Determination of Convex Bodies by Projection Functions*

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Abstract

This paper is concerned with an investigation to what extent a convex body is determined by projection functions. We introduce the notion of convex bodies that are almost determined by their brightness function and give a geometric characterization of these bodies. We further prove that, for i ∈ {2, …, d−2}, a polytope is determined by its ith projection function, if all of its (i+1)-faces are parallelepipeds. Both results extend work by Gardner and Volčič [4].

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