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Equiprojective polyhedra
, 2003
"... 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,isakgon. We address an open question posed by Shepherd [11], and reported in [5], by characterizing equiprojective polyhedra, and g ..."
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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,isakgon. We address an open question posed by Shepherd [11], and reported in [5], by characterizing equiprojective polyhedra
(Non)Equiprojectivity and (Non)Biprojectivity of Simplicial Polyhedra
"... A convex polyhedron P is equiprojective (similarly, biprojective) if, for some xed k, the orthogonal projection (or "shadow") of P in every direction, except those directions parallel to faces of P, is a kgon (similarly, k or (k + 1)gon). Since 1968, it is an open problem to construct ..."
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all equiprojective polyhedra, while the only results include a characterization, a recognition algorithm, and some discrete nontrivial examples of equiprojective polyhedra. In this paper, we show that simplicial polyhedra can not be equiprojective. Then, we extend the idea of equiprojectivity
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"... Abstract A convex polyhedron P is equiprojective if, for some k, the orthogonal projection (or "shadow") of P inevery direction, except those directions parallel to faces of P, is a kgon. We address an open question posed by Shepherd [11], and reported in [5], by characterizing e ..."
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equiprojective polyhedra, and givingan O(n log n) time recognition algorithm. 1 Introduction A convex polyhedron P is kequiprojective ifits shadow is a kgon in every direction, except directions parallel to faces of
The Open Problems Project
, 2012
"... This is the beginning of a project 1 to record open problems of interest to researchers in computational geometry and related fields. It commenced with the publication of thirty problems in Computational Geometry Column 42 [MO01] (see Problems 1–30), but has grown much beyond that. We encourage corr ..."
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This is the beginning of a project 1 to record open problems of interest to researchers in computational geometry and related fields. It commenced with the publication of thirty problems in Computational Geometry Column 42 [MO01] (see Problems 1–30), but has grown much beyond that. We encourage correspondence