Parallel coordinates: a tool for visualizing multi-dimensional geometry

A methodology for visualizing analytic and synthetic geometry in R^N is presented. It is based on a system of parallel coordinates which induces a nonprojective mapping between N-dimensional and two-dimensional sets. Hypersurfaces are represented by their planar images which have some geometrical properties analogous to the properties of the hypersurface that they represent. A point ← → line duality when N=2 generalizes to lines and hyperplanes enabling the representation of polyhedra in R ^N. The representation of a class of convex and non-convex hypersurfaces is discussed, together with an algorithm for constructing and displaying any interior point. The display shows some local properties of the hypersurface and provides information on the point´s proximity to the boundary. Applications are discussed