An Optimal G^2-Hermite Interpolation by Rational Cubic Bézier Curves

Subject Areas : International Journal of Mathematical Modelling & Computations

Driss Sbibih ¹ , Bachir Belkhatir ²

1 - Department of Mathematics, Faculty of Sciences, University Mohammed First
2 - LANO Laboratory, University Mohammed First, Oujda, Morocco

Received: 2018-02-26 Accepted : 2018-10-06 Published : 2018-01-01

Keywords: Optimization, Hermite interpolation, Rational curve, G^2 continuity, Geometric conditions,

Abstract :

In this paper, we study a geometric G^2 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^2 parametric curves to be connected with G2 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.