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