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Digital Curves in 3D Space and a Linear-Time Length Estimation Algorithm
July 2002 (vol. 24 no. 7)
pp. 962-970

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. This 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.

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Index Terms:
Digital geometry, curve length, space curves, cellular complexes.
Thomas Bülow, Reinhard Klette, "Digital Curves in 3D Space and a Linear-Time Length Estimation Algorithm," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 7, pp. 962-970, July 2002, doi:10.1109/TPAMI.2002.1017622
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