# Size of BSP tree for a simple polygon?

Is there a known bound on the size of a BSP tree for a simple polygon? I am aware of the result by Toth which gives a tight $\Theta(n \log(n) / \log(\log(n)) )$ bound on the size of a BSP consisting of $n$ disjoint segments, but I wonder if it is possible to do better given some of the special properties of simple polygons. For example, it is trivial to show that convex polygons can be represented by BSP trees using at most $O(n)$ nodes. Is it possible to represent simple polygons in linear space as well?