Determination of Convex Bodies by Projection Functions

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 Voli [4].