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Sains Malaysiana 40(10)(2011): 1173–1178
Improved Sufficient Conditions for Monotonic Piecewise
Rational Quartic Interpolation
(Syarat Cukup yang
Lebih Baik untuk Interpolasi Kuartik Nisbah Cebis Demi Cebis Berekanada)
Abd
Rahni Mt Piah*
School
of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM Pulau
Pinang, Malaysia
Keith
Unsworth
Department
of Applied Computing, P.O. Box 84,Lincoln University, Lincoln 7647 , Christchurch,
New Zealand
Received:
7 July 2010/Accepted: 17 January 2011
ABSTRACT
In 2004, Wang and Tan
described a rational Bernstein-Bézier curve interpolation scheme using a
quartic numerator and linear denominator. The scheme has a unique
representation, with parameters that can be used either to change the shape of
the curve or to increase its smoothness. Sufficient conditions are derived by
Wang and Tan for preserving monotonicity, and for achieving either C1 or
C2 continuity. In this paper, improved sufficient conditions are
given and some numerical results presented.
Keywords: Continuity; interpolation;
monotonicity; rational Bernstein-Bézier
ABSTRAK
Pada tahun 2004, Wang and
Tan telah memerikan suatu skema interpolasi lengkung Bernstein-Bézier nisbah menggunakan pembilang kuartik dan penyebut linear. Skema tersebut mempunyai
suatu perwakilan yang unik, dengan parameter yang boleh digunakan untuk menukar
sama ada bentuk lengkung atau untuk meningkatkan kelicinan lengkung. Syarat
cukup diterbitkan oleh Wang & Tan untuk mengekalkan keekanadaan, dan untuk
mencapai keselanjaran sama ada C1 atau C2.
Dalam kertas kerja ini, syarat perlu yang lebih baik dan beberapa keputusan
berangka diberikan.
Kata kunci: Interpolasi; keekanadaan; keselanjaran;Bernstein-Bézier
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*Corresponding author; e-mail: arahni@cs.usm.my
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