A n ew internal structure for simple polygons, the straight s k eleton, is introduced and discussed. It is composed of pieces of angular bisectores which partition the i n terior of a given n-gon P in a tree-like fashion into n monotone polygons. Its straight-line structure and its lower combinatorial complexity m ay make t he straight skeleton preferable to t he widely used medial axis of a polygon. As a seemingly unrelated application, the straight s k eleton provides a canonical way of constructing a polygonal roof above a general layout of ground w alls.

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{ oai oh, auren}%igi, tu-graz, ar at I n t r o d u c t i o nA planar straight line graph, G, on n points in the Euclidean plane is a set of noncrossing line segments spanned by these points. A skeleton of G is a partition of the plane into faces that reflect the shape of G in an appropriate manner. The well-known and widely used examples of skeletons are the medial axis of a simple polygon or, more generally, the (closest-point) Voronoi diagram of G. Skeletons have numerous applications, for example in biology, geography, pattern recognition, robotics, and computer graphics; see e.g. [Ki, L, Y] for a short history.The Voronoi diagram of G consists of all points in the plane which have more than one closest object in G. Typically, it contains curved arcs in the neighborhood of the vertices of G. This is considered a disadvantage in the computer representation and construction, and sometimes also in the application, of this type of skeleton.There have been several attempts to linearize and simplify Voronoi diagrams of planar straight line graphs, mainly for the sake of efficient point location and motion planning [CD, KM, MKS]. The compact Voronoi diagram for convex polygons in [MKS] is particularly suited to these applications as its complexity is linear in the number of polygons rather than in the number of edges. However, its faces do not reflect much of the shape of the polygons which might restrict its application when being used as a skeleton for polygonal figures.In the present paper, a novel type of skeleton, the straight skeleton of G, is introduced and discussed. Its arcs are pieces of angular bisectors of the edges of G. Its combinatorial complexity is in general is even less than the complexity of the Voronoi diagram of G. Still, G can be reconstructed easily from its straight skeleton. This fact is considered important in certain applications of skeletons [PR]. Beside its use as a skeleton, we describe two applications that come from a spatial interpretation of straight skeletons. One concerns the question of constructing a roof above a general polygonal outline of ground walls. The other application is the reconstruction of a geographical terrain from a given map that delineates coasts, lakes, and rivers.

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