Hermite interpolation by triangular cubic patches with small Willmore energy

Abstract

In this paper, a construction of a cubic Bézier spline surface that interpolates prescribed spatial points and the corresponding normal directions of tangent planes is proposed. Boundary curves of each triangular patch minimize the approximated strain energy. A comparison of optimal boundary curves is given. The interpolant minimizes Willmore energy functional. Some numerical examples and applications of the interpolation scheme are presented: surface approximation, hole filling and condensation of parameters.

Keywords:

• strain energy
• Willmore energy
• cubic spline surface
• Hermite interpolation
• minimization

2010 AMS Subject Classifications :

• 65D05
• 65D07
• 65D17

Acknowledgements

Operation part-financed by the European Union, European Social Fund.