The riches of rectangles

  • Derick Wood
Chapter 3 Algorithmics
Part of the Lecture Notes in Computer Science book series (LNCS, volume 381)


In this paper we consider some of the rectangle problems that have been studied in the literature of computational geometry. Our aim is to demonstrate that although rectangles are, perhaps, the simplest of geometrical figures, they occur naturally in many situations and, thus they are a rich source for intriguing and challenging problems.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    M.J. Atallah and M.T. Goodrich. Output-sensitive hidden surface elimination for rectangles. Technical Report 88-13, The John Hopkin's University, Department of Computer Science, Baltimore, 1988.Google Scholar
  2. [2]
    J.L. Bentley and D. Wood. An optimal worst case algorithm for reporting intersections of rectangles. IEEE Transactions on Computers, EC-29:571–576, 1980.Google Scholar
  3. [3]
    M. Bern. Hidden surface removal for rectangles. In Proceedings of the 4th ACM Symposium on Computational Geometry, pages 183–192, 1988.Google Scholar
  4. [4]
    H. Edelsbrunner. Dynamic rectangle intersection searching. Technical Report F 47, Institut für Informationsverarbeitung, Technische Universität Graz, 1980.Google Scholar
  5. [5]
    H. Edelsbrunner. New approach to rectangle intersections: Part I. International Journal of Computer Mathematics, 13:209–219, 1983.Google Scholar
  6. [6]
    H. Edelsbrunner. New approach to rectangle intersections: Part II. International Journal of Computer Mathematics, 13:221–229, 1983.Google Scholar
  7. [7]
    H. Edelsbrunner. Algorithms in Combinatorial Geometry. Springer-Verlag, New York, 1987.Google Scholar
  8. [8]
    H. Edelsbrunner, J. van Leeuwen, Th. Ottmann, and D. Wood. Computing the connected components of simple rectilinear geometrical objects in d-space. RAIRO Informatique théorique, 18:171–183, 1984.Google Scholar
  9. [9]
    D.E. Field. Fast hit detection for disjoint rectangles. Technical Report 85-53, Department of Computer Science, University of Waterloo, 1985.Google Scholar
  10. [10]
    J. Kratochvil. String graphs I: The number of critical nonstring graphs is infinite. Technical Report 88-83, Charles University, Department of Mathematics and Physics, Prague, Czechoslovakia, 1988.Google Scholar
  11. [11]
    J. Kratochvil. String graphs II: Recognizing string graphs is NP-hard. Technical Report 88-86, Charles University, Department of Mathematics and Physics, Prague, Czechoslovakia, 1988.Google Scholar
  12. [12]
    E.M. McCreight. Efficient algorithms for enumerating intersecting intervals and rectangles. Technical Report CSL-80-9, Xerox Palo Alto Research Center, 1980.Google Scholar
  13. [13]
    E.M. McCreight. Priority search trees. SIAM Journal on Computing, 14:257–276, 1985.Google Scholar
  14. [14]
    J. Nievergelt, H. Hinterberger, and K.C. Sevcik. The grid file: An adaptable, symmetric multikey file structure. ACM Transactions on Database Systems, 9:38–71, 1984.Google Scholar
  15. [15]
    F.P. Preparata and M.I. Shamos. Computational Geometry. Springer-Verlag, New York, 1985.Google Scholar
  16. [16]
    F.P. Preparata, J.S. Vitter, and M. Yvinec. Computation of the axial view of a set of isothetic parallelopipeds. Technical Report 88-1, Labatoire d'Informatique de l'Ecole Normale Supérieure, Paris, France, 1988.Google Scholar
  17. [17]
    F.S. Roberts. Graph Theory and Its Applications to Problems of Society. Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, 197?Google Scholar
  18. [18]
    N. Sarnak and R.E. Tarjan. Planar point location using persistent search trees. Communications of the ACM, 29:669–679, 1986.Google Scholar
  19. [19]
    H.-W. Six and P. Widmayer. Spatial searching in geometric databases. Technical Report 176, Institut für Angewandte Informatik, Universität Karlsruhe, 1987.Google Scholar
  20. [20]
    H.-W. Six and D. Wood. Counting and reporting intersections of d-ranges. IEEE Transactions on Computers, C-31:181–187, 1982.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Derick Wood
    • 1
  1. 1.Data Structuring Group Department of Computer ScienceUniversity of WaterlooWaterlooCanada

Personalised recommendations