We consider simple cube-curves in the orthogonal 3D grid. 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 one general algorithm called rubber-band algorithm was known for the approximative calculation of such an MLP. A proof that this algorithm always converges to the correct curve, is still an open problem. This paper proves that the rubber-band algorithm is correct for the family of first-class simple cube-curves. © Springer-Verlag Berlin Heidelberg 2005.
CITATION STYLE
Li, F., & Klette, R. (2005). Minimum-length polygons of first-class simple cube-curves. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3691 LNCS, pp. 321–329). Springer Verlag. https://doi.org/10.1007/11556121_40
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