Representing and computing some configuration properties for the n-dimensional orthogonal pseudo-polytopes

A Euclidean polytope is defined as a finite region of n-dimensional space enclosed by a finite number of (n-1)-dimensional hyperplanes. We present a set of formulations that describe some properties of the configurations that can represent n-dimensional orthogonal pseudo-polytopes (nD-OPP). Moreover, we develop a useful representation for these configurations from which it is possible to obtain and to manage some specific geometric information: the application of geometric transformations and the comparison of configurations. Through such developments, we have a better performance, in terms of memory and time complexity, compared with traditional procedures. The proposed formulations and binary representation for the configurations in the nD-OPPs have been successfully applied in the following applications: representation and management of multimedia content, specifically color 2D and 3D animations through 4D and 5D orthogonal polytopes, respectively; visualization and analysis of geographical data through the extrusions to the 5D color space of 2D color images.