Visualizing P-flats in N-space using parallel coordinates
Visualizing P-flats in N-space using parallel coordinates
Multidimensional lines I: representation
SIAM Journal on Applied Mathematics
Multidimensional lines II: proximity and applications
SIAM Journal on Applied Mathematics
Visualizing multi-dimensional polytopes and topologies for tolerances
Visualizing multi-dimensional polytopes and topologies for tolerances
Parallel Coordinates: Visual Multidimensional Geometry and Its Applications
Parallel Coordinates: Visual Multidimensional Geometry and Its Applications
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An overview of themethodology 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.