Representation of orthogonal regions by vertices

Abstract Denote by X a finite union of orthogonal regions in n dimensions, and by ∂X its boundary with self-intersections allowed. Corner vertices are divided into two mutually exclusive types, depending on the parity of the number of orthants with tips within X incident on them. We present simple algorithms for recovering both X and ∂X from the set of corner vertices together with specifications of their types, in serial and parallel versions.