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

Document Type : Review Article


1 Department of Mathematics, Faculty of Sciences, University Mohammed First

2 LANO Laboratory, University Mohammed First, Oujda, Morocco


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.