@inbook {IOPORT.02194202, author = {Li, Fajie and Klette, Reinhard}, title = {Minimum-length polygon of a simple cube-curve in 3D space.}, year = {2004}, booktitle = {Combinatorial image analysis.. 10th international workshop, IWCIA 2004, Auckland, New Zealand, December 1--3, 2004. Proceedings.}, isbn = {3-540-23942-1}, pages = {502-511}, publisher = {Berlin: Springer}, doi = {10.1007/b103936}, abstract = {Summary: We consider simple cube-curves in the orthogonal 3D grid of cells. The union of all cells contained in such a curve (also called the tube of this curve) is a polyhedrally bounded set. The curve's length is defined to be that of the minimum-length polygonal curve (MLP) fully contained and complete in the tube of the curve. So far, only a ``rubber-band algorithm'' is known to compute such a curve approximately. We provide an alternative iterative algorithm for the approximative calculation of the MLP for curves contained in a special class of simple cube-curves (for which we prove the correctness of our alternative algorithm), and the obtained results coincide with those calculated by the rubber-band algorithm.}, identifier = {02194202}, }