WRAPPING ELLIPSES AROUND A CONVEX SKELETON

et F and G denote two closed convex curves in the (X, Z)-plane and in the (Y, Z)-plane, correspondingly, that are symmetric about the Z-axis and cross al two points. Let S denote the solid that results From wra pping (X, Y)-parallel ellipses around F and G. Surprisingly, S need no t be convex (though all intersections with planes containing the Z-axi s-are!). We analyze under which condition the solid S is convex, and p rovide one necessary and one sufficient criterion that are easy to use in practice.