Multidimensional Lines. I: Representation

Abstract

Based on a system of parallel coordinates, a methodology for visualizing multivariate relations (i.e., subsets of $R^N $) by mapping them uniquely into indexed subsets of $R^2 $ was introduced earlier. Here, the foundations for the representation mapping in general are given, and the representation of lines in $R^N $ by $N - 1$ planar points indexed by a pair of distinct integers from $\{ 0,1,2, \cdots ,N \}$ in $R^2 $ is obtained. This yields construction and display algorithms for the representation of lines, points on lines, changes of parameterization, and line transformations.