Sains Malaysiana 45(10)(2016): 1557–1563

 

A Univariate Rational Quadratic Trigonometric Interpolating Spline to Visualize

Shaped Data

(Suatu Nisbah Kuadratik Trigonometri Univariat Menginterpolasikan Splin untuk Menggambarkan Data Berbentuk)

 

UZMA BASHIR1* & JAMALUDIN MD. ALI2

 

1Lahore College for Women University, Lahore, Pakistan

 

2School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Pulau Pinang

Malaysia

 

Diserahkan: 21 Mac 2015/Diterima: 25 Februari 2016

 

ABSTRACT

This study was concerned with shape preserving interpolation of 2D data. A piecewise C1 univariate rational quadratic trigonometric spline including three positive parameters was devised to produce a shaped interpolant for given shaped data. Positive and monotone curve interpolation schemes were presented to sustain the respective shape features of data. Each scheme was tested for plentiful shaped data sets to substantiate the assertion made in their construction. Moreover, these schemes were compared with conventional shape preserving rational quadratic splines to demonstrate the usefulness of their construction.

 

Keywords: Continuity; interpolation; rational trigonometric spline; shape preserving

 

ABSTRAK

Kajian ini adalah berkaitan dengan pemeliharaan bentuk interpolasi data 2D. Suatu cebisan splin nisbah kuadratik trigonometri univariat termasuk tiga parameter positif dirangka untuk menghasilkan interpolasi yang terbentuk daripada bentuk data yang diberikan. Skim lengkung interpolasi positif dan berekanada dibentangkan bagi mengekalkan ciri bentuk data masing-masing. Setiap skim diuji daripada banyak bentuk set data untuk menyokong kenyataan yang dibuat pembinaan berdasarkan skim tersebut. Selain itu, skim ini dibandingkan dengan bentuk konvensional splin nisbah kuadratik untuk menunjukkan kegunaan pembinaannya.

 

Kata kunci: Interpolasi; keselanjaran; pemeliharaan bentuk; splin nisbah trigonometri

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*Pengarang untuk surat-menyurat; email: missheikh92@gmail.com

 

 

 

 

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