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Congruence, similarity, and symmetries of geometric objects

  • Published: 01 September 1988
  • Volume 3, pages 237–256, (1988)
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Discrete & Computational Geometry Aims and scope Submit manuscript
Congruence, similarity, and symmetries of geometric objects
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  • Helmut Alt1,
  • Kurt Mehlhorn2,
  • Hubert Wagener3 &
  • …
  • Emo Welzl1,4 
  • 2148 Accesses

  • 181 Citations

  • 14 Altmetric

  • 1 Mention

  • Explore all metrics

Abstract

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).

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Freie Universität Berlin, Arnimallee 2-6, D-1000, Berlin 33, Federal Republic of Germany

    Helmut Alt & Emo Welzl (Research associate of IIG)

  2. Fachbereich Informatik, Universität des Saarlandes, D-6600, Saarbrücken, Federal Republic of Germany

    Kurt Mehlhorn

  3. Fachbereich Informatik, Technische Universität Berlin, Franklinstrasse 28/29, D-1000, Berlin 10, Federal Republic of Germany

    Hubert Wagener

  4. Institutes for Information Processing, Technical University of Graz, Austria

    Emo Welzl (Research associate of IIG)

Authors
  1. Helmut Alt
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  2. Kurt Mehlhorn
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  3. Hubert Wagener
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  4. Emo Welzl
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Additional information

Part of this research was supported by the DFG under Grants Me 620/6-1 and Al 253/1-1.

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Alt, H., Mehlhorn, K., Wagener, H. et al. Congruence, similarity, and symmetries of geometric objects. Discrete Comput Geom 3, 237–256 (1988). https://doi.org/10.1007/BF02187910

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  • Received: 10 May 1987

  • Revised: 10 November 1987

  • Published: 01 September 1988

  • Issue date: September 1988

  • DOI: https://doi.org/10.1007/BF02187910

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Keywords

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

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