A Combinatorial 3-Coordinate System for the Face Centered Cubic Grid

Abstract

A new combinatorial 3-coordinate system for cells in the face centered cubic grid is presented, and some of its properties are detailed. Three independent coordinates are used to address the voxels (rhombic dodecahedra), their faces (rhombs), their edges and the points at their corners. The incidence (boundary and co-boundary) and adjacency relations between the cells can easily be captured by these coordinate values. The new coordinate system can effectively by applied in various image processing morphological and topological operations.