Search

Abstract: The aim of this paper is to show that the supercover of an -flat (i.e. a Euclidean affine subspace of dimension ) in Euclidean -space is a discrete analytical object. The supercover of a Euclidean object is a discrete object consisting of all the voxels that intersect . A discrete analytical object is a set of discrete points that is defined by a finite set of inequalities. A method to determine the inequalities defining the supercover of an -flat is provided. [Copyright &y& Elsevier]

In this paper we study discretizations of objects in higher dimensions. We introduce a large class of object discretizations, called k-discretizations. This class is natural and quite general, including as special cases some known discretizations, like the standard covers and the naive discretizations. Various results are obtained in the proposed general setting. [Copyright &y& Elsevier]