Testing congruence and symmetry for general 3-dimensional objects

Authors:
Peter Brass;Christian Knauer
Affiliations:
Department of Computer Science, City College, CUNY, Convent Avenue at 138th Street, New York, NY;Institut für Informatik, Freie Universität Berlin, Takustrasse 9, D-14195 Berlin, Germany
Venue:
Computational Geometry: Theory and Applications - Special issue on computational geometry - EWCG'02
Year:
2004

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Abstract

Congruence and symmetry testing in 3-dimensional space seems an old and well-studied problem, but it is optimally solved only for (labelled) finite point sets and convex polytopes. In this paper we present a very general class of geometric objects in 3-dimensional space and give algorithms to test congruence or symmetry of such objects, also in O(n log n) time. For this we use the classification of 3-dimensional symmetry groups.