by Li, F and Klette, R
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 algorithmïs 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. © Springer-Verlag 2004.
Reference:
Minimum-Length Polygon of a Simple Cube-Curve in 3D Space (Li, F and Klette, R), In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), volume 3322, 2004.
Bibtex Entry:
@article{li2004minimum-lengthspace,
author = "Li, F and Klette, R",
journal = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "502--511",
title = "Minimum-Length Polygon of a Simple Cube-Curve in 3D Space",
volume = "3322",
year = "2004",
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. © Springer-Verlag 2004.",
issn = "0302-9743",
eissn = "1611-3349",
language = "eng",
}