**O. Aichholzer, D. Alberts, F. Aurenhammer, and B. Gaertner**

A new internal structure for simple polygons, the straight skeleton, is
introduced and discussed. It is a tree and partitions the interior of a given
-gon into monotone polygons, one for each edge of . Its
straight-line structure and its lower combinatorial complexity may make the
straight skeleton preferable to the widely used medial axis of . We
show that has no Voronoi diagram structure and give an
time and space construction algorithm, where counts the reflex
vertices of . As a seemingly unrelated application, the straight skeleton
provides a canonical way of constructing a roof of given slope above a
polygonal layout of ground walls.