On shape orientation when the standard method does not work

Abstract

In this paper we consider some questions related to the orientation of shapes when the standard method does not work. A typical situation is when a shapes under consideration has more than two axes of symmetry or if the shape is n-fold rotationally symmetric, when n > 2. Those situations are well studied in literature, Here, we give a very simple proof of the main result from [11] and slightly adapt their definition of principal axes for rotationally symmetric shapes. We show some desirable properties that hold if the orientation of such shapes is computed in such a modified way.