Order Types of Convex Bodies

• DOI: 10.1007/s11083-010-9156-2
• Publication Date: 2010-05-24T04:06:44Z
• Authors: Alfredo Hubard; Luis Montejano; Emiliano Mora; Andrew Suk
• Keywords: Oriented matroid; Krein–Milman theorem; Convex polytope; Order type; Mixed volume

We give new bounds on the Erdos-Szekeres theorems for convex bodies of Bisztriczky and Fejes Toth and of Pach and Toth. We derive them from a combinatorial characterization of convex position of a family of planar convex bodies. This characterization confirms that the concept of Order Type for points can be extended to noncrossing families of convex bodies in a geometrically meaningful way.