Representation of piecewise biharmonic surfaces using biquadratic B-Splines

[摘要] 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. (C) 2015 Elsevier B.V. All rights reserved.

[发布日期] 2015-12-15

[关键词] Biharmonic;Biquadratic B-Spline;Block tridiagonal matrix;Non-singularity