A Note on \(\mathbf{0}\)-Gaps in 3D Digital Curves

In Digital Geometry, gaps represent basic portions of a digital object that a discrete ray can traverse without intersecting any voxel of the object itself. This concept is essential in combinatorial image analysis and has significant applications in fields such as CAD and Computer Graphics. In this paper, we show that the number of \(0\) -gaps in a \(3\) D digital curve can be represented as a linear combination of the numbers of its \(i\) -cells, where \(i\) ranges from \(0\) to \(3\) .