Equiprojective polyhedra

Authors:
Masud Hasan;Anna Lubiw
Affiliations:
Department of Computer Science and Engineering, Bangladesh University of Engineering and Technology, Dhaka-1000, Bangladesh;David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada
Venue:
Computational Geometry: Theory and Applications
Year:
2008

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Abstract

A convex polyhedron P is equiprojective if, for some k, the orthogonal projection (or ''shadow'') of P in every direction, except those directions parallel to faces of P, is a k-gon. We address an open question posed by Shepherd and reported in Croft, Falconer, and Guy's ''Unsolved Problems in Geometry'', by characterizing equiprojective polyhedra, and giving an O(nlogn)-time recognition algorithm.