Abstract
Roundness of a 3-D massive solid is a population but fundamental quantity which is hard to describe in the global sense. This paper presents such a new roundness index of Sphericity as a natural 3D-extention of the roundness measure by Cox for 2D-figures. The meaning and usefulness of the scalar indices are tested and confirmed for typical geometrical solids. Sphericity represents not only the roundness but also the general feature of the simple solids. Secondly a structural explanation consisting of three transformations has been introduced to the concept of Sphericity, which yields analytical/synthetic procedures of the indices and could lead to an enough understanding of them through a method of vector evaluation. Because the acquisition of a complete set of 3D-data is not necessarily easy, a route to the index evaluation under imperfect data would also be of practical importance. Lastly a model-based method of evaluating Sphricity has been proposed and confirmed by experiments for simple cases. The relation between indices for 3D and 2D-sample figure will also be shown.
