An Optimal G^۲-Hermite Interpolation by Rational Cubic Bézier Curves

In this paper, we study a geometric G^۲ Hermite interpolation by planar rational cubic Bézier 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 C^۲ parametric curves to be connected with G۲ continuity. Locally, the free parameters within a rational cubic Bézier 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.