Anaglyphen 3D — A Program for the Interactive Representation of Three-Dimensional Perspective Plots of Statistical Data

Abstract

Two projections of a three-dimensional figure, usually drawn in the complementary colours red and green, are looked at through filter glasses of the corresponding colours. Then the onlooker obtains the impression of a three-dimensional object. This kind of representation is called anaglyphs. Although anaglyphs have been used in geometry as in Pal (1974) and Fejes- Toth (1965), in architecture, and in chemistry for a long time, only fast computers with a high-resolution colour-screen allow an easy calculation and fast representation of the two required projections especially if in motion. The use of anaglyphs for analyzing statistical data has been proposed by Hering in 1987 and has been realized by von der Weydt (1988/89) and Symanzik (1990/91). In contrast to a single scatter plot, where only a pair of the factors of multi-dimensional data is to be seen in a single graph, and in contrast to the well-known static scatter plot matrices, anaglyphs allow the presentation of three factors at the same time in motion pictures. Further, the use of anaglyphs allows a good plastic impression of bivariate probability density functions, e. g. to emphasize the differences between bivariate normal-, Cauchy-, and t-distributions. Based on a few operations on matrices to calculate the red and green biplots, presented in Graf (1987), the program Anaglyphen 3D has been developed for Sun and Sparc workstations, allowing interactive work on anaglyphs.