A Combinatorial 4-Coordinate System for the Diamond Grid

Abstract

A new combinatorial coordinate system for cells in the diamond grid is presented, and some of its properties are detailed. Four dependent coordinates are used to address the voxels (triakis truncated tetrahedra), their faces (hexagons and triangles), their edges and the points at their corners. The incidence (boundary and co-boundary) and adjacency relations of the cells can easily be captured by these coordinate values. Therefore, the new coordinate system can effectively by applied in morphological and topological operations.