Parallel coordinates: a tool for visualizing multi-dimensional geometry
Параллельные координаты: инструмент визуализации многомерной геометрии
2002-12-04
SCID: 54.1/xhxkgf6h
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hypersurface planar imageparallel coordinatesparallel coordinates mappingpoint–line dualityvisualizing multi-dimensional geometry
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Abstract (AI)
A methodology for visualizing analytic and synthetic geometry in R/sup N/ is presented. It is based on a system of parallel coordinates which induces a nonprojective mapping between N-dimensional and two-dimensional sets. Hypersurfaces are represented by their planar images which have some geometrical properties analogous to the properties of the hypersurface that they represent. A point from to line duality when N=2 generalizes to lines and hyperplanes enabling the representation of polyhedra in R/sup N/. The representation of a class of convex and non-convex hypersurfaces is discussed, together with an algorithm for constructing and displaying any interior point. The display shows some local properties of the hypersurface and provides information on the point's proximity to the boundary. Applications are discussed.>
Key Findings
1
Discusses applications of the parallel coordinates representation for visualizing multi-dimensional geometry.
2
Generalizes the point-to-line duality (when N=2) to lines and hyperplanes, enabling representation of polyhedra in R^N.
3
Introduces a methodology using parallel coordinates to visualize analytic and synthetic geometry in R^N by a nonprojective mapping to 2D.
4
Provides an algorithm to construct and display any interior point of certain convex and non-convex hypersurfaces, showing local properties and proximity to boundaries.
5
Represents hypersurfaces via planar images whose geometric properties are analogous to those of the original hypersurfaces.
Research Object
Hypersurfaces and polyhedra in R^N visualized via parallel coordinates
Research Subject
The use of a parallel-coordinates nonprojective mapping to represent and display geometrical properties, local boundary proximity, and interior-point construction algorithms for convex and non-convex hypersurfaces and polyhedra in R^N
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2002-12-04
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