Range restricted positivity-preserving G1 scattered data interpolation

The construction of a range restricted bivariate 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 th...

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Main Authors: Mt Piah, Abd Rahni, Saaban, Azizan, Abd Majid, Ahmad
Format: Conference or Workshop Item
Language:English
Published: 2006
Subjects:
Online Access:https://repo.uum.edu.my/id/eprint/4337/1/Ab_Ran.pdf
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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 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 quartic Bézier triangular patches are always positive and satisfy G1 continuity conditions. The gradients at the data sites are then calculated (and modified if necessary) to ensure that these conditions are satisfied. Its construction is local and easily extended to include as upper and lower constraints to the interpolating surfaces of the form z = C(x,y) where C is a polynomial of degree less or equal to 4. Moreover, G1 piecewise polynomial surfaces consisting of polynomial pieces of the form z = C(x,y) on the triangulation of the data sites are also admissible constraints. A number of examples are presented.
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spelling uum-43372011-12-27T01:40:18Z https://repo.uum.edu.my/id/eprint/4337/ Range restricted positivity-preserving G1 scattered data interpolation Mt Piah, Abd Rahni Saaban, Azizan Abd Majid, Ahmad QA Mathematics The construction of a range restricted bivariate 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 quartic Bézier triangular patches are always positive and satisfy G1 continuity conditions. The gradients at the data sites are then calculated (and modified if necessary) to ensure that these conditions are satisfied. Its construction is local and easily extended to include as upper and lower constraints to the interpolating surfaces of the form z = C(x,y) where C is a polynomial of degree less or equal to 4. Moreover, G1 piecewise polynomial surfaces consisting of polynomial pieces of the form z = C(x,y) on the triangulation of the data sites are also admissible constraints. A number of examples are presented. 2006 Conference or Workshop Item NonPeerReviewed application/pdf en https://repo.uum.edu.my/id/eprint/4337/1/Ab_Ran.pdf Mt Piah, Abd Rahni and Saaban, Azizan and Abd Majid, Ahmad (2006) Range restricted positivity-preserving G1 scattered data interpolation. In: 2nd IMT-GT Regional Conference on Mathematics, Statistics and Applications, June 13-15, 2006, Universiti Sains Malaysia, Penang. (Unpublished) http://math.usm.my/research/OnlineProc/index.html
spellingShingle QA Mathematics
Mt Piah, Abd Rahni
Saaban, Azizan
Abd Majid, Ahmad
Range restricted positivity-preserving G1 scattered data interpolation
title Range restricted positivity-preserving G1 scattered data interpolation
title_full Range restricted positivity-preserving G1 scattered data interpolation
title_fullStr Range restricted positivity-preserving G1 scattered data interpolation
title_full_unstemmed Range restricted positivity-preserving G1 scattered data interpolation
title_short Range restricted positivity-preserving G1 scattered data interpolation
title_sort range restricted positivity preserving g1 scattered data interpolation
topic QA Mathematics
url https://repo.uum.edu.my/id/eprint/4337/1/Ab_Ran.pdf
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