Parallel Coordinates: a Tool for Visualizing Multi-Dimensional Geometry

A methodology for visualizing analytic and synthetic geometry in RN is presented. It is based on a system of parallel coordinates which induces a non-projective mapping between N-Dimensional and 2-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 RN. 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 to Air Traffic Control, Robotics, Computer Vision, Computational Geometry, Statistics, Instrumentation and other areas are discussed.