10.71932/

An Optimal G2-Hermite Interpolation by Rational Cubic B´ezier Curves

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  • Driss Sbibih1,
  • Bachir Belkhatir1,
  1. LANO Laboratoty, University Mohammed First, Faculty of Sciences, Morocco.

Published in Issue 13-07-2025

Copyright (c) 2025 Driss Sbibih, Bachir Belkhatir (Author)

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Sbibih, D., & Belkhatir, B. (2025). An Optimal G2-Hermite Interpolation by Rational Cubic B´ezier Curves. International Journal of Mathematical Modelling & Computations, 8(01). https://doi.org/10.71932/
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Abstract

In this paper, we study a geometric G2 Hermite interpolation by planar rational cubic B´ ezier 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 C2 parametric curves to be connected with G2 continuity. Locally, the free parameters within a rational cubic B´ ezier 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. 

Keywords

  • Hermite interpolation,
  • Rational curve,
  • G2 continuity,
  • Geometric conditions,
  • Optimization
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