The Common Exterior of Convex Polygons in the Plane

@article{Aronov1997TheCE,
  title={The Common Exterior of Convex Polygons in the Plane},
  author={Boris Aronov and Micha Sharir},
  journal={Comput. Geom.},
  year={1997},
  volume={8},
  pages={139-149}
}
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

From This Paper

Topics from this paper.
21 Citations
23 References
Similar Papers

References

Publications referenced by this paper.
Showing 1-10 of 23 references

Svo$ istvo vypuklyh mno estv i ego prilo enie

  • M. D. Kovalev
  • Matemati- qeskie Zametki, 44
  • 1988
Highly Influential
3 Excerpts

On a problem of L

  • G. O. Katona
  • Fejes T oth, Stud. Sci. Math. Hung. 12
  • 1977
Highly Influential
3 Excerpts

Planar realization of non - linear DavenportSchinzel sequencesby segments , Discrete Comput

  • M. Sharir
  • Geom .
  • 1995

The complexity of many faces in the overlay of arrangements

  • S. Har Peled
  • M.Sc. Thesis, Department of Computer Sciences…
  • 1995
1 Excerpt

Arrangements of polytopes with applications

  • B. Aronov, M. Bern, D. Eppstein
  • manuscript
  • 1992
1 Excerpt

Similar Papers

Loading similar papers…