The Construction of Cubic Bezier Curve

The Construction of Cubic Bezier Curve

Authors

  • Siti Sarah Raseli Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Perlis Branch
  • Nur Ain Mohd Khusairy Faisal Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Perlis Branch
  • Norpah Mahat Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Perlis Branch

DOI:

https://doi.org/10.24191/jcrinn.v7i2.291

Keywords:

Bezier curves, Cubic Bezier Curve

Abstract

The construction of Bezier curves is one of the curves that are commonly discussed in Computer-Aided Geometric Design (CAGD). This study focuses on cubic Bezier curve. The objectives in this study are to review the properties of cubic Bezier curve and construct the cubic Bezier curves. In this study, the expanding equations from the basis function of the curve is used to construct the cubic Bezier curve. Future researchers can expand the degree of the Bezier curves, which is more useful in Computer-Aided Design (CAD), CAGD and engineering. The next studies in Bezier curve are recommended as a contribution for further research.

Downloads

Download data is not yet available.

References

Abbas, M., Jamal, E., & Ali, J. M. (2011). Bezier curve interpolation constrained by a line. Applied Mathematical Sciences, 5(37), 1817–1832. https://www.researchgate.net/publication/315099476_Bezier_Curve_Interpolation_Constrained_by_a_Line_Mathematics_Subject_Classification_68U05_68U07_65D05_65D07_65D18_1818

Bashir, U., Abbas, M., & Ali, J. M. (2013). The G^2 and C^2 rational quadratic trigonometric Bézier curve with two shape parameters with applications. Applied Mathematics and Computation, 219(2013), 10183–10197. https://doi.org/10.1016/j.amc.2013.03.110

Bashir, U., Abbas, M., Awang, M. N. H., & Ali, J. M. (2012). The quadratic trigonometric Bezier curve with single shape parameter. Journal of Basic and Applied Scientific Research, 2(3), 2541–2546. https://doi.org/10.4028/www.scientific.net/AMR.468-471.2463

Du, P., Liu, Y., & Xun, E. (2019). The techniques and evaluation method for beautification of handwriting Chinese characters based on cubic Bezier curve and convolutional neural network. 14th International Conference on Computer Science and Education, ICCSE 2019, (pp. 502–511). https://doi.org/10.1109/ICCSE.2019.8845418

Fang (2014, September 9). What is the difference between cubic Bezier and quadratic Bezier and their use cases?. Stack Overflow. https://stackoverflow.com/questions/18814022/what-is-the-difference-between-cubic-bezier-and-quadratic-bezier-and-their-use-c

Fitter, H. N., Pandey, A. B., Patel, D. D., & Mistry, J. M. (2014). A review on approaches for handling Bézier curves in CAD for manufacturing. Procedia Engineering, 97(2014), 1155–1166. https://doi.org/10.1016/j.proeng.2014.12.394

Khan, M. (2009). Approximation of circle using cubic Bezier curve. https://www.mathworks.com/matlabcentral/fileexchange/6844-approximation-of-circle-using-cubic-bezier-curve?s_tid=srchtitle_approximation%20cubic%20bezier_2

Kilicoglu, S., & Senyurt, S. (2019). On the cubic Bezier curves in E^3. Ordu University Journal of Science and Technology, 9(2), 83–97. https://dergipark.org.tr/en/pub/ordubtd/issue/51531/625391

Kilicoglu, S., & Senyurt, S. (2020). On the involute of the cubic Bezier curve by using matrix representation in E^3. European Journal of Pure and Applied Mathematics, 13(2), 216–226. https://doi.org/10.29020/nybg.ejpam.v13i2.3648

Majeed, A., Piah, A. R. M., Gobithaasan, R. U., & Yahya, Z. R. (2015). Craniofacial reconstruction using rational cubic Ball curves. Plos One, 10(4), 1-14. https://doi.org/10.1371/journal.pone.0122854

Mathematics of Computer Graphic and Virtual Environments. (2015, March 9). Bezier curves [Video]. YouTube. https://youtu.be/2HvH9cmHbG4

Misro, M. Y., Ramli, A., Ali, J.M., (2017). Quintic Trigonometric Curve with Two Shape Parameters. Sains Malaysiana, 46(5), 825-831. http://dx.doi.org/10.17576/jsm-2017-4605-17

Nelson Darwin Pak Tech. (2020, September 25). How to write text MATLAB plot | Insert text in plotting axes (MATLAB) [Video]. YouTube. https://youtu.be/3TJmKOy7eI0

Rizal, S., & Kim, D. S. (2015). Image transmission in military network using Bezier curve. Journal of Advances in Computer Networks, 3(2), 141–145. https://doi.org/10.7763/jacn.2015.v3.156

Rusdi, N. A., & Yahya, Z. R. (2015). Reconstruction of generic shape with cubic Bezier using least square method. AIP Conference Proceedings, (pp. 050004-1-050004-6). https://doi.org/http://dx.doi.org/10.1063/1.4915637

Sarfraz, M., & Masood, A. (2007). Capturing outlines of planar images using Bezier cubic. Computers and Graphics, 31(2007), 719–729. https://doi.org/10.1016/j.cag.2007.05.002

The Lazy Engineer. (2017, June 28). What are Bezier curves and how can I draw them in MATLAB [Video]. YouTube. https://youtu.be/uRhe_A4DWPA

Zhang, H., & Feng, J. (2006). Bezier curves and surfaces (1). http://www.cad.zju.edu.cn/home/zhx/GM/004/00-bcs1.pdf

Downloads

Published

2022-09-01

How to Cite

Raseli, S. S., Mohd Khusairy Faisal, N. A., & Mahat, N. (2022). The Construction of Cubic Bezier Curve . Journal of Computing Research and Innovation, 7(2), 111–120. https://doi.org/10.24191/jcrinn.v7i2.291

Issue

Section

General Computing
Loading...