Abstract
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.
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Li, F., Klette, R. (2004). Minimum-Length Polygon of a Simple Cube-Curve in 3D Space. In: Klette, R., Žunić, J. (eds) Combinatorial Image Analysis. IWCIA 2004. Lecture Notes in Computer Science, vol 3322. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30503-3_36
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DOI: https://doi.org/10.1007/978-3-540-30503-3_36
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23942-0
Online ISBN: 978-3-540-30503-3
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