NEW RATIONAL QUARTIC SPLINE FOR POSITIVITY PRESERVING INTERPOLATION

The work on interpolation schemes by previous researches had limitations such as, the inability to produce positive interpolating curves on the entire given intervals, interpolating curves and surfaces that are not smooth and visually pleasing. Smoothness and visually pleasing curves are importan...

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Main Author: HARIM, NOOR ADILLA
Format: Thesis
Language: English
Institution: Universiti Teknologi Petronas
Record Id / ISBN-0: utp-utpedia.20525 /
Published: 2020
Subjects:
Q Science (General)
Online Access: http://utpedia.utp.edu.my/20525/1/Noor%20Adilla%20Harim_18001410.pdf
http://utpedia.utp.edu.my/20525/
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spelling utp-utpedia.205252021-08-30T16:29:45Z http://utpedia.utp.edu.my/20525/ NEW RATIONAL QUARTIC SPLINE FOR POSITIVITY PRESERVING INTERPOLATION HARIM, NOOR ADILLA Q Science (General) The work on interpolation schemes by previous researches had limitations such as, the inability to produce positive interpolating curves on the entire given intervals, interpolating curves and surfaces that are not smooth and visually pleasing. Smoothness and visually pleasing curves are important for computer graphics display. Hence, these schemes are not suitable for shape preserving interpolation. In this study, a new rational quartic spline function with three parameters of the form quartic numerator and quadratic denominator is proposed to overcome these problems. These free parameters can be used to modify the final shape of the interpolating curve as well as to reduce the interpolation error. The proposed rational spline has a first order of parametric continuity, C1. Furthermore, the proposed rational spline also can achieve C2 continuity without the need to solve any tri-diagonal systems of linear equations unlike some other splines that need linear systems of equation to be solved. The proposed scheme is tested for 2D data interpolation as well as positivity-preserving interpolation. The main advantage of the proposed scheme is that it will produce positive curves everywhere for positive datasets unlike other schemes. Furthermore, an error analysis by calculating the absolute error and root mean square error (RMSE) indicates that the proposed scheme is better than some existing schemes. 2020-09 Thesis NonPeerReviewed application/pdf en http://utpedia.utp.edu.my/20525/1/Noor%20Adilla%20Harim_18001410.pdf HARIM, NOOR ADILLA (2020) NEW RATIONAL QUARTIC SPLINE FOR POSITIVITY PRESERVING INTERPOLATION. Masters thesis, Universiti Teknologi PETRONAS.
institution Universiti Teknologi Petronas
collection UTPedia
language English
topic Q Science (General)
spellingShingle Q Science (General)
HARIM, NOOR ADILLA
NEW RATIONAL QUARTIC SPLINE FOR POSITIVITY PRESERVING INTERPOLATION
description The work on interpolation schemes by previous researches had limitations such as, the inability to produce positive interpolating curves on the entire given intervals, interpolating curves and surfaces that are not smooth and visually pleasing. Smoothness and visually pleasing curves are important for computer graphics display. Hence, these schemes are not suitable for shape preserving interpolation. In this study, a new rational quartic spline function with three parameters of the form quartic numerator and quadratic denominator is proposed to overcome these problems. These free parameters can be used to modify the final shape of the interpolating curve as well as to reduce the interpolation error. The proposed rational spline has a first order of parametric continuity, C1. Furthermore, the proposed rational spline also can achieve C2 continuity without the need to solve any tri-diagonal systems of linear equations unlike some other splines that need linear systems of equation to be solved. The proposed scheme is tested for 2D data interpolation as well as positivity-preserving interpolation. The main advantage of the proposed scheme is that it will produce positive curves everywhere for positive datasets unlike other schemes. Furthermore, an error analysis by calculating the absolute error and root mean square error (RMSE) indicates that the proposed scheme is better than some existing schemes.
format Thesis
author HARIM, NOOR ADILLA
author_sort HARIM, NOOR ADILLA
title NEW RATIONAL QUARTIC SPLINE FOR POSITIVITY PRESERVING INTERPOLATION
title_short NEW RATIONAL QUARTIC SPLINE FOR POSITIVITY PRESERVING INTERPOLATION
title_full NEW RATIONAL QUARTIC SPLINE FOR POSITIVITY PRESERVING INTERPOLATION
title_fullStr NEW RATIONAL QUARTIC SPLINE FOR POSITIVITY PRESERVING INTERPOLATION
title_full_unstemmed NEW RATIONAL QUARTIC SPLINE FOR POSITIVITY PRESERVING INTERPOLATION
title_sort new rational quartic spline for positivity preserving interpolation
publishDate 2020
url http://utpedia.utp.edu.my/20525/1/Noor%20Adilla%20Harim_18001410.pdf
http://utpedia.utp.edu.my/20525/
_version_ 1741195631535325184
score 11.62408

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