Recognising symmetry in solid models

Abstract

Although the symmetry of solids has been studied for over 50 years, it is still not easy to find a method for detecting symmetry in objects represented by B-rep solid models documented in the literature. The need for such a method comes from the requirements of an environment for ‘Assembly Oriented Design’ which includes ‘Design for Assembly’ analyses. This paper begins with definition of terminology used to describe the different types of symmetry that may occur in components and then gives a detailed review in which the benefits and limitations of the many existing methods used for symmetry detection in other applications are discussed. Since none of the methods appear to provide a solution, which can be easily adapted to the Assembly Oriented Design application, the requirements of any new method are then more precisely identified. It appears that human perception of symmetry is considerably more robust than any computational method in existence and therefore the cognitive processes involved in human symmetry detection are examined to attempt to identify promising directions for an alternative approach. As a result of this study, a new method for symmetry detection, which uses the comparison of face loops has been devised. This proves to be an effective technique for the detection of symmetry, which also satisfies the requirements of the particular application. One implementation of a procedure is described in detail together with results of its use on several test cases. Finally, since this method has a demanding practical application, the computational efficiency of the method is examined at length.