Gift-wrapping based preimage computation algorithm

The aim of the paper is to define an algorithm for computing preimages - roughly the sets of naive digital planes containing a finite subset S of Z(3). The method is based on theoretical results: the preimage is a polytope that vertices can be decomposed in three subsets, the upper vertices, the lower vertices and the intermediary ones (equatorial). We provide a geometrical understanding (as facets on S or S circle minus S) of each kind of vertices. These properties are used to compute the preimage by gift-wrapping some regions of the convex hull of S or of S circle minus S boolean OR{(0, 0, 1)}.