Bernard Dimsdale

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 points proximity to the boundary. Applications to Air Traffic Control, Robotics, Computer Vision, Computational Geometry, Statistics, Instrumentation and other areas are discussed.

Multidimensional lines I: representation

Based on a system of parallel coordinates, a methodology for visualizing multivariate relations (i.e., subsets of

Multidimensional lines II: proximity and applications

R^N

On direction-preserving maps of graphs*

) by mapping them uniquely into indexed subsets of

Parallel coordinates: survey of recent results

R^2

Bicubic patch surfaces for high-speed numerical control processing

was introduced earlier. Here, the foundations for the representation mapping in general are given, and the representation of lines in

Parallel Coordinates A Tool for Visualizing Multivariate Relations

R^N

Convex cubic splines

by

Visualizing multi-variate relations with parallel coordinates

N - 1

Multi-dimensional lines I and II: Representations and proximity applications

planar points indexed by a pair of distinct integers from