Regular algebraic curve segments (III)—applications in interactive design and data fitting
In this paper (part three of the trilogy) we use low degree G 1 and G 2 continuous regular algebraic spline curves defined within parallelograms, to interpolate an ordered set of data points in the plane. We explicitly characterize curve families whose members have the required interpolating propert...
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| Veröffentlicht in: | Computer aided geometric design 2001-04, Vol.18 (3), p.149-173 |
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| container_title | Computer aided geometric design |
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| creator | Bajaj, Chandrajit L. Xu, Guoliang |
| description | In this paper (part three of the trilogy) we use low degree
G
1
and
G
2
continuous regular algebraic spline curves defined within parallelograms, to interpolate an ordered set of data points in the plane. We explicitly characterize curve families whose members have the required interpolating properties and possess a minimal number of inflection points. The regular algebraic spline curves considered here have many attractive features: They are easy to construct. There exist convenient geometric control handles to locally modify the shape of the curve. The error of the approximation is controllable. Since the spline curve is always inside the parallelogram, the error of the fit is bounded by the size of the parallelogram. The spline curve can be rapidly displayed, even though the algebraic curve segments are implicitly defined. |
| doi_str_mv | 10.1016/S0167-8396(01)00010-3 |
| format | Article |
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G
1
and
G
2
continuous regular algebraic spline curves defined within parallelograms, to interpolate an ordered set of data points in the plane. We explicitly characterize curve families whose members have the required interpolating properties and possess a minimal number of inflection points. The regular algebraic spline curves considered here have many attractive features: They are easy to construct. There exist convenient geometric control handles to locally modify the shape of the curve. The error of the approximation is controllable. Since the spline curve is always inside the parallelogram, the error of the fit is bounded by the size of the parallelogram. The spline curve can be rapidly displayed, even though the algebraic curve segments are implicitly defined.</description><identifier>ISSN: 0167-8396</identifier><identifier>EISSN: 1879-2332</identifier><identifier>DOI: 10.1016/S0167-8396(01)00010-3</identifier><identifier>CODEN: CAGDEX</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Algebraic curve ; Applied sciences ; Computer aided design ; Computer science; control theory; systems ; Exact sciences and technology ; Parallelogram ; Polygonal chain ; Software ; Tensor product</subject><ispartof>Computer aided geometric design, 2001-04, Vol.18 (3), p.149-173</ispartof><rights>2001 Elsevier Science B.V.</rights><rights>2001 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c366t-464c3a12fa4a0ff99c40b2a1362ae3c6c0508564bd5e22b664169c0b32388e6c3</citedby><cites>FETCH-LOGICAL-c366t-464c3a12fa4a0ff99c40b2a1362ae3c6c0508564bd5e22b664169c0b32388e6c3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0167839601000103$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65306</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=980684$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Bajaj, Chandrajit L.</creatorcontrib><creatorcontrib>Xu, Guoliang</creatorcontrib><title>Regular algebraic curve segments (III)—applications in interactive design and data fitting</title><title>Computer aided geometric design</title><description>In this paper (part three of the trilogy) we use low degree
G
1
and
G
2
continuous regular algebraic spline curves defined within parallelograms, to interpolate an ordered set of data points in the plane. We explicitly characterize curve families whose members have the required interpolating properties and possess a minimal number of inflection points. The regular algebraic spline curves considered here have many attractive features: They are easy to construct. There exist convenient geometric control handles to locally modify the shape of the curve. The error of the approximation is controllable. Since the spline curve is always inside the parallelogram, the error of the fit is bounded by the size of the parallelogram. The spline curve can be rapidly displayed, even though the algebraic curve segments are implicitly defined.</description><subject>Algebraic curve</subject><subject>Applied sciences</subject><subject>Computer aided design</subject><subject>Computer science; control theory; systems</subject><subject>Exact sciences and technology</subject><subject>Parallelogram</subject><subject>Polygonal chain</subject><subject>Software</subject><subject>Tensor product</subject><issn>0167-8396</issn><issn>1879-2332</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2001</creationdate><recordtype>article</recordtype><recordid>eNqFkMlKxEAQhhtRcFweQQgIMh6ivSRtchIZXAYGBJeb0FQqldCS6YzdHcGbD-ET-iRGR7wKRdXl-6uoj7EDwU8EF_r0fmxnaaFKPeXimHMueKo22EQUZ2UqlZKbbPKHbLOdEJ5HSIpST9jTHbVDBz6BrqXKg8UEB_9KSaB2SS6GZDqfz48_3z9gteosQrS9C4l1Y0XygNGOcE3Bti4BVyc1REgaG6N17R7baqALtP87d9nj1eXD7CZd3F7PZxeLFJXWMc10hgqEbCAD3jRliRmvJAilJZBCjTznRa6zqs5JykrrTOgSeaWkKgrSqHbZ0XrvyvcvA4VoljYgdR046odgpNY8F5kcwXwNou9D8NSYlbdL8G9GcPPt0vy4NN-iDBfmx6VRY-7w9wAEhK7x4NCGv3BZcF1kI3W-pmj89dWSNwEtOaTaesJo6t7-c-cLRCeIuw</recordid><startdate>20010401</startdate><enddate>20010401</enddate><creator>Bajaj, Chandrajit L.</creator><creator>Xu, Guoliang</creator><general>Elsevier B.V</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20010401</creationdate><title>Regular algebraic curve segments (III)—applications in interactive design and data fitting</title><author>Bajaj, Chandrajit L. ; Xu, Guoliang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c366t-464c3a12fa4a0ff99c40b2a1362ae3c6c0508564bd5e22b664169c0b32388e6c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2001</creationdate><topic>Algebraic curve</topic><topic>Applied sciences</topic><topic>Computer aided design</topic><topic>Computer science; control theory; systems</topic><topic>Exact sciences and technology</topic><topic>Parallelogram</topic><topic>Polygonal chain</topic><topic>Software</topic><topic>Tensor product</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bajaj, Chandrajit L.</creatorcontrib><creatorcontrib>Xu, Guoliang</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Computer aided geometric design</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bajaj, Chandrajit L.</au><au>Xu, Guoliang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Regular algebraic curve segments (III)—applications in interactive design and data fitting</atitle><jtitle>Computer aided geometric design</jtitle><date>2001-04-01</date><risdate>2001</risdate><volume>18</volume><issue>3</issue><spage>149</spage><epage>173</epage><pages>149-173</pages><issn>0167-8396</issn><eissn>1879-2332</eissn><coden>CAGDEX</coden><abstract>In this paper (part three of the trilogy) we use low degree
G
1
and
G
2
continuous regular algebraic spline curves defined within parallelograms, to interpolate an ordered set of data points in the plane. We explicitly characterize curve families whose members have the required interpolating properties and possess a minimal number of inflection points. The regular algebraic spline curves considered here have many attractive features: They are easy to construct. There exist convenient geometric control handles to locally modify the shape of the curve. The error of the approximation is controllable. Since the spline curve is always inside the parallelogram, the error of the fit is bounded by the size of the parallelogram. The spline curve can be rapidly displayed, even though the algebraic curve segments are implicitly defined.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/S0167-8396(01)00010-3</doi><tpages>25</tpages></addata></record> |
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| ispartof | Computer aided geometric design, 2001-04, Vol.18 (3), p.149-173 |
| issn | 0167-8396 1879-2332 |
| language | eng |
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| source | Elsevier ScienceDirect Journals |
| subjects | Algebraic curve Applied sciences Computer aided design Computer science control theory systems Exact sciences and technology Parallelogram Polygonal chain Software Tensor product |
| title | Regular algebraic curve segments (III)—applications in interactive design and data fitting |
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