Visualizing multi-dimensional polytopes and topologies for tolerances
Alfred Inselberg, Avijit Chatterjee · 1995
A representation for multi-dimensional polytopes in parallel coordinates is presented where the connectivity and containment of the faces can be visualized. From the half-spaces bounding the polytope and their adjacency the connectivity of the highest dimensional faces can be constructed. This construction generates the convex hull of a non-convex polytope. Also a representation for bounded convex multi-dimensional objects is provided as an envelope of hyperplanes that do not intersect their interior. The envelope of hyperplanes is bounded by an h-star (generalized hyperbola) in parallel coordinates. This is used to geometrically construct a cutting plane in order to reduce the search space of a linear programming problem. To accommodate the imprecision on geometric data the notion of Line and Planar Topologies are introduced from which detection algorithms for lines and hyperplanes are obtained.