Testing congruence and symmetry for general 3-dimensional objects

摘要

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 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.