Box skeletons of discrete objects

Abstract: "In a previous report, it was suggested that the Medial Axis Transform (MAT) would be an extremely useful design tool, if only algorithms could be defined for transforming a conventional geometric representation to one using MAT's. Certain specific properties of the MAT were shown to be the useful ones. It was also pointed out that the MAT can be regarded as a special case of a class of objects called skeletons, based upon the euclidean metric. We then proposed that a different set, defined using the box metric, can be used in place of the MAT for at least some engineering applications. In that report, a procedure was defined which, we claimed, identified the box skeleton. The purpose of this report is to prove that claim. This report describes the procedure, and then proves that the procedure yields the box skeleton."