Much of the practical interest attached to curves and surfaces derives from features of roughness, rather than smoothness. For example, considerable attention has been paid to fractal models of curves and surfaces, for which the notions of a normal and curvature are usually not well defined. Nevertheless, these quantities are sometimes measurable, because the device for recording a rough surface (such as a stylus or ``compass'') adds its own intrinsic smoothness. In this paper we address the effect of such smoothing operations on the multivariate statistical properties of a normal to the surface. Particular attention is paid to the validity of commonly assumed unimodal approximations to the distribution of the normal. It is shown that the actual distribution may have more than one mode, although in a range of situations the unimodal approximation is valid.
1996 Academic Press, Inc.
1. Introduction
In many practical problems of surface analysis it is the roughness of the surface which produces interesting features, not any smoothness which it might possess. For example, there has been considerable interest in fractal article no.