Advertisement

New algorithms for special cases of the hidden line elimination problem

  • Ralf Hartmut Güting
  • Thomas Ottmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 182)

Abstract

Hidden line elimination is a well-known problem in computer graphics and many practical solutions have been proposed. Only recently the problem has been studied from a theoretical point of view, taking asymptotic worst-case time- and spacebounds into account. Here we study three special cases of increasing difficulty and generality of the hidden line elimination problem. Applying some methods from computational geometry these problems can be solved with better worst-case bounds than those of the best known algorithms for the general problem.

Keywords

Line Segment Query Point Binary Search Tree Edge Orientation Segment 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. [Bel]
    Bentley, J.L., Solutions to Klee's rectangle problems. Carnegie-Mellon University, Department of Computer Science, unpublished manuscript, 1977.Google Scholar
  2. [BeW]
    Bentley, J.L. and D. Wood, An optimal worst-case algorithm for reporting intersections of rectangles. IEEE Transactions on Computers C-29, 571–577, 1980.Google Scholar
  3. [Gi]
    Giloi, W., Interactive computer graphics. Prentice-Hall, Englewood Cliffs, N.J., 1978.Google Scholar
  4. [Gü2]
    Güting, R.H., Stabbing c-oriented polygons. Information Processing Letters 16, 35–40, 1983.Google Scholar
  5. [Gü2]
    Güting, R.H., Dynamic c-oriented polygonal intersection searching. Universität Dortmund, Abteilung Informatik, Report 175, 1984.Google Scholar
  6. [GüO]
    Güting, R.H. and Th. Ottmann, New algorithms for special cases of the hidden line elimination problem. Universität Dortmund, Abteilung Informatik, Report 184, 1984.Google Scholar
  7. [NiP]
    Nievergelt, J. and F.P. Preparata, Plane-sweep algorithms for intersecting geometric figures. Communications of the ACM 25, 739–747, 1982.Google Scholar
  8. [Nu]
    Nurmi, O., A fast line-sweep algorithm for hidden line elimination. Universität Karlsruhe, Institut für Angewandte Informatik und Formale Beschreibungsverfahren, Report 134, 1984, to appear in: BIT.Google Scholar
  9. [OWW]
    Ottmann, Th., P. Widmayer and D. Wood, A worst-case efficient algorithm for hidden line elimination. Universität Karlsruhe, Institut für Angewandte Informatik und Formale Beschreibungsverfahren, Report 119, 1982.Google Scholar
  10. [Sch]
    Schmitt, A., On the time and space complexity of certain exact hidden line algorithms. Universität Karlsruhe, Fakultät für Informatik, Report 24/81, 1981.Google Scholar
  11. [Sh]
    Shamos, M.I., Computational geometry. Yale University, Ph.D. Thesis, 1978.Google Scholar
  12. [ShH]
    Shamos, M.I. and D. Hoey, Geometric intersection problems. Proceedings of the 17th Annual IEEE Symposium on Foundations of Computer Science, 208–215, 1976.Google Scholar
  13. [SiW]
    Six, H.W. and D. Wood, Counting and reporting intersections of d-ranges. IEEE Transactions on Computers C-31, 181–187, 1982.Google Scholar
  14. [SuSS]
    Sutherland, I.E., R.F. Sproull and R.A. Schumacker, A characterization of ten hidden-surface algorithms. Computing Surveys 6, 1–55, 1974.Google Scholar
  15. [VaW]
    Vaishnavi, V.K. and D. Wood, Rectilinear line segment intersection, layered segment trees and dynamization. Journal of Algorithms 2, 160–176, 1981.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Ralf Hartmut Güting
    • 1
  • Thomas Ottmann
    • 2
  1. 1.Lehrstuhl Informatik VIUniversität DortmundDortmund 50West Germany
  2. 2.Institut für Angewandte Informatik und Formale BeschreibungsverfahrenUniversität KarlsruheKarlsruheWest Germany

Personalised recommendations