Visualization provides insight through images , and can be considered as a collection of application specific mappings: problem domain → visual range. For the visualization of multivariate problems a multidimensional system of Parallel Coordinates is studied which provides a one-to-one mapping between subsets of N-space and subsets of 2-space. The result is a systematic and rigorous way of doing and seeing analytic and synthetic N-dimensional geometry. Lines in N-space are represented by N-1 indexed points. In fact all p-flats (planes of dimension p in N-space) are represented by indexed points where the number of indices depends on p and N. The representations are generalized to enable the visualization of polytopes and certain kinds of hypersurfaces as well as recognition of convexity. Several algorithms for constructing and displaying intersections, proximities and points interior/exterior/or on a hypersurface have been obtained. The methodology has been applied to visual data mining, process control, medicine, finance, retailing, collision avoidance algorithms for air traffic control, optimization and others.
KeywordsPolygonal Line Interior Point Algorithm Smooth Hypersurface Tangent Hyperplane Convex Hypersurface
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- 1.E.W. Bassett, Ibm’s ibm fix. Industrial Computing, 14 (41): 23–25, 1995.Google Scholar
- 2.A. Chatterjee, Visualizing Multidimensioal Polytopes and Topologies for Tolerances. Ph.D. Thesis USC, 1995.Google Scholar
- 4.J. Eickemeyer, Visualizing p-flats in N-space using Parallel Coordinates. Ph.D. Thesis UCLA, 1992.Google Scholar
- 6.C.K. Hung, A New Representation of Surfaces Using Parallel Coordinates. Submitted for Publication, 1996.Google Scholar
- 7.A. Inselberg, N-Dimensional Graphics, Part I - Lines and Hyperplanes, in IBM LASC Tech. Rep. G320–2711, 140 pages. IBM LA Scientific Center, 1981.Google Scholar
- 9.A. Inselberg, Parallel Coordinates: A Guide for the Perplexed, in Hot Topics Proc. of IEEE Conf. on Visualization, 35–38. IEEE Comp. Soc., Los Alamitos, CA, 1996.Google Scholar
- 10.A. Inselberg and B. Dimsdale, Parallel Coordinates: A Tool For Visualizing Multidimensional Geometry, in Proc. of IEEE Conf. on Vis. ‘80, 361–378. IEEE Comp. Soc., Los Alamitos, CA, 1990.Google Scholar
- 14.B. H. Mccormick, T. A. Defanti, and M. D. Brown, Visualization in Scientific Computing. Computer Graphics 21–6, ACM SIGGRAPH, New York, 1987.Google Scholar
- 15.E. R. Tufte, The Visual Display of Quantitative Information. Graphic Press, Connecticut, 1983.Google Scholar
- 16.E. R. Tufte, Envisioning Information. Graphic Press, Connecticut, 1990.Google Scholar