A brief description of the parallel coordinate system is provided, followed by an application to exploratory data analysis of certain multivariate data. The calculation of minimum distance (L2) between trajectories (timed paths) is considered next and close bounds via L1 distance are obtained, a simplification of importance in Air Traffic Control. Line neighborhoods are defined as the totality of lines satisfying certain parameters. The point region defined by the set of points belonging to these sets of lines in general leads to ambiguities as to lines actually belonging to the line neighborhood. This is of importance in applications involving line detection. Eickemeyer's representation of p-flats in N-space is applied to the representation of polytopes. It is shown that this representation permits analysis and display of convexity or non-convexity of the polytope being represented. Finally the representation of surfaces in three dimensions is exhibited. In general such surfaces are represented by two regions, together with a point-by-point association of points in the two regions. For developable surfaces the regions are replaced by curves, the point-by-point association being of a simple nature.