Discrete & Computational Geometry

, Volume 3, Issue 3, pp 237–256 | Cite as

Congruence, similarity, and symmetries of geometric objects

  • Helmut Alt
  • Kurt Mehlhorn
  • Hubert Wagener
  • Emo Welzl


We consider the problem of computing geometric transformations (rotation, translation, reflexion) that map a point setA exactly or approximately into a point setB. We derive efficient algorithms for various cases (Euclidean or maximum metric, translation or rotation, or general congruence).


Symmetry Group Voronoi Diagram Discrete Comput Geom Binary Search Geometric Object 
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.


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Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

  • Helmut Alt
    • 1
  • Kurt Mehlhorn
    • 2
  • Hubert Wagener
    • 3
  • Emo Welzl
    • 1
    • 4
  1. 1.Fachbereich MathematikFreie Universität BerlinBerlin 33Federal Republic of Germany
  2. 2.Fachbereich InformatikUniversität des SaarlandesSaarbrückenFederal Republic of Germany
  3. 3.Fachbereich InformatikTechnische Universität BerlinBerlin 10Federal Republic of Germany
  4. 4.Institutes for Information ProcessingTechnical University of GrazAustria

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