Complexity of projected images of convex subdivisions

Let S be a subdivision of R^d into n convex regions. We consider the combinatorial complexity of the image of the (k - 1)-skeleton of S orthogonally projected into a k-dimensional subspace. We give an upper bound of the complexity of the projected image by reducing it to the complexity of an arrangement of polytopes. If k = d - 1, we construct a subdivision whose projected image has Ω(n^{⌊(3d-2)/2⌋}) complexity, which is tight when d ≤ 4. We also investigate the number of topological changes of the projected image when a three-dimensional subdivision is rotated about a line parallel to the projection plane.