OICC Press International Journal of Mathematical Modelling & Computations 2228-6233 8 01 2025 07 13 An Optimal G2-Hermite Interpolation by Rational Cubic B´ezier Curves 10.71932/ EN Driss Sbibih LANO Laboratoty, University Mohammed First, Faculty of Sciences, Morocco. Bachir Belkhatir LANO Laboratoty, University Mohammed First, Faculty of Sciences, Morocco. Journal Article 2025 07 13 In this paper, we study a geometric G2 Hermite interpolation by planar rational cubic B´ ezier curves. Two data points, two tangent vectors and two signed curvatures interpolated per each rational segment. We give the necessary and the sufficient intrinsic geometric conditions for two C2 parametric curves to be connected with G2 continuity. Locally, the free parameters within a rational cubic B´ ezier curve should be determined by minimizing a maximum error. We finish by proving and justifying the efficiently of the approaching method with some comparative numerical and graphical examples.