An Optimal G2-Hermite Interpolation by Rational Cubic Bezier Curves

In this paper, we study a geometric G2 Hermite interpolation by planar rational cubic Bezier curves. Two data points, two tangent vectors and two signed curvatures interpo- lated 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 Bezier curve should be determined by minimizing a maximum error. We nish by proving and justifying the efficiently of the approaching method with some comparative numerical and graphical examples.