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...
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| creator | Li, Fajie Klette, Reinhard |
| description | 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. |
| doi_str_mv | 10.1007/11556121_40 |
| format | Conference Proceeding |
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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.</description><identifier>ISSN: 0302-9743</identifier><identifier>ISBN: 9783540289692</identifier><identifier>ISBN: 3540289690</identifier><identifier>EISSN: 1611-3349</identifier><identifier>EISBN: 9783540320111</identifier><identifier>EISBN: 3540320113</identifier><identifier>DOI: 10.1007/11556121_40</identifier><language>eng</language><publisher>Berlin, Heidelberg: Springer Berlin Heidelberg</publisher><subject>Applied sciences ; Artificial intelligence ; Computer science; control theory; systems ; Critical Line ; Exact sciences and technology ; Motion Planning Problem ; Pattern recognition. Digital image processing. Computational geometry ; Polygonal Curve ; Robot Motion Planning ; Usual Topology</subject><ispartof>Computer Analysis of Images and Patterns, 2005, p.321-329</ispartof><rights>Springer-Verlag Berlin Heidelberg 2005</rights><rights>2005 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/11556121_40$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/11556121_40$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>309,310,779,780,784,789,790,793,4050,4051,27925,38255,41442,42511</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=17182634$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><contributor>Philips, Wilfried</contributor><contributor>Gagalowicz, André</contributor><creatorcontrib>Li, Fajie</creatorcontrib><creatorcontrib>Klette, Reinhard</creatorcontrib><title>Minimum-Length Polygons of First-Class Simple Cube-Curves</title><title>Computer Analysis of Images and Patterns</title><description>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.</description><subject>Applied sciences</subject><subject>Artificial intelligence</subject><subject>Computer science; control theory; systems</subject><subject>Critical Line</subject><subject>Exact sciences and technology</subject><subject>Motion Planning Problem</subject><subject>Pattern recognition. Digital image processing. Computational geometry</subject><subject>Polygonal Curve</subject><subject>Robot Motion Planning</subject><subject>Usual Topology</subject><issn>0302-9743</issn><issn>1611-3349</issn><isbn>9783540289692</isbn><isbn>3540289690</isbn><isbn>9783540320111</isbn><isbn>3540320113</isbn><fulltext>true</fulltext><rsrctype>conference_proceeding</rsrctype><creationdate>2005</creationdate><recordtype>conference_proceeding</recordtype><recordid>eNpNkDtPwzAURs1LopRO_IEsDAwGX1_Hzh1R1AJSEUjAbNmJUwJ5KW6R-u8pKkJM33COvuEwdgHiGoQwNwBpqkGCVeKAzchkmCqBUgDAIZuABuCIio7-mMxIkzxmE4FCcjIKT9lZjB9CCGlIThg91l3dblq-DN1q_Z4898121Xcx6atkUY9xzfPGxZi81O3QhCTf-MDzzfgV4jk7qVwTw-x3p-xtMX_N7_ny6e4hv13yQQKtuYGycIgZavRKOqdRO1QmeK9UKkoiAu8zSENACj41VGVOVr4oURZlwAKn7HL_O7hYuKYaXVfU0Q5j3bpxa8FAJjWqnXe19-IOdaswWt_3n9GCsD_t7L92-A1IdlqQ</recordid><startdate>2005</startdate><enddate>2005</enddate><creator>Li, Fajie</creator><creator>Klette, Reinhard</creator><general>Springer Berlin Heidelberg</general><general>Springer</general><scope>IQODW</scope></search><sort><creationdate>2005</creationdate><title>Minimum-Length Polygons of First-Class Simple Cube-Curves</title><author>Li, Fajie ; Klette, Reinhard</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p219t-71dca338363b42aa636a347ebb4450d9991bb815ee39eb579f8a2fbcd32cde3c3</frbrgroupid><rsrctype>conference_proceedings</rsrctype><prefilter>conference_proceedings</prefilter><language>eng</language><creationdate>2005</creationdate><topic>Applied sciences</topic><topic>Artificial intelligence</topic><topic>Computer science; control theory; systems</topic><topic>Critical Line</topic><topic>Exact sciences and technology</topic><topic>Motion Planning Problem</topic><topic>Pattern recognition. Digital image processing. Computational geometry</topic><topic>Polygonal Curve</topic><topic>Robot Motion Planning</topic><topic>Usual Topology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Li, Fajie</creatorcontrib><creatorcontrib>Klette, Reinhard</creatorcontrib><collection>Pascal-Francis</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Li, Fajie</au><au>Klette, Reinhard</au><au>Philips, Wilfried</au><au>Gagalowicz, André</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>Minimum-Length Polygons of First-Class Simple Cube-Curves</atitle><btitle>Computer Analysis of Images and Patterns</btitle><date>2005</date><risdate>2005</risdate><spage>321</spage><epage>329</epage><pages>321-329</pages><issn>0302-9743</issn><eissn>1611-3349</eissn><isbn>9783540289692</isbn><isbn>3540289690</isbn><eisbn>9783540320111</eisbn><eisbn>3540320113</eisbn><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 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.</abstract><cop>Berlin, Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/11556121_40</doi><tpages>9</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0302-9743 |
| ispartof | Computer Analysis of Images and Patterns, 2005, p.321-329 |
| issn | 0302-9743 1611-3349 |
| language | eng |
| recordid | cdi_pascalfrancis_primary_17182634 |
| source | Springer Books |
| subjects | Applied sciences Artificial intelligence Computer science control theory systems Critical Line Exact sciences and technology Motion Planning Problem Pattern recognition. Digital image processing. Computational geometry Polygonal Curve Robot Motion Planning Usual Topology |
| title | Minimum-Length Polygons of First-Class Simple Cube-Curves |
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