The family of universal axes

Abstract

The family of universal axes (UA) is introduced in this paper. This family has infinitely many members, each of which generates a method that is universal in the sense that each generated method can define shape orientation for almost any kind of shape and once the numerical computing system has been set up, the users of this orientation detection system need not supply the system the information about whether a given shape is mirror-symmetric, rotationally symmetric, irregular, etc. Some mathematical properties of the proposed UA are investigated and numerical techniques for implementing UA are discussed. The method of universal principal axes (UPA) introduced recently is just one of the infinitely many members of the proposed family of UA. The UPA method yields at least two orientations for each shape and thus must be combined with another non-universal single-orientation method in order to reduce the time needed to match irregular shapes. Most members of the proposed UA family do not need to be supplemented by a single-orientation method in this way.