Advertisement

Maintaining Extremal Points and Its Applications to Deciding Optimal Orientations

  • Sang Won Bae
  • Chunseok Lee
  • Hee-Kap Ahn
  • Sunghee Choi
  • Kyung-Yong Chwa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4835)

Abstract

We consider two non-convex enclosing shapes with the minimum area; the L-shape and the quadrant hull. This paper proposes efficient algorithms computing each of two shapes enclosing a set of points with the minimum area over all orientations. The algorithms run in time quadratic in the number of given points by efficiently maintaining the set of extremal points.

Keywords

Convex Hull Extremal Point Event Orientation Optimal Orientation Partition Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Agarwal, P.K., Erickson, J.: Geometric range searching and its relatives. In: Chazelle, B., Goodman, J.E., Pollack, R. (eds.) Advances in Discrete and Computational Geometry. Contemporary Mathematics, vol. 233, pp. 1–56. American Mathematical Society Press, Providence (1999)Google Scholar
  2. 2.
    de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry: Algorithms and Applications, 2nd edn. Springer, Heidelberg (2000)zbMATHGoogle Scholar
  3. 3.
    Karlsson, R.G., Overmars, M.H.: Scanline algorithms on a grid. BIT Numerical Mathematics 28(2), 227–241 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Matoušek, J., Plecháč, P.: On functional separately convex hulls. Discrete Comput. Geom. 19, 105–130 (1998)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Matoušek, J.: Efficient partition trees. Discrete Comput. Geom. 8, 315–334 (1992)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Matoušek, J.: Range searching with efficient hierarchical cuttings. Discrete Comput. Geom. 10, 157–182 (1993)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Montuno, D.Y., Fournier, A.: Finding the x − y convex hull of a set of x − y polygons. Technical Report 148, University of Toronto (1982)Google Scholar
  8. 8.
    Nicholl, T.M., Lee, D.T., Liao, Y.Z., Wong, C.K.: On the X − Y convex hull of a set of X − Y polygons. BIT Numerical Mathematics 23(4), 456–471 (1983)zbMATHCrossRefGoogle Scholar
  9. 9.
    Ottman, T., Soisalon-Soisinen, E., Wood, D.: On the definition and computation of rectilinear convex hulls. Information Sciences 33, 157–171 (1984)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Preparata, F.P., Hong, S.J.: Convex hulls of finite sets of points in two and three dimensions. Communications of the ACM 20(2), 87–93 (1977)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Schwarzkopf, O., Fuchs, U., Rote, G., Welzl, E.: Approximation of convex figures by pairs of rectangles. In: Proc. 7th Ann. Symp. on Theoretical Aspects of Computer Science, pp. 240–249 (1990)Google Scholar
  12. 12.
    Welzl, E.: Smallest enclosing disks (balls and ellipsoids). In: Maurer, H.A. (ed.) New Results and New Trends in Computer Science. LNCS, vol. 555, pp. 359–370. Springer, Heidelberg (1991)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Sang Won Bae
    • 1
  • Chunseok Lee
    • 1
  • Hee-Kap Ahn
    • 2
  • Sunghee Choi
    • 1
  • Kyung-Yong Chwa
    • 1
  1. 1.Division of Computer Science, KAIST, DaejeonKorea
  2. 2.Department of Computer Science and Engineering, POSTECH, PohangKorea

Personalised recommendations