Discrete analytical objects in the body-centered cubic grid

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. & COPY; 2023 Elsevier Ltd. All rights reserved.

Automated summary

This article proposes a characterization of discrete analytical spheres, planes, and lines in the body-centered cubic (BCC) grid using both Cartesian and alternative compact coordinate systems. Spheres and planes are defined through double Diophantine inequalities, and their topological features, such as functionality, thickness, connectivity, and separation properties, are investigated. Lines are defined as the intersection of planes. The number of planes is equal to the number of pairs of faces of a BCC voxel parallel to the line.