Exact Analysis of Optimal Configurations in Radii Computations

We propose a novel characterization of (radii-) minimal projections of polytopes onto j-dimensional subspaces. Applied on simplices this characterization allows to reduce the computation of an outer radius to a computation in the circumscribing case or to the computation of an outer radius of a lower-dimensional simplex. This allows to close a gap in the knowledge on optimal configurations in radii computations, such as determining the radii of smallest enclosing cylinders of regular simplices in general dimension.      «

We propose a novel characterization of (radii-) minimal projections of polytopes onto j-dimensional subspaces. Applied on simplices this characterization allows to reduce the computation of an outer radius to a computation in the circumscribing case or to the computation of an outer radius of a lower-dimensional simplex. This allows to close a gap in the knowledge on optimal configurations in radii computations, such as determining the radii of smallest enclosing cylinders of regular simplice...     »