Sains Malaysiana 46(5)(2017): 825–831

http://dx.doi.org/10.17576/jsm-2017-4605-17

 

Quintic Trigonometric Bézier Curve with Two Shape Parameters

(Lengkung Bézier Trigonometri Kuintik dengan Dua Parameter Bentuk)

 

MISRO, M.Y.*, RAMLI, A. & ALI, J.M.

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

Malaysia

 

Received: 22 January 2016/Accepted: 1 November 2016

 

ABSTRACT

The fifth degree of trigonometric Bézier curve called quintic with two shapes parameter is presented in this paper. Shape parameters provide more control on the shape of the curve compared to the ordinary Bézier curve. This technique is one of the crucial parts in constructing curves and surfaces because the presence of shape parameters will allow the curve to be more flexible without changing its control points. Furthermore, by changing the value of shape parameters, the curve still preserves its geometrical features thus makes it more convenient rather than altering the control points. But, to interpolate curves from one point to another or surface patches, we need to satisfy certain continuity constraints to ensure the smoothness not just parametrically but also geometrically.

 

Keywords: Bézier curve; parameterization; quintic trigonometric Bézier; shape parameter; trigonometric function

 

ABSTRACT

Tahap kelima lengkung Bézier trigonometri yang dipanggil kuintik dengan dua parameter bentuk dibincangkan dalam kertas ini. Parameter bentuk memberikan lebih kawalan kepada bentuk lengkung berbanding lengkung Bézier biasa. Teknik ini penting dalam membina lengkung dan permukaan kerana kehadiran parameter bentuk akan membantu lengkung menjadi lebih fleksibel tanpa mengubah titik kawalannya. Tambahan pula, dengan menukarkan nilai parameter bentuk, lengkung tersebut masih mengekalkan ciri geometri sedia ada, maka lebih mudah daripada mengubah titik kawalan. Tetapi, untuk membuat interpolasi lengkung dari satu titik ke satu titik yang lain atau permukaan tampalan, kekangan keselanjaran tertentu perlu dipenuhi untuk memastikan kelicinan bukan sahaja secara parameter tetapi juga secara geometri.

 

Kata kunci: Bézier trigonometri kuintik; fungsi trigonometri; lengkung Bézier; parameteran; parameter bentuk

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*Corresponding author; email: redorange_91@yahoo.com