Two Approximative Algorithms for Calculating Minimum-Length Polygons in 3D Space

Li, Fajie; Klette, Reinhard

dc.contributor.author	Li, Fajie	en
dc.contributor.author	Klette, Reinhard	en
dc.date.accessioned	2008-08-21T01:57:01Z	en
dc.date.available	2008-08-21T01:57:01Z	en
dc.date.issued	2005	en
dc.identifier.citation	Communication and Information Technology Research Technical Report 173, (2005)	en
dc.identifier.issn	1178-3572	en
dc.identifier.uri	http://hdl.handle.net/2292/2797	en
dc.description	You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the original CITR web site; http://citr.auckland.ac.nz/techreports/ under terms that include this permission. All other rights are reserved by the author(s).	en
dc.description.abstract	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 no provable general algorithm is known for the approximative calculation of such an MLP. This paper presents two approximative algorithms for computing the MLP of a general simple cube-curve in $O(n^4)$ time, where $n$ is the total number of critical edges of the given simple cube-curve.	en
dc.publisher	CITR, The University of Auckland, New Zealand	en
dc.relation.ispartofseries	Communication and Information Technology Research (CITR) Technical Report Series	en
dc.rights	Copyright CITR, The University of Auckland. You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the original CITR web site under terms that include this permission. All other rights are reserved by the author(s).	en
dc.rights.uri	https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm	en
dc.source.uri	http://citr.auckland.ac.nz/techreports/2005/CITR-TR-173.pdf	en
dc.title	Two Approximative Algorithms for Calculating Minimum-Length Polygons in 3D Space	en
dc.type	Technical Report	en
dc.subject.marsden	Fields of Research::280000 Information, Computing and Communication Sciences	en