Quartic Rational Said-Ball-Like Basis with Tension Shape Parameters and Its Application
Four new quartic rational Said-Ball-like basis functions, which include the cubic Said-Ball basis functions as a special case, are constructed in this paper. The new basis is applied to generate a class of C1 continuous quartic rational Hermite interpolation splines with local tension shape paramete...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/857840 |
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| author | Yuanpeng Zhu Xuli Han Shengjun Liu |
| author_facet | Yuanpeng Zhu Xuli Han Shengjun Liu |
| author_sort | Yuanpeng Zhu |
| collection | DOAJ |
| description | Four new quartic rational Said-Ball-like basis functions, which include the cubic Said-Ball basis functions as a special case, are constructed in this paper. The new basis is applied to generate a class of C1 continuous quartic rational Hermite interpolation splines with local tension shape parameters. The error estimate expression of the proposed interpolant is given and the sufficient conditions are derived for constructing a C1 positivity- or monotonicity- preserving interpolation spline. In addition, we extend the quartic rational Said-Ball-like basis to a triangular domain which has three tension shape parameters and includes the cubic triangular Said-Ball basis as a special case. In order to compute the corresponding patch stably and efficiently, a new de Casteljau-type algorithm is developed. Moreover, the G1 continuous conditions are deduced for the joining of two patches. |
| format | Article |
| id | doaj-art-337f8ad1f1624a95a248f91797a281f2 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-337f8ad1f1624a95a248f91797a281f22025-02-03T01:23:49ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/857840857840Quartic Rational Said-Ball-Like Basis with Tension Shape Parameters and Its ApplicationYuanpeng Zhu0Xuli Han1Shengjun Liu2School of Mathematics and Statistics, Central South University, Changsha 410083, ChinaSchool of Mathematics and Statistics, Central South University, Changsha 410083, ChinaSchool of Mathematics and Statistics, Central South University, Changsha 410083, ChinaFour new quartic rational Said-Ball-like basis functions, which include the cubic Said-Ball basis functions as a special case, are constructed in this paper. The new basis is applied to generate a class of C1 continuous quartic rational Hermite interpolation splines with local tension shape parameters. The error estimate expression of the proposed interpolant is given and the sufficient conditions are derived for constructing a C1 positivity- or monotonicity- preserving interpolation spline. In addition, we extend the quartic rational Said-Ball-like basis to a triangular domain which has three tension shape parameters and includes the cubic triangular Said-Ball basis as a special case. In order to compute the corresponding patch stably and efficiently, a new de Casteljau-type algorithm is developed. Moreover, the G1 continuous conditions are deduced for the joining of two patches.http://dx.doi.org/10.1155/2014/857840 |
| spellingShingle | Yuanpeng Zhu Xuli Han Shengjun Liu Quartic Rational Said-Ball-Like Basis with Tension Shape Parameters and Its Application Journal of Applied Mathematics |
| title | Quartic Rational Said-Ball-Like Basis with Tension Shape Parameters and Its Application |
| title_full | Quartic Rational Said-Ball-Like Basis with Tension Shape Parameters and Its Application |
| title_fullStr | Quartic Rational Said-Ball-Like Basis with Tension Shape Parameters and Its Application |
| title_full_unstemmed | Quartic Rational Said-Ball-Like Basis with Tension Shape Parameters and Its Application |
| title_short | Quartic Rational Said-Ball-Like Basis with Tension Shape Parameters and Its Application |
| title_sort | quartic rational said ball like basis with tension shape parameters and its application |
| url | http://dx.doi.org/10.1155/2014/857840 |
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