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

Diserahkan: 7 Julai 2010 / Diterima: 17 Januari 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 nisbah

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*Pengarang untuk surat-menyurat; e-mail: arahni@cs.usm.my