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Sains Malaysiana 46(5)(2017): 825–831 http://dx.doi.org/10.17576/jsm-2017-4605-17
Quintic
Trigonometric B巣ier Curve with Two Shape Parameters (Lengkung
B巣ier 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 Diserahkan: 22 Januari 2016/Diterima: 1 November 2016 The fifth degree of trigonometric B巣ier 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 B巣ier 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: B巣ier curve; parameterization; quintic trigonometric B巣ier;
shape parameter; trigonometric function ABSTRACT Tahap kelima lengkung B巣ier trigonometri yang dipanggil kuintik
dengan dua parameter bentuk dibincangkan dalam kertas ini. Parameter
bentuk memberikan lebih kawalan kepada bentuk lengkung berbanding
lengkung B巣ier 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: B巣ier trigonometri
kuintik; fungsi trigonometri; lengkung B巣ier; parameteran; parameter
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