Description Of Surfaces In Parallel Coordinates By Linked Planar Regions
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII（2007）
摘要
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 R-3 with generalizations to R-N 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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关键词
USA patent,air traffic control,arbitrary dimension,avoidance algorithm,computer vision,data mining,efficient visual detection,multidimensional line,non-convex surface,planar region
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