An Optimal G^2-Hermite Interpolation by Rational Cubic Bézier Curves
الموضوعات : فصلنامه ریاضی
Driss Sbibih
1
(Department of Mathematics, Faculty of Sciences, University Mohammed First)
Bachir Belkhatir
2
(LANO Laboratory, University Mohammed First, Oujda, Morocco)
الکلمات المفتاحية: Optimization, Hermite interpolation, Rational curve, G^2 continuity, Geometric conditions,
ملخص المقالة :
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.
