Continuity conditions for tensor product Q-Bézier surfaces of degree (m,n)
Based on a kind of Q-Bézier surfaces with shape parameters, the basic properties of the surfaces and the geometric significance of the shape parameters are analyzed. To resolve the problem of shape control and adjustment of composite surfaces, the continuity conditions for Q-Bézier surfaces of degre...
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| Veröffentlicht in: | Computation and applied mathematics 2018-09, Vol.37 (4), p.4237-4258 |
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| container_title | Computation and applied mathematics |
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| creator | Hu, Gang Bo, Cuicui Qin, Xinqiang |
| description | Based on a kind of Q-Bézier surfaces with shape parameters, the basic properties of the surfaces and the geometric significance of the shape parameters are analyzed. To resolve the problem of shape control and adjustment of composite surfaces, the continuity conditions for Q-Bézier surfaces of degree (
m
,
n
) are investigated. Taking advantage of the terminal properties of generalized Bernstein basis functions, we derive the conditions of
G
1
and
G
2
continuity between two adjacent Q-Bézier surfaces. In addition, the specific steps of smooth continuity between Q-Bézier surfaces and the shape adjustment function of shape parameters for composite surfaces are discussed. The modeling examples show that the proposed smooth continuity conditions are not only intuitive and easy to implement, but also greatly enhance the shape adjustability, which provide a useful method for constructing complex surfaces in engineering design. |
| doi_str_mv | 10.1007/s40314-017-0568-0 |
| format | Article |
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m
,
n
) are investigated. Taking advantage of the terminal properties of generalized Bernstein basis functions, we derive the conditions of
G
1
and
G
2
continuity between two adjacent Q-Bézier surfaces. In addition, the specific steps of smooth continuity between Q-Bézier surfaces and the shape adjustment function of shape parameters for composite surfaces are discussed. The modeling examples show that the proposed smooth continuity conditions are not only intuitive and easy to implement, but also greatly enhance the shape adjustability, which provide a useful method for constructing complex surfaces in engineering design.</description><identifier>ISSN: 0101-8205</identifier><identifier>ISSN: 2238-3603</identifier><identifier>EISSN: 1807-0302</identifier><identifier>DOI: 10.1007/s40314-017-0568-0</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Applications of Mathematics ; Applied physics ; Basis functions ; Computational mathematics ; Computational Mathematics and Numerical Analysis ; CONTROL ; DESIGN ; Design engineering ; FUNCTIONS ; GEOMETRY ; Mathematical Applications in Computer Science ; Mathematical Applications in the Physical Sciences ; MATHEMATICAL METHODS AND COMPUTING ; Mathematics ; Mathematics and Statistics ; Parameters ; SHAPE ; Shape control ; SIMULATION ; SURFACES ; TENSORS</subject><ispartof>Computation and applied mathematics, 2018-09, Vol.37 (4), p.4237-4258</ispartof><rights>SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2018</rights><rights>Copyright Springer Science & Business Media 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c3250-80fdb68750416af8e81f7cd916969433a13db48cb4f1716ffa7c07a9acd73d3f3</citedby><cites>FETCH-LOGICAL-c3250-80fdb68750416af8e81f7cd916969433a13db48cb4f1716ffa7c07a9acd73d3f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s40314-017-0568-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40314-017-0568-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,881,27901,27902,41464,42533,51294</link.rule.ids><backlink>$$Uhttps://www.osti.gov/biblio/22783744$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Hu, Gang</creatorcontrib><creatorcontrib>Bo, Cuicui</creatorcontrib><creatorcontrib>Qin, Xinqiang</creatorcontrib><title>Continuity conditions for tensor product Q-Bézier surfaces of degree (m,n)</title><title>Computation and applied mathematics</title><addtitle>Comp. Appl. Math</addtitle><description>Based on a kind of Q-Bézier surfaces with shape parameters, the basic properties of the surfaces and the geometric significance of the shape parameters are analyzed. To resolve the problem of shape control and adjustment of composite surfaces, the continuity conditions for Q-Bézier surfaces of degree (
m
,
n
) are investigated. Taking advantage of the terminal properties of generalized Bernstein basis functions, we derive the conditions of
G
1
and
G
2
continuity between two adjacent Q-Bézier surfaces. In addition, the specific steps of smooth continuity between Q-Bézier surfaces and the shape adjustment function of shape parameters for composite surfaces are discussed. The modeling examples show that the proposed smooth continuity conditions are not only intuitive and easy to implement, but also greatly enhance the shape adjustability, which provide a useful method for constructing complex surfaces in engineering design.</description><subject>Applications of Mathematics</subject><subject>Applied physics</subject><subject>Basis functions</subject><subject>Computational mathematics</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>CONTROL</subject><subject>DESIGN</subject><subject>Design engineering</subject><subject>FUNCTIONS</subject><subject>GEOMETRY</subject><subject>Mathematical Applications in Computer Science</subject><subject>Mathematical Applications in the Physical Sciences</subject><subject>MATHEMATICAL METHODS AND COMPUTING</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Parameters</subject><subject>SHAPE</subject><subject>Shape control</subject><subject>SIMULATION</subject><subject>SURFACES</subject><subject>TENSORS</subject><issn>0101-8205</issn><issn>2238-3603</issn><issn>1807-0302</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kM1KAzEUhYMoWLQP4G7AjYLRm0kmySy1-IcFEXQd0kxSp9ikJplFfSOfwxczpUJX3s3hwjmHez-ETghcEgBxlRhQwjAQgaHhEsMeGhEJZaNQ76MRECBY1tAconFKCyjDAEjNR-hpEnzu_dDndWWC7_rcB58qF2KVrU9FVjF0g8nVC775-f7qbazSEJ02NlXBVZ2dR2urs-WFPz9GB05_JDv-0yP0dnf7OnnA0-f7x8n1FBtaN4AluG7GpWiAEa6dtJI4YbqW8Ja3jFJNaDdj0syYI4Jw57QwIHSrTSdoRx09Qqfb3pByr5LpszXv5XhvTVZ1LSQVjO1c5YHPwaasFmGIvhymamgbziVroLjI1mViSClap1axX-q4VgTUBq7awlUFrtrAVZtMvc2k4vVzG3fN_4d-Aedqeu0</recordid><startdate>20180901</startdate><enddate>20180901</enddate><creator>Hu, Gang</creator><creator>Bo, Cuicui</creator><creator>Qin, Xinqiang</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>OTOTI</scope></search><sort><creationdate>20180901</creationdate><title>Continuity conditions for tensor product Q-Bézier surfaces of degree (m,n)</title><author>Hu, Gang ; Bo, Cuicui ; Qin, Xinqiang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3250-80fdb68750416af8e81f7cd916969433a13db48cb4f1716ffa7c07a9acd73d3f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Applications of Mathematics</topic><topic>Applied physics</topic><topic>Basis functions</topic><topic>Computational mathematics</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>CONTROL</topic><topic>DESIGN</topic><topic>Design engineering</topic><topic>FUNCTIONS</topic><topic>GEOMETRY</topic><topic>Mathematical Applications in Computer Science</topic><topic>Mathematical Applications in the Physical Sciences</topic><topic>MATHEMATICAL METHODS AND COMPUTING</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Parameters</topic><topic>SHAPE</topic><topic>Shape control</topic><topic>SIMULATION</topic><topic>SURFACES</topic><topic>TENSORS</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hu, Gang</creatorcontrib><creatorcontrib>Bo, Cuicui</creatorcontrib><creatorcontrib>Qin, Xinqiang</creatorcontrib><collection>CrossRef</collection><collection>OSTI.GOV</collection><jtitle>Computation and applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hu, Gang</au><au>Bo, Cuicui</au><au>Qin, Xinqiang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Continuity conditions for tensor product Q-Bézier surfaces of degree (m,n)</atitle><jtitle>Computation and applied mathematics</jtitle><stitle>Comp. Appl. Math</stitle><date>2018-09-01</date><risdate>2018</risdate><volume>37</volume><issue>4</issue><spage>4237</spage><epage>4258</epage><pages>4237-4258</pages><issn>0101-8205</issn><issn>2238-3603</issn><eissn>1807-0302</eissn><abstract>Based on a kind of Q-Bézier surfaces with shape parameters, the basic properties of the surfaces and the geometric significance of the shape parameters are analyzed. To resolve the problem of shape control and adjustment of composite surfaces, the continuity conditions for Q-Bézier surfaces of degree (
m
,
n
) are investigated. Taking advantage of the terminal properties of generalized Bernstein basis functions, we derive the conditions of
G
1
and
G
2
continuity between two adjacent Q-Bézier surfaces. In addition, the specific steps of smooth continuity between Q-Bézier surfaces and the shape adjustment function of shape parameters for composite surfaces are discussed. The modeling examples show that the proposed smooth continuity conditions are not only intuitive and easy to implement, but also greatly enhance the shape adjustability, which provide a useful method for constructing complex surfaces in engineering design.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s40314-017-0568-0</doi><tpages>22</tpages></addata></record> |
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| subjects | Applications of Mathematics Applied physics Basis functions Computational mathematics Computational Mathematics and Numerical Analysis CONTROL DESIGN Design engineering FUNCTIONS GEOMETRY Mathematical Applications in Computer Science Mathematical Applications in the Physical Sciences MATHEMATICAL METHODS AND COMPUTING Mathematics Mathematics and Statistics Parameters SHAPE Shape control SIMULATION SURFACES TENSORS |
| title | Continuity conditions for tensor product Q-Bézier surfaces of degree (m,n) |
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