Packing Lines, Planes, etc.: Packings in Grassmannian Space
J.H. Conway, R.H. Hardin, N.J.A. Sloane

TL;DR
This paper explores optimal arrangements of subspaces in Euclidean space using computational methods and a new sphere-based reformulation, with applications to data visualization.
Contribution
It introduces a novel sphere-based reformulation for packing subspaces, enabling the identification of many optimal packings and improving visualization techniques.
Findings
Computed new packings for modest N, n, m values
Reformulated the packing problem using sphere representations
Proved many packings are optimal
Abstract
This paper addresses the question: how should N n-dimensional subspaces of m-dimensional Euclidean space be arranged so that they are as far apart as possible? The results of extensive computations for modest values of N, n, m are described, as well as a reformulation of the problem that was suggested by these computations. The reformulation gives a way to describe n-dimensional subspaces of m-space as points on a sphere in dimension (m-1)(m+2)/2, which provides a (usually) lower-dimensional representation than the Pluecker embedding, and leads to a proof that many of the new packings are optimal. The results have applications to the graphical display of multi-dimensional data via Asimov's "Grand Tour" method.
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Taxonomy
Topicsgraph theory and CDMA systems · Digital Image Processing Techniques · Computational Geometry and Mesh Generation
