Minimum-Length Polygon of a Simple Cube-Curve in 3D Space
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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- 2.Burden, R.L., Faires, J.D.: BF Numerical Analysis, 7th edn. Brooks Cole, Pacific Grove (2000)Google Scholar
- 4.Sloboda, F., Zaťko, B., Klette, R.: On the topology of grid continua. In: SPIE Vision Geometry VII, vol. 3454, pp. 52–63 (1998)Google Scholar
- 5.Sloboda, F., Zaťko, B., Stoer, J.: On approximation of planar one-dimensional continua. In: Klette, R., Rosenfeld, A., Sloboda, F. (eds.) Advances in Digital and Computational Geometry, pp. 113–160. Springer, Singapore (1998)Google Scholar