A cyclic basis for closed curve and surface modeling
We define a cyclic basis for the vectorspace of truncated Fourier series. The basis has several nice properties, such as positivity, summing to 1, that are often required in computer aided design, and that are used by designers in order to control curves by manipulating control points. Our curves ha...
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| Veröffentlicht in: | Computer aided geometric design 2009-06, Vol.26 (5), p.528-546 |
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| container_title | Computer aided geometric design |
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| creator | Róth, Ágoston Juhász, Imre Schicho, Josef Hoffmann, Miklós |
| description | We define a cyclic basis for the vectorspace of truncated Fourier series. The basis has several nice properties, such as positivity, summing to 1, that are often required in computer aided design, and that are used by designers in order to control curves by manipulating control points. Our curves have cyclic symmetry, i.e. the control points can be cyclically arranged and the curve does not change when the control points are cyclically permuted. We provide an explicit formula for the elevation of the degree from
n to
n
+
r
,
r
⩾
1
and prove that the control polygon of the degree elevated curve converges to the curve itself if
r tends to infinity. Variation diminishing property of the curve is also verified. The proposed basis functions are suitable for the description of closed curves and surfaces with
C
∞
continuity at all of their points. |
| doi_str_mv | 10.1016/j.cagd.2009.02.002 |
| format | Article |
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n to
n
+
r
,
r
⩾
1
and prove that the control polygon of the degree elevated curve converges to the curve itself if
r tends to infinity. Variation diminishing property of the curve is also verified. The proposed basis functions are suitable for the description of closed curves and surfaces with
C
∞
continuity at all of their points.</description><identifier>ISSN: 0167-8396</identifier><identifier>EISSN: 1879-2332</identifier><identifier>DOI: 10.1016/j.cagd.2009.02.002</identifier><identifier>CODEN: CAGDEX</identifier><language>eng</language><publisher>Kidlington: Elsevier B.V</publisher><subject>Applied sciences ; Closed curve ; Closed surface ; Computer aided design ; Computer science; control theory; systems ; Degree elevation ; Exact sciences and technology ; Mechanical engineering. Machine design ; Software ; Trigonometric basis function ; Variation diminishing</subject><ispartof>Computer aided geometric design, 2009-06, Vol.26 (5), p.528-546</ispartof><rights>2009 Elsevier B.V.</rights><rights>2009 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c393t-87899521a48dcaffae4b82f2745c92e4dc65b7492d68a2eaead779db6cd90a373</citedby><cites>FETCH-LOGICAL-c393t-87899521a48dcaffae4b82f2745c92e4dc65b7492d68a2eaead779db6cd90a373</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.cagd.2009.02.002$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=21506918$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Róth, Ágoston</creatorcontrib><creatorcontrib>Juhász, Imre</creatorcontrib><creatorcontrib>Schicho, Josef</creatorcontrib><creatorcontrib>Hoffmann, Miklós</creatorcontrib><title>A cyclic basis for closed curve and surface modeling</title><title>Computer aided geometric design</title><description>We define a cyclic basis for the vectorspace of truncated Fourier series. The basis has several nice properties, such as positivity, summing to 1, that are often required in computer aided design, and that are used by designers in order to control curves by manipulating control points. Our curves have cyclic symmetry, i.e. the control points can be cyclically arranged and the curve does not change when the control points are cyclically permuted. We provide an explicit formula for the elevation of the degree from
n to
n
+
r
,
r
⩾
1
and prove that the control polygon of the degree elevated curve converges to the curve itself if
r tends to infinity. Variation diminishing property of the curve is also verified. The proposed basis functions are suitable for the description of closed curves and surfaces with
C
∞
continuity at all of their points.</description><subject>Applied sciences</subject><subject>Closed curve</subject><subject>Closed surface</subject><subject>Computer aided design</subject><subject>Computer science; control theory; systems</subject><subject>Degree elevation</subject><subject>Exact sciences and technology</subject><subject>Mechanical engineering. Machine design</subject><subject>Software</subject><subject>Trigonometric basis function</subject><subject>Variation diminishing</subject><issn>0167-8396</issn><issn>1879-2332</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><recordid>eNp90DtLA0EQwPFFFIyPL2B1jVrdua_sA2yC-IKAjdbLZHYubLjc6W4i5Nt7IWJpNc1vZuDP2JXgjeDC3K0ahGVsJOe-4bLhXB6xiXDW11IpecwmI7K1U96csrNSVnwUwpsJ07MKd9glrBZQUqnaIVfYDYVihdv8TRX0sSrb3AJStR4idalfXrCTFrpCl7_znH08Pb4_vNTzt-fXh9m8RuXVpnbWeT-VArSLCG0LpBdOttLqKXpJOqKZLqz2MhoHkoAgWuvjwmD0HJRV5-z2cPczD19bKpuwTgWp66CnYVuC58pIw7UZ5c2_UmktrNNqhPIAMQ-lZGrDZ05ryLsgeNinDKuwTxn2KQOXYQw1Ll3_XoeC0LUZekzlb1OKKTdeuNHdHxyNUb4T5VAwUY8UUybchDik_978AAjjiF0</recordid><startdate>20090601</startdate><enddate>20090601</enddate><creator>Róth, Ágoston</creator><creator>Juhász, Imre</creator><creator>Schicho, Josef</creator><creator>Hoffmann, Miklós</creator><general>Elsevier B.V</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20090601</creationdate><title>A cyclic basis for closed curve and surface modeling</title><author>Róth, Ágoston ; Juhász, Imre ; Schicho, Josef ; Hoffmann, Miklós</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c393t-87899521a48dcaffae4b82f2745c92e4dc65b7492d68a2eaead779db6cd90a373</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Applied sciences</topic><topic>Closed curve</topic><topic>Closed surface</topic><topic>Computer aided design</topic><topic>Computer science; control theory; systems</topic><topic>Degree elevation</topic><topic>Exact sciences and technology</topic><topic>Mechanical engineering. Machine design</topic><topic>Software</topic><topic>Trigonometric basis function</topic><topic>Variation diminishing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Róth, Ágoston</creatorcontrib><creatorcontrib>Juhász, Imre</creatorcontrib><creatorcontrib>Schicho, Josef</creatorcontrib><creatorcontrib>Hoffmann, Miklós</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</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>Róth, Ágoston</au><au>Juhász, Imre</au><au>Schicho, Josef</au><au>Hoffmann, Miklós</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A cyclic basis for closed curve and surface modeling</atitle><jtitle>Computer aided geometric design</jtitle><date>2009-06-01</date><risdate>2009</risdate><volume>26</volume><issue>5</issue><spage>528</spage><epage>546</epage><pages>528-546</pages><issn>0167-8396</issn><eissn>1879-2332</eissn><coden>CAGDEX</coden><abstract>We define a cyclic basis for the vectorspace of truncated Fourier series. The basis has several nice properties, such as positivity, summing to 1, that are often required in computer aided design, and that are used by designers in order to control curves by manipulating control points. Our curves have cyclic symmetry, i.e. the control points can be cyclically arranged and the curve does not change when the control points are cyclically permuted. We provide an explicit formula for the elevation of the degree from
n to
n
+
r
,
r
⩾
1
and prove that the control polygon of the degree elevated curve converges to the curve itself if
r tends to infinity. Variation diminishing property of the curve is also verified. The proposed basis functions are suitable for the description of closed curves and surfaces with
C
∞
continuity at all of their points.</abstract><cop>Kidlington</cop><pub>Elsevier B.V</pub><doi>10.1016/j.cagd.2009.02.002</doi><tpages>19</tpages></addata></record> |
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| ispartof | Computer aided geometric design, 2009-06, Vol.26 (5), p.528-546 |
| issn | 0167-8396 1879-2332 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_903626046 |
| source | Access via ScienceDirect (Elsevier) |
| subjects | Applied sciences Closed curve Closed surface Computer aided design Computer science control theory systems Degree elevation Exact sciences and technology Mechanical engineering. Machine design Software Trigonometric basis function Variation diminishing |
| title | A cyclic basis for closed curve and surface modeling |
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