Elementary Partitions of Line Segments in the Plane
نویسندگان
چکیده
Given a set S of line segments in the plane, we introduce a new family of partitions of the convex hull of S called elementary partitions of S. The set of faces of such a partition is a maximal set of disjoint triangles that cut S at, and only at, their vertices. Surprisingly, several properties of point set triangulations extend to elementary partitions. Thus, the number of their faces is an invariant of S. In the same way, if S is in general position, there exists a unique elementary partition of S whose faces are inscribable in circles whose interiors do not intersect S. This partition, called elementary Delaunay partition, is dual to the segment Voronoi diagram. The main result of this paper is that the local optimality which characterizes point set Delaunay triangulations [8] extends to elementary Delaunay partitions. A similar result holds for elementary partitions with same topology as the Delaunay one.
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