Digital curves in 3D space and a linear-time length estimation algorithm

We consider simple digital curves in a 3D orthogonal grid as special polyhedrally bounded sets. These digital curves model digitized curves or arcs in three-dimensional Euclidean space. The length of such a simple digital curve is defined to be the length of the minimum-length polygonal curve fully contained and complete in the tube of this digital curve. So far, no algorithm was known for the calculation of such a shortest polygonal curve. The paper provides an iterative algorithmic solution for approximating the minimum-length polygon of a given simple digital space-curve. The theoretical foundations of this algorithm are presented as well as experimental results.