Range restricted positivity-preserving scattered data interpolation
The construction of a range restricted bivariate C1( or G1) interpolant to scattered data is considered in which the interpolant is positive everywhere if the original data are positive. This study is motivated by earlier work in which sufficient conditions are derived on Bézier points in order to...
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| Format: | Article |
| Language: | English |
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Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia
2006
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| Online Access: | https://repo.uum.edu.my/id/eprint/4334/1/19-63.pdf |
| _version_ | 1825740302779940864 |
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| author | Mt Piah, Abd Rahni Saaban, Azizan Abd Majid, Ahmad |
| author_facet | Mt Piah, Abd Rahni Saaban, Azizan Abd Majid, Ahmad |
| author_sort | Mt Piah, Abd Rahni |
| collection | UUM |
| description | The construction of a range restricted bivariate C1( or G1) interpolant to scattered data is considered in which the
interpolant is positive everywhere if the original data are positive. This study is motivated by earlier work in which
sufficient conditions are derived on Bézier points in order to ensure that surfaces comprising cubic Bézier triangular
patches are always positive and satisfy C1 continuity conditions. In the current work, simpler and more relaxed
conditions are derived on the Bézier points. The gradients at the data sites are then calculated (and modified if
necessary) to ensure that these conditions are satisfied. Each triangular patch of the interpolating surface is formed as a convex combination of three quartic Bézier triangular patches.Its construction is local and easily extended to include as upper and lower constraints to the interpolant surfaces of the form z = P(x,y) where P is a polynomial of degree less or equal to 4. Moreover, C1 ( or G1 ) piecewise polynomial surfaces consisting of polynomial pieces of the form z = P(x,y) on the triangulation of the data sites are also admissible constraints. A number of examples are presented. |
| first_indexed | 2024-07-04T05:24:48Z |
| format | Article |
| id | uum-4334 |
| institution | Universiti Utara Malaysia |
| language | English |
| last_indexed | 2024-07-04T05:24:48Z |
| publishDate | 2006 |
| publisher | Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia |
| record_format | eprints |
| spelling | uum-43342012-02-16T08:22:14Z https://repo.uum.edu.my/id/eprint/4334/ Range restricted positivity-preserving scattered data interpolation Mt Piah, Abd Rahni Saaban, Azizan Abd Majid, Ahmad QA Mathematics The construction of a range restricted bivariate C1( or G1) interpolant to scattered data is considered in which the interpolant is positive everywhere if the original data are positive. This study is motivated by earlier work in which sufficient conditions are derived on Bézier points in order to ensure that surfaces comprising cubic Bézier triangular patches are always positive and satisfy C1 continuity conditions. In the current work, simpler and more relaxed conditions are derived on the Bézier points. The gradients at the data sites are then calculated (and modified if necessary) to ensure that these conditions are satisfied. Each triangular patch of the interpolating surface is formed as a convex combination of three quartic Bézier triangular patches.Its construction is local and easily extended to include as upper and lower constraints to the interpolant surfaces of the form z = P(x,y) where P is a polynomial of degree less or equal to 4. Moreover, C1 ( or G1 ) piecewise polynomial surfaces consisting of polynomial pieces of the form z = P(x,y) on the triangulation of the data sites are also admissible constraints. A number of examples are presented. Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia 2006-07 Article PeerReviewed application/pdf en https://repo.uum.edu.my/id/eprint/4334/1/19-63.pdf Mt Piah, Abd Rahni and Saaban, Azizan and Abd Majid, Ahmad (2006) Range restricted positivity-preserving scattered data interpolation. Journal of Fundamental Sciences, 2 (1-2). pp. 63-75. ISSN 1823-626X http://www.ibnusina.utm.my/jfs |
| spellingShingle | QA Mathematics Mt Piah, Abd Rahni Saaban, Azizan Abd Majid, Ahmad Range restricted positivity-preserving scattered data interpolation |
| title | Range restricted positivity-preserving scattered data interpolation |
| title_full | Range restricted positivity-preserving scattered data interpolation |
| title_fullStr | Range restricted positivity-preserving scattered data interpolation |
| title_full_unstemmed | Range restricted positivity-preserving scattered data interpolation |
| title_short | Range restricted positivity-preserving scattered data interpolation |
| title_sort | range restricted positivity preserving scattered data interpolation |
| topic | QA Mathematics |
| url | https://repo.uum.edu.my/id/eprint/4334/1/19-63.pdf |
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