Positivity-preserving interpolation of positive data by rational cubics

Malik Zawwar Hussain; Muhammad Sarfraz

doi:10.1016/j.cam.2007.05.023

Positivity-preserving interpolation of positive data by rational cubics

Malik Zawwar Hussain^*
, Muhammad Sarfraz

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

92 Scopus citations

Abstract

This work is a contribution towards the graphical display of data when it is positive. The data are required to be represented in such a way that its visual display looks smooth and pleasant, its positive shape is preserved everywhere and the computation cost is economical. A C¹ piecewise rational cubic function, in its most general form, has been utilized for this objective. The method is implemented for the 1D data initially and then it is extended to an interpolating rational bicubic form for the data arranged over a rectangular grid. Simple sufficient conditions are developed on the free parameters in the description of the rational function to visualize the positive data in the form of positive curves and surfaces.

Original language	English
Pages (from-to)	446-458
Number of pages	13
Journal	Journal of Computational and Applied Mathematics
Volume	218
Issue number	2
DOIs	https://doi.org/10.1016/j.cam.2007.05.023
State	Published - 1 Sep 2008

Bibliographical note

Funding Information:
The authors are pleased to acknowledge the anonymous referees whose valuable and healthy comments made this manuscript more useful. The second author acknowledges King Fahd University of Petroleum and Minerals for support of this work against the Project # ICS/REVERSE ENG./312.

Keywords

Free parameters
Positivity
Rational bicubics
Rational cubics
Visualization

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

Access to Document

10.1016/j.cam.2007.05.023

Cite this

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title = "Positivity-preserving interpolation of positive data by rational cubics",

abstract = "This work is a contribution towards the graphical display of data when it is positive. The data are required to be represented in such a way that its visual display looks smooth and pleasant, its positive shape is preserved everywhere and the computation cost is economical. A C1 piecewise rational cubic function, in its most general form, has been utilized for this objective. The method is implemented for the 1D data initially and then it is extended to an interpolating rational bicubic form for the data arranged over a rectangular grid. Simple sufficient conditions are developed on the free parameters in the description of the rational function to visualize the positive data in the form of positive curves and surfaces.",

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N2 - This work is a contribution towards the graphical display of data when it is positive. The data are required to be represented in such a way that its visual display looks smooth and pleasant, its positive shape is preserved everywhere and the computation cost is economical. A C1 piecewise rational cubic function, in its most general form, has been utilized for this objective. The method is implemented for the 1D data initially and then it is extended to an interpolating rational bicubic form for the data arranged over a rectangular grid. Simple sufficient conditions are developed on the free parameters in the description of the rational function to visualize the positive data in the form of positive curves and surfaces.

AB - This work is a contribution towards the graphical display of data when it is positive. The data are required to be represented in such a way that its visual display looks smooth and pleasant, its positive shape is preserved everywhere and the computation cost is economical. A C1 piecewise rational cubic function, in its most general form, has been utilized for this objective. The method is implemented for the 1D data initially and then it is extended to an interpolating rational bicubic form for the data arranged over a rectangular grid. Simple sufficient conditions are developed on the free parameters in the description of the rational function to visualize the positive data in the form of positive curves and surfaces.

KW - Free parameters

KW - Positivity

KW - Rational bicubics

KW - Rational cubics

KW - Visualization

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JF - Journal of Computational and Applied Mathematics

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ER -

Positivity-preserving interpolation of positive data by rational cubics

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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