Representation of piecewise biharmonic surfaces using biquadratic B-Splines

• Xuli Han ^[1] ; Jing Han ^[1]
  1. [1] Central South University

     Central South University

     China

     
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 290, Nº 1, 2015, págs. 403-411
• Idioma: inglés
• DOI: 10.1016/j.cam.2015.05.025
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• Resumen

  • Piecewise biquadratic B-Spline surface satisfying biharmonic condition is studied in this paper. By applying biharmonic PDE, biquadratic B-Spline surface is fully determined by boundary control vertices. A linear system for solving inner control vertices is established. Its coefficient matrix is block tridiagonal and the proof of non-singularity of coefficient matrix is presented under the condition that all knots do not coincide with each other. A few examples are given to show the effectiveness of piecewise biharmonic biquadratic B-Spline surface. An interpolation method on given boundary points is presented if boundary curves are open.