title: A topological coordinate system for the diamond cubic grid.
abstract: Topological coordinate systems are used to address all cells of abstract cell complexes. In this paper, a topological coordinate system for cells in the diamond cubic 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. Boundary and co-boundary relations, as well as adjacency relations between the cells, can easily be captured by the coordinate values. Thus, this coordinate system is apt for implementation in various applications, such as visualizations, morphological and topological operations and shape analysis.
authors: Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia.
authors: Lidija
authors: L
authors: Čomić
authors: Department of Mathematics, Eastern Mediterranean University, Salamis Yolu, Famagusta, North Cyprus, Mersin-10, Turkey.
authors: Benedek
authors: B
authors: Nagy
keywords: abstract cell complexes; diamond cubic grid; non-traditional three-dimensional grids; topological coordinate system; topological operations