A topological 4-coordinate system for the face centered cubic grid

Abstract

© 2016 Elsevier B.V. Non traditional 3D grids, such as face centered cubic and body centered cubic, have some advantages over the traditional cubic grid. They offer, combined with the use of topological coordinates that address not only the voxels, but also the lower dimensional cells of the grid, a way to avoid some topological paradoxes of digital geometry. In this paper, a symmetric topological 4-coordinate system is presented for the face centered cubic grid. Incidence (boundary and co-boundary) and adjacency relations between cells can easily be deduced from cell coordinates through simple integer operations. An application of the proposed coordinate system to graphics/visualization area is shown.