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Range restricted positivity-preserving scattered data interpolation


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

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Abstract

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.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: College of Arts and Sciences
Depositing User: Mrs. Norazmilah Yaakub
Date Deposited: 16 Feb 2012 08:22
Last Modified: 16 Feb 2012 08:22
URI: http://repo.uum.edu.my/id/eprint/4334

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