Abstract
An overview of the methodology covers the representation (i.e. visualization) of multidimensional lines, planes, flats, hyperplanes, and curves. Starting with the visualization of hypercubes of arbitrary dimension the representation of smooth surfaces is developed in terms of linked planar regions. The representation of developable, ruled, non-orientable, convex and non-convex surfaces in ℝ3 with generalizations to ℝN are presented enabling efficient visual detection of surface properties. The parallel coordinates methodology has been applied to collision avoidance algorithms for air traffic control (3 USA patents), computer vision (1 USA patent), data mining (1 USA patent), optimization and elsewhere.
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References
Inselberg, A.: Don’t panic.. do it in parallel! Comput. Statit. 14, 53–77 (1999)
Inselberg, A.: Parallel Coordinates: VISUAL Multidimensional Geometry and its Applications. Springer, Heidelberg (2007)
Inselberg, A., Dimsdale, B.: Multidimensional lines ii: Proximity and applications. SIAM J. of Applied Math. 54(2), 578–596 (1994)
Inselberg, A., Dimsdale, B.: Multidimensional lines i: Representation. SIAM J. of Applied Math. 54(2), 559–577 (1994)
Chatterjee, A.: Visualizing Multidimensional Polytopes and Topologies for Tolerances. Ph.D. Thesis, Dept. Comp. Sci. Univ. of S. Calif (1995)
Eickemeyer, J.: Visualizing p-flats in N-space using Parallel Coordinates. Ph.D. Thesis, Dept. Comp. Sc. UCLA (1992)
Beardon, A.: The Geometry of Discrete Groups. Springer, Heidelberg (1983)
Fischer, G.: Plane Algebraic Curves. Amer. Math. Soc. Press, Providence (2001)
Ernstrom, L.: A plucker formula for the singular projective varieties. Commut. Algebra 5(9), 2897–2901 (1997)
Ya, V.O.: Some integral calculus based on euler characteristic, lect. notes. Amer. Math. Monthly 1346, 127–138 (1988)
Mathcurve.com: Surfaces (2006), http://www.mathcurve.com/surfaces/surfaces.shtml
Brannan, D.A., Esplen, M., Gray, J.J.: Geometry. Cambridge University Press, New York (1999)
Boltyanskii, V.G.: Envelopes, R.B. Brown translator (original in Russian). Pergamon Press, New York (1964)
Matskewich, T., Inselberg, A., Bercovier, M.: Approximated Planes in Parallel Coordinates. In: Proc. Geom. Model. Conf. St. Malo, Vanderbilt Univ. Press, pp. 257–266 (2000)
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Hung, CK., Inselberg, A. (2007). Description of Surfaces in Parallel Coordinates by Linked Planar Regions. In: Martin, R., Sabin, M., Winkler, J. (eds) Mathematics of Surfaces XII. Mathematics of Surfaces 2007. Lecture Notes in Computer Science, vol 4647. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73843-5_12
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DOI: https://doi.org/10.1007/978-3-540-73843-5_12
Publisher Name: Springer, Berlin, Heidelberg
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