A best-fit curve is required to reconstruct craniofacial fracture to ensure the preciseness of the reconstructed contour. A genetic algorithm (GA) is applied to get the best-fit curve in reconstructing the fractured part. This method provides a fast decision in obtaining suitable sets of control points to interpolate both boundary regions to form a reconstructed part without any try-and-error approach that requires altering the control points several times. The optimised sets of control points with different degrees of continuity are used to develop the reconstructed part using the quintic Bézier curve to generate a smooth curve. The best-fit curvature value of the quintic Bézier curve for each degree of continuity is compared, and the curve with the lowest absolute error of curvature is chosen as the inner and outer parts of the craniofacial fracture reconstruction.

• Abdel-Aziz, H. S., Zanaty, E. A., Ali, H. A., & Saad, M. K. (2021). Generating Bézier curves for medical image reconstruction. Results in Physics, 23, Article 103996. https://doi.org/10.1016/j.rinp.2021.103996

• Adi, D. I. S., Shamsuddin, S. M., & Ali, A. (2009). Particle swarm optimization for NURBS curve fitting. In 2009 Sixth International Conference on Computer Graphics, Imaging and Visualization (pp. 259-263). IEEE Publishing. https://doi.org/10.1109/CGIV.2009.64

• 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, Article 040009). AIP Publishing LLC. https://doi.org/10.1063/5.0018099

• Ali, N. S. S., Ramli, A., & Rahman, N. A. (2020), October. Searching an optimum parameter value for radial basis function by bootstrap error analysis for 2D craniofacial reconstruction. In AIP Conference Proceedings (Vol. 2266, No. 1, Article 050008). AIP Publishing LLC. https://doi.org/10.1063/5.0018115

• 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, 194, 744-763. https://doi.org/10.1016/j.matcom.2021.12.011

• Amorim, P. H., Moraes, T. F., Silva, J. V., Pedrini, H., & Ruben, R. B. (2020). Reconstruction of panoramic dental images through Bézier function optimization. Frontiers in Bioengineering and Biotechnology, 8, 794. https://doi.org/10.3389/fbioe.2020.00794

• BiBi, S., Misro, M. Y., Abbas, M., Majeed, A., & Nazir, T. (2021). G3 Shape adjustable GHT-Bézier developable surfaces and their applications. Mathematics, 9(19), Article 2350. https://doi.org/10.3390/math9192350

• Carr, J. (2014). An introduction to genetic algorithms. Senior Project, 1(40), 1-40.

• Chen, B., Gao, Q., Song, H., & Xu, M. (2017) Retrospective study of experience of craniofacial reconstruction. International Wound Journal, 14(2), 399-407. https://doi.org/10.1111/iwj.12613

• Eliou, N., & Kaliabetsos, G. (2014). A new, simple and accurate transition curve type, for use in road and railway alignment design. European Transport Research Review, 6, 171-179. https://doi.org/10.1007/s12544-013-0119-8

• Ibrahim, M. F., Misro, M. Y., Ramli, A., & Ali, J. M. (2017). Maximum safe speed estimation using planar quintic Bézier curve with C2 continuity. In AIP Conference Proceedings (Vol. 1870, No. 1, Article 050006). AIP Publishing LLC. https://doi.org/10.1063/1.4995916

• Lee, W. J., & Shin, D. H. (2020). Craniofacial reconstruction in mummy studies. In D. H. Shin & R. Bianucci (Eds.), The Handbook of Mummy Studies (pp. 1-14). Springer. https://doi.org/10.1007/978-981-15-1614-6_5-1

• Loucera, C., Gálvez, A., & Iglesias, A. (2014). Simulated annealing algorithm for Bézier curve approximation. In 2014 International Conference on Cyberworlds (pp. 182-189). IEEE Publishing. https://doi.org/10.1109/CW.2014.33

• Ma, Y., Pollick, F., & Hewitt, W. T. (2004). Using b-spline curves for hand recognition. In 17th International Conference on Pattern Recognition, 2004 (ICPR) (Vol. 3, pp. 274-277). IEEE Publishing. https://doi.org/10.1109/ICPR.2004.1334520

• Majeed, A., Abbas, M., & Miura, K. T. (2022). A comparative study of different schemes based on Bézier-like functions with an application of craniofacial fractures reconstruction. Mathematics, 10(8), Article 1269. https://doi.org/10.3390/math10081269

• Majeed, A., Abbas, M., Miura, K. T., Kamran, M., & Nazir, T. (2020). Surface modeling from 2D contours with an application to craniofacial fracture construction. Mathematics, 8(8), Article 1246. https://doi.org/10.3390/math8081246

• Majeed, A., Piah, A. R. M., Gobithaasan, R. U., & Yahya, Z. R. (2015). Craniofacial reconstruction using rational cubic ball curves. PLOS One, 10(4), Article e0122854. https://doi.org/10.1371/journal.pone.0122854

• Mansour, R. F., (2020). Evolutionary computing enriched ridge regression model for craniofacial reconstruction. Multimedia Tools and Applications, 79, 22065-22082. https://doi.org/10.1007/s11042-017-5015-0

• Misro, M. Y., Ramli, A., & Ali, J. M. (2017). S-shaped and c-shaped transition curve using cubic trigonometric Bézier. In AIP Conference Proceedings (Vol. 1870, No. 1, Article 050005). AIP Publishing LLC. https://doi.org/10.1063/1.4995915

• Misro, M. Y., Ramli, A., & Ali, J. M. (2018). Quintic trigonometric Bézier curve and its maximum speed estimation on highway designs. In AIP Conference Proceedings (Vol. 1974, No. 1, Article 020089). AIP Publishing LLC. https://doi.org/10.1063/1.5041620

• Moiduddin, K., Mian, S. H., Elseufy, S. M., Abdo, B. M. A., Aboudaif, M. K., & Alkhalefah, H. (2022). Craniofacial reconstruction with personalized lightweight scaffold fabricated using electron-beam additive manufacturing. Metals, 12(4), Article 552. https://doi.org/10.3390/met12040552

• Suputra, P. H., Sensusiati, A. D., Yuniarno, E. M., Purnomo, M. H., & Purnama, I. K. E. (2020). 3D Laplacian surface deformation for template fitting on craniofacial reconstruction. In Proceedings of the 8th International Conference on Computer and Communications Management (pp. 27-32). ACM Digital Library. https://doi.org/10.1145/3411174.3411175

• Ueda, E. K., Tsuzuki, M. S. G., & Barari, A. (2018). Piecewise Bézier curve fitting of a point cloud boundary by simulated annealing. In 2018 13th IEEE International Conference on Industry Applications (INDUSCON) (pp. 1335-1340). IEEE Publishing. https://doi.org/10.1109/INDUSCON.2018.8627161

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