Local Lagrange Interpolation By Bivariate Splines Of Degree Seven On Triangulated Quadrangulation

In the theory of spline interpolations, there are generally two methods: Hermite interpolation and Lagrange interpolation. We discuss Lagrange interpolation in this paper.Firstly, a Lagrange interpolation set is constructed for bivariate spline space S₇^2,3((?)) on triangulated quadrangulation by using coloring algorithm, the method of Bézier-net and the technique of minimal determining sets. Secondly, a set of dual basis is given. Finally, we prove that the corresponding fundamental splines have local supports.