A plate-based definition of discrete surfaces

By the use of certain discrete plates in the role of polygonal faces we mimic the definition of a combinatorial surface to produce, for each adjacency pair (k, (k) over bar) not equal (6,6), k, (k) over bar epsilon {6; 18, 26}, a new family S-kk of discrete surfaces, termed (k, (k) over bar)-surfaces, in the grid Z(3) that strictly contains several well-known families of surfaces, such as the strong and simplicity surfaces, as well as other objects considered as surfaces in the literature. Moreover, the number of possible configurations in the 26-neighbourhood of a (26,6)-surface voxel is estimated to rise up to 10,580. In addition, we show that S-kk is the largest set of discrete surfaces that can be defined within the framework for Digital Topology in (Ayala et al., 2002). (c) 2011 Elsevier B.V. All rights reserved.