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Sains Malaysiana 46(5)(2017): 825–831 http://dx.doi.org/10.17576/jsm-2017-4605-17
Quintic
Trigonometric Bˇzier Curve with Two Shape Parameters (Lengkung
Bˇzier 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 Bˇzier 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 Bˇzier 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: Bˇzier curve; parameterization; quintic trigonometric Bˇzier;
shape parameter; trigonometric function ABSTRACT Tahap kelima lengkung Bˇzier trigonometri yang dipanggil kuintik
dengan dua parameter bentuk dibincangkan dalam kertas ini. Parameter
bentuk memberikan lebih kawalan kepada bentuk lengkung berbanding
lengkung Bˇzier 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: Bˇzier trigonometri
kuintik; fungsi trigonometri; lengkung Bˇzier; parameteran; parameter
bentuk RUJUKAN Ahmad, A., Amat, A.H. & Ali, J.M. 2014. A generalization
of Bˇzier-like curve. EDUCATUM- Journal of Science, Mathematics
and Technology 1(2): 56-58. Chen, Q. & Wang, G. 2003. A class of Bˇzier-like curves.
Computer Aided Geometric Design 20(1): 29-39. Dube, M. & Yadav, B. 2014. The quintic trigonometric Bˇzier
curve with single shape parameter. International Journal Scientific
and Research Publications 4(3): 2250-3153. Dube, M. & Sharma, R. 2013. Quartic trigonometric Bˇzier
curve with a shape parameter. International Journal of Mathematics
and Computer Applications Research 3(3): 89-96. Gobithaasan, R.U., Karpagavalli, R. & Miura, K.T. 2013.
Shape analysis of generalized log-aesthetic curves. International
Journal of Mathematical Analysis 7(33-36): 1751-1759. Han, X.A., Ma, Y. & Huang, X. 2009. The cubic trigonometric
Bˇzier curve with two shape parameters. Applied Mathematics
Letters 22(2): 226-231. Hoschek, J., Lasser, D. & Schumaker, L.L. 1993. Fundamentals
of Computer Aided Geometric Design. AK Peters, Ltd. Mainar, E., Pe–a, J.M. & S‡nchez-Reyes, J. 2001. Shape
preserving alternatives to the rational Bˇzier model. Computer
Aided Geometric Design 18(1): 37-60. Misro, M.Y., Ramli, A. & Ali, J.M. 2015. Approximating
maximum speed on road from curvature information of Bˇzier curve.
International Journal of Mathematical, Computational, Physical,
Electrical and Computer Engineering 9(12): 705-712. Misro, M.Y., Ramli, A. & Ali, J.M. 2017. S-shaped and C-shaped
transition curve using cubic trigonometric Bˇzier. Proceedings
of 24th Malaysian National Symposium of Mathematical Sciences
(SKSM24). AIP Publishing. In Press. Uzma, B., Abbas, M., Awang, M.N.H. & Ali, J.M. 2013. A
class of quasi-quintic trigonometric Bˇzier curve with two shape
parameters. ScienceAsia 39: 11-15. Uzma, B., Abbas, M., Awang, M.N.H. & Ali, J.M. 2012. The
quadratic trigonometric Bˇzier curve with single shape parameter.
Journal of Basic and Applied Scientific Research 2(3):
2541-2546. Zhu, Y., Han, X. & Han, J. 2012. Quartic trigonometric
Bˇzier curves and shape preserving interpolation curves. Journal
of Computational Information Systems 8(2): 905-914. *Pengarang untuk surat-menyurat; email: redorange_91@yahoo.com
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