FOLD PRINCIPAL AXIS - A NEW TOOL FOR DEFINING THE ORIENTATIONS OF ROTATIONALLY SYMMETRICAL SHAPES

Abstract

A new type of principal axis, namely, fold principal axis, is introduced in this paper, which can be used to define the orientations of rotationally symmetric shapes. A given shape is first transformed into a new shape on which the well-defined traditional principal axis is detected. The traditional principal axis is then transformed back to obtain the proposed fold principal axes of the given shape. The properties of such axes, including the uniqueness, existence, and invariance under rotation, translation, and scaling, are investigated. Some illustrative examples are also given.