness of this work has been that only one-dimensional parameters have been evaluated. The present contribution extends the theory to include two-dimensional parameters of the surface which are expressed in terms of between four and seven points on the autocorrelation function depending on the type of surface. It is shown that this technique provides an alternative to traditional mapping methods. It is shown also that as a general rule results obtained from the discrete analysis do not converge to those obtained from the continuous theory. The nature and magnitude of the differences between the two approaches are discussed in detail. Finally, the theoretical results are confirmed experimentally and the general significance of discrete methods reviewed.