Minimum-Length Polygons of First-Class Simple Cube-Curves

13 years 3 months ago
Minimum-Length Polygons of First-Class Simple Cube-Curves
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.
Fajie Li, Reinhard Klette
Added 26 Jun 2010
Updated 26 Jun 2010
Type Conference
Year 2005
Where CAIP
Authors Fajie Li, Reinhard Klette
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