Almost strictly total positivity of NUAT B-spline basis
Total positivity of spline basis has been well known in the theory of computer aided geometry design, which is highly related with good shape preserving property. Almost strictly total positivity is stronger, which could determine the positive minors while the other is zero. In this paper, a geometr...
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| Published in | Science China. Information sciences Vol. 56; no. 9; pp. 46 - 51 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.09.2013
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1674-733X 1869-1919 |
| DOI | 10.1007/s11432-013-4995-2 |
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| Abstract | Total positivity of spline basis has been well known in the theory of computer aided geometry design, which is highly related with good shape preserving property. Almost strictly total positivity is stronger, which could determine the positive minors while the other is zero. In this paper, a geometrical approach is proposed to prove the collection matrices of NUAT B-spline basis are almost strictly totally positive. In this paper, knot insertion algorithm combined with coefficient variation of NUAT B-spline function, we put forward an intuitive and geometrical method. |
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| AbstractList | Total positivity of spline basis has been well known in the theory of computer aided geometry design, which is highly related with good shape preserving property. Almost strictly total positivity is stronger, which could determine the positive minors while the other is zero. In this paper, a geometrical approach is proposed to prove the collection matrices of NUAT B-spline basis are almost strictly totally positive. In this paper, knot insertion algorithm combined with coefficient variation of NUAT B-spline function, we put forward an intuitive and geometrical method. |
| Author | WEI WeiLi WANG GuoZhao |
| AuthorAffiliation | Mathematics Department, Zhejiang University, Hangzhou 310027, China |
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| Cites_doi | 10.1016/j.cad.2012.10.022 10.1016/0024-3795(87)90313-2 10.1090/S0025-5718-1985-0804938-2 10.1016/j.cagd.2003.10.002 10.1007/BF02145387 10.1512/iumj.1976.25.25043 10.1016/B978-0-12-460515-2.50027-5 |
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| Copyright | Science China Press and Springer-Verlag Berlin Heidelberg 2013 Science China Press and Springer-Verlag Berlin Heidelberg 2013. |
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| Keywords | ASTP NUAT B-spline basis knot insertion algorithm coefficient variation |
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| Notes | Total positivity of spline basis has been well known in the theory of computer aided geometry design, which is highly related with good shape preserving property. Almost strictly total positivity is stronger, which could determine the positive minors while the other is zero. In this paper, a geometrical approach is proposed to prove the collection matrices of NUAT B-spline basis are almost strictly totally positive. In this paper, knot insertion algorithm combined with coefficient variation of NUAT B-spline function, we put forward an intuitive and geometrical method. WEI WeiLi ＆ WANG GuoZhao Mathematics Department, Zhejiang University, Hangzhou 310027, China 11-5847/TP ASTP; NUAT B-spline basis; knot insertion algorithm; coefficient variation ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 |
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| References | De Boor, DeVore (CR5) 1985; 172 De Boor (CR6) 1976; 25 Xu, Mourrain, Duvigneau (CR3) 2013; 45 Gasca, Micchelli, Pena (CR2) 1992; 2 Wang, Chen, Zhou (CR1) 2004; 21 Goodman (CR4) 1989 Ando (CR8) 1987; 90 Wei, Wang (CR7) 2012; 9 W L Wei (4995_CR7) 2012; 9 G Xu (4995_CR3) 2013; 45 C Boor De (4995_CR6) 1976; 25 T Goodman (4995_CR4) 1989 T Ando (4995_CR8) 1987; 90 G Z Wang (4995_CR1) 2004; 21 M Gasca (4995_CR2) 1992; 2 C Boor De (4995_CR5) 1985; 172 |
| References_xml | – volume: 45 start-page: 395 year: 2013 end-page: 404 ident: CR3 article-title: Analysis-suitable volume parametrization of multi-block computational domain in isogeometric applications publication-title: Comput Aid Des doi: 10.1016/j.cad.2012.10.022 – volume: 90 start-page: 165 year: 1987 end-page: 219 ident: CR8 article-title: Totally positive matrices publication-title: Linear Algebra Appl doi: 10.1016/0024-3795(87)90313-2 – volume: 172 start-page: 497 year: 1985 end-page: 594 ident: CR5 article-title: A geometric Proof of total positivity for spline interpolation publication-title: Math Comput doi: 10.1090/S0025-5718-1985-0804938-2 – volume: 21 start-page: 193 year: 2004 end-page: 205 ident: CR1 article-title: NUAT B-spline curves publication-title: Comput Aided Geom Design doi: 10.1016/j.cagd.2003.10.002 – volume: 9 start-page: 731 year: 2012 end-page: 735 ident: CR7 article-title: Total positivity of NUAHT B-spline basis publication-title: J Inf Comput Sci – volume: 2 start-page: 225 year: 1992 end-page: 236 ident: CR2 article-title: Almost strictly totally positive matrices publication-title: Numer Algorithms doi: 10.1007/BF02145387 – start-page: 333 year: 1989 end-page: 357 ident: CR4 publication-title: Shape Preserving Representations in Mathematical Methods in Computer Aided Geometric Design – volume: 25 start-page: 541 year: 1976 end-page: 551 ident: CR6 article-title: Total positivity of the spline collocation matrix publication-title: Indiana Univ J Math doi: 10.1512/iumj.1976.25.25043 – volume: 21 start-page: 193 year: 2004 ident: 4995_CR1 publication-title: Comput Aided Geom Design doi: 10.1016/j.cagd.2003.10.002 – volume: 90 start-page: 165 year: 1987 ident: 4995_CR8 publication-title: Linear Algebra Appl doi: 10.1016/0024-3795(87)90313-2 – volume: 25 start-page: 541 year: 1976 ident: 4995_CR6 publication-title: Indiana Univ J Math doi: 10.1512/iumj.1976.25.25043 – volume: 172 start-page: 497 year: 1985 ident: 4995_CR5 publication-title: Math Comput doi: 10.1090/S0025-5718-1985-0804938-2 – volume: 9 start-page: 731 year: 2012 ident: 4995_CR7 publication-title: J Inf Comput Sci – volume: 2 start-page: 225 year: 1992 ident: 4995_CR2 publication-title: Numer Algorithms doi: 10.1007/BF02145387 – start-page: 333 volume-title: Shape Preserving Representations in Mathematical Methods in Computer Aided Geometric Design year: 1989 ident: 4995_CR4 doi: 10.1016/B978-0-12-460515-2.50027-5 – volume: 45 start-page: 395 year: 2013 ident: 4995_CR3 publication-title: Comput Aid Des doi: 10.1016/j.cad.2012.10.022 |
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| SubjectTerms | Algorithms B spline functions B样条函数 B样条基 CAD China Coefficient of variation Collection Computer aided design Computer Science Information Systems and Communication Service Knot insertion Mathematical analysis Mathematical models Research Paper Splines 几何方法 变异系数 插入算法 未成年人 计算机辅助几何设计 阳性 |
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| Title | Almost strictly total positivity of NUAT B-spline basis |
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