Discrete analytical objects in the body-centered cubic grid

• Published in: Pattern recognition Vol. 142; p. 109693
• Main Authors: Čomić, Lidija, Largeteau-Skapin, Gaëlle, Zrour, Rita, Biswas, Ranita, Andres, Eric
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2023; Elsevier
• Subjects: 3D Coordinate system; BCC Grid; Computer Science; Discrete analytical line; Discrete analytical plane; Discrete analytical sphere; Discrete geometry; Image Processing; Discrete geometry; Discrete analytical plane; Discrete analytical sphere; BCC Grid; Discrete analytical line; 3D Coordinate system
• ISSN: 0031-3203; 1873-5142
• DOI: 10.1016/j.patcog.2023.109693

•The body centered cubic grid is a viable alternative to the cubic grid.•A coordinate system provides one to one correspondence with the cubic grid.•Discrete analytical planes and spheres defined through double Diophantine inequalities.•Topological separation and connectivity properties depend on the chosen thickness.•Discrete analytical lines defined as the intersection of up to six plane. We propose a characterization of discrete analytical spheres, planes and lines in the body-centered cubic (BCC) grid, both in the Cartesian and in the recently proposed alternative compact coordinate system, in which each integer triplet addresses some voxel in the grid. We define spheres and planes through double Diophantine inequalities and investigate their relevant topological features, such as functionality or the interrelation between the thickness of the objects and their connectivity and separation properties. We define lines as the intersection of planes. The number of the planes (up to six) is equal to the number of the pairs of faces of a BCC voxel that are parallel to the line.