The Common Exterior of Convex Polygons in the Plane

  title={The Common Exterior of Convex Polygons in the Plane},
  author={Boris Aronov and Micha Sharir},
  journal={Comput. Geom.},
We establish several combinatorial bounds on the complexity (number of vertices and edges) of the complement of the union (also known as the common exterior) of k convex polygons in the plane, with a total of n edges. We show: 1. The maximum complexity of the entire common exterior is (nn(k) + k 2). 1 2. The maximum complexity of a single cell of the common exterior is (nn(k)). 3. The complexity of m distinct cells in the common exterior is O(m 2=3 k 2=3 log 1=3 (k 2 m)+ n logk) and can be (m 2… CONTINUE READING

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