A digital 3D Jordan-Brouwer separation theorem

Abstract

We introduce a connectedness in the digital space ℤ3 induced by a quaternary relation. Using this connectedness, we prove a digital 3D Jordan-Brouwer separation theorem for boundary surfaces of the digital polyhedra that may be face-to-face tiled with certain digital tetrahedra in ℤ3. An advantage of the digital Jordan surfaces obtained over those given by the Khalimsky topology is that the former may bend at the acute dihedral angle π4{\pi \over 4}.

Keywords

• digital space
• digital jordan surface
• connectedness
• quaternary relation
• digital 3d tiling
• 68u05
• 52c22
• 68r99