Moving discs between polygons

  • Hans Rohnert
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 317)


An algorithm is given for finding a collision free path for a disc between a collection of polygons having n corners in total. The polygons are fixed and can be preprocessed. One query specifies the radius r of the disc to be moved and start and destination point of the center of the disc. The answer whether a feasible path exists is given in time O(log n). Returning a feasible path is done in additional time proportional to the length of the description of the path. Preprocessing time is O(n log n) and space complexity is O(n).


Motion Planning polygonal obstacles computational geometry 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

7. References

  1. [1]
    H. EDELSBRUNNER: “An Optimal Solution for Searching in General Planar Subdivisions”, Technical Report 1983, Institutes for Information Processing, Technical University of Graz, AustriaGoogle Scholar
  2. [2]
    S. FORTUNE: “A Sweepline Algorithm for Voronoi Diagrams”, Proc. of the Second Symp. on Computational Geometry 1986, pp. 313–322Google Scholar
  3. [3]
    D. HAREL, R. E. TARJAN: “Fast Algorithms for Finding Nearest Common Ancestors”, SIAM Journal on Computing, Vol. 13, No. 2, 1984, pp. 338–355Google Scholar
  4. [4]
    D. G. KIRKPATRICK: “Efficient Computation of Continuous Skeletons”, IEEE FOCS 1979, pp. 18–27Google Scholar
  5. [5]
    D. T. LEE, F. P. PREPARATA: “Location of a point in a planar subdivision and its applications”, SIAM Journal on Computing, Vol. 6, 1977, pp. 594–606Google Scholar
  6. [6]
    K. MEHLHORN: “Data Structures and Algorithms”, Vol. 1, pp. 296–304, published 1984 by Springer-Verlag, Berlin Heidelberg New York TokyoGoogle Scholar
  7. [7]
    C. Ó'DÚNLAING, C. K. YAP: “A ‘Retraction’ Method for Planning the Motion of a Disc”, Journal of Algorithms, Vol. 6, pp. 104–111 (1985)Google Scholar
  8. [8]
    T. OTTMANN, P. WIDMEYER, D. WOOD: “A Fast Algorithm for Boolean Mask Operations”, Inst. für Angew. Mathematik und Formale Beschreibungsverfahren, D-7500 Karlsruhe, Rept. No. 112 (1982)Google Scholar
  9. [9]
    M. I. SHAMOS: “Geometric Complexity”, Proc. of the Seventh Annual ACM Symposium on Theory of Computing, pp. 224–233 (1975)Google Scholar
  10. [10]
    R. E. TARJAN: “Efficiency of a Good But Not Linear Set Union Algorithm”, Journal of the ACM, Vol. 22, No. 2, pp. 215–225 (1975)Google Scholar
  11. [11]
    C. K. YAP: “An O(n log n) Algorithm for the Voronoi Diagram of a Set of Simple Curve Segments”, Technical Report No. 161, New York University, Dept. of Computer Science, May 1985Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Hans Rohnert
    • 1
  1. 1.FB 10, Universität des SaarlandesWest Germany

Personalised recommendations