PERTANIKA JOURNAL OF SCIENCE AND TECHNOLOGY

Bézier curves and surfaces are very important in many areas, especially the manufacturing and aerospace. Surface inspection through visualisation is required to create high-quality surfaces and reduce unwanted products. The smoothness of the surface can be quantified using curvature. In this research, different surfaces types will be generated using the quintic trigonometric Bézier basis function. All the surfaces will be evaluated and analysed using Gaussian and mean curvature. Finally, curvature for each surface type will be mapped using colour-coded mapping and can be further characterised based on their positive and negative curvature values. This insight can also help the designer produce a smooth surface and develop quality products.

• Adnan, S. B. Z., Ariffin, A. A. M., & Misro, M. Y. (2020). Curve fitting using quintic trigonometric Bézier curve. In AIP Conference Proceedings (Vol. 2266, No. 1, p. 040009). AIP Publishing LLC. https://doi.org/10.1063/5.0018099

• Ammad, M., & Misro, M. Y. (2020). Construction of local shape adjustable surfaces using quintic trigonometric Bézier curve. Symmetry, 12(8), Article 1205. https://doi.org/10.3390/sym12081205

• Ammad, M., Misro, M. Y., & Ramli, A. (2022). A novel generalized trigonometric Bézier curve: Properties, continuity conditions and applications to the curve modeling. Mathematics and Computers in Simulation, 19, 744-763. https://doi.org/10.1016/j.matcom.2021.12.011

• Bartkowiak, T., & Brown, C. A. (2019). Multiscale 3D curvature analysis of processed surface textures of aluminum alloy 6061 T6. Materials, 12(2), Article 257. https://doi.org/10.3390/ma12020257

• Beck, J. M., Farouki, R. T., & Hinds, J. K. (1986). Surface analysis methods. IEEE Computer Graphics and Applications, 6(12), 18-36. https://doi.org/10.1109/MCG.1986.276587

• Besl, P. J. (2012). Surfaces in range image understanding. Springer Science & Business Media.

• Bibi, S., Abbas, M., Misro, M. Y., Majeed, A., & Nazir, T. (2021). Construction of generalized hybrid trigonometric Bézier surfaces with shape parameters and their applications. Journal of Mathematical Imaging and Vision, 63(9), 1118-1142. https://doi.org/10.1007/s10851-021-01046-y

• Chang, K. H. (2016). e-Design: computer-aided engineering design. Academic Press.

• Chen, Q., & Wang, G. (2003). A class of Bézier-like curves. Computer Aided Geometric Design, 20(1), 29-39. https://doi.org/10.1016/S0167-8396(03)00003-7

• Devaraj, A. (2020). An overview of curvature. Retrieved May 5, 2021, from https://web.ma.utexas.edu/users/drp/files/Spring2020Projects/DRP_spring2020_final%20-%20Ashwin%20Devaraj.pdf

• Dill, J. C. (1981). An application of color graphics to the display of surface curvature. In Proceedings of the 8th annual conference on Computer graphics and interactive techniques (pp. 153-161). ACM Publishing. https://doi.org/10.1145/800224.806801

• Farin, G. (2014). Curves and surfaces for computer-aided geometric design: A practical guide. Elsevier.

• Farin, G., Hoschek, J., & Kim, M. S. (Eds.). (2002). Handbook of computer aided geometric design. Elsevier. https://doi.org/10.1016/B978-0-444-51104-1.X5000-X

• Garcia, D. R., Linke, B. S., & Farouki, R. T. (2021). Optimised routine of machining distortion characterization based on Gaussian surface curvature. In 2nd International Conference of the DFG International Research Training Group 2057–Physical Modeling for Virtual Manufacturing (iPMVM 2020) (pp. 1-17). Schloss Dagstuhl-Leibniz-Zentrum für Informatik. https://doi.org10.4230/OASIcs.iPMVM.2020.5

• Gatzke, T., Grimm, C., Garland, M., & Zelinka, S. (2005). Curvature maps for local shape comparison. In International Conference on Shape Modeling and Applications 2005 (SMI’05) (pp. 244-253). IEEE Publishing. https://doi.org/10.1109/SMI.2005.13

• Hahmann, S. (1999). Visualisation techniques for surface analysis. In C. Bajaj (Ed.), Advanced visualization techniques (pp. 49-74). JohnWiley.

• Hu, G., Wu, J., & Qin, X. (2018). A novel extension of the Bézier model and its applications to surface modeling. Advances in Engineering Software, 125, 27-54. https://doi.org/10.1016/j.advengsoft.2018.09.002

• Ismail, N. H. M., & Misro, M. Y. (2020). Surface construction using continuous trigonometric Bézier curve. In AIP Conference Proceedings (Vol. 2266, No. 1, p. 040012). AIP Publishing LLC. https://doi.org/10.1063/5.0018101

• Magid, E., Soldea, O., & Rivlin, E. (2007). A comparison of Gaussian and mean curvature estimation methods on triangular meshes of range image data. Computer Vision and Image Understanding, 107(3), 139-159. https://doi.org/10.1016/j.cviu.2006.09.007

• Marsh, D. (2005). Applied geometry for computer graphics and CAD. Springer Science & Business Media. https://doi.org/10.1007/b138823

• Misro, M. Y., Ramli, A., & Ali, J. M. (2017). Quintic trigonometric Bézier curve with two shape parameters. Sains Malaysiana, 46(5), 825-831. http://dx.doi.org/10.17576/jsm-2017-4605-17

• Misro, M. Y., Ramli, A., & Ali, J. M. (2019). Extended analysis of dynamic parameters on cubic trigonometric Bézier transition curves. In 2019 23rd International Conference in Information Visualization–Part II (pp. 141-146). IEEE Publishing. https://doi.org/10.1109/IV-2.2019.00036

• Oxman, N. (2007). Get real towards performance-driven computational geometry. International Journal of Architectural Computing, 5(4), 663-684. https://doi.org/10.1260/147807707783600771

• Piegl, L., & Tiller, W. (1996). The NURBS book. Springer Science & Business Media. https://doi.org/10.1007/978-3-642-59223-2

• Pressley, A. N. (2010). Elementary differential geometry. Springer Science & Business Media. https://doi.org/10.1007/978-1-84882-891-9

• Razdan, A., & Bae, M. (2005). Curvature estimation scheme for triangle meshes using biquadratic Bézier patches. Computer-Aided Design, 37(14), 1481-1491. https://doi.org/10.1016/j.cad.2005.03.003

• Seidenberg, L. R., Jerard, R. B., & Magewick, J. (1992). Surface curvature analysis using color. In Proceedings Visualization’92 (pp. 260-267). IEEE Publishing. https://doi.org/10.1109/VISUAL.1992.235200

• Tan, X., & Zhu, Y. (2019). Quasi-quintic trigonometric Bézier curves with two shape parameters. Computational and Applied Mathematics, 38(4), 1-13. https://doi.org/10.1007/s40314-019-0961-y

• Zain, S. A. A. A. S. M., Misro, M. Y., & Miura, K. T. (2021). Generalised fractional Bézier curve with shape parameters. Mathematics, 9(17), Article 2141. https://doi.org/10.3390/math9172141

• Zheng, J., & Sederberg, T. W. (2003). Gaussian and mean curvatures of rational Bézier patches. Computer Aided Geometric Design, 20(6), 297-301. https://doi.org/10.1016/j.cagd.2003.06.002