Minimum zone separation functionals: The spatial case

The minimum radial separation measure associated with a convex polytope is computed using basic geometric techniques and an exhaustive search procedure. The minimum volume difference center extends an analogous measure in the plane, and a new measure, the minimum surface-area difference, is defined and computed. The separation functionals associated with perfect cubic forms and regular polytope shapes, as well as a generalized family of convex perfect form are computed for an arbitrary three-dimensional measurement data set. Examples are used to illustrate the methodology and computational experience is described.