Cubic Spline Interpolation on a Class of Triangulations

摘要

In this paper,we consider spaces of cubic C^1-spline on a class of trian- gulations.By using the inductive algorithm,the posed Lagrange interpolation sets are constructed for cubic spline space.It is shown that the class of triangulations considered in this paper are nonsingular for S(1/3) spaces.Moreover,the dimensions of those spaces exactly equal to L.L.Schumaker's low bounds of the dimensions.At the end of this paper,we present an approach to construct triangulations from any scattered planar points,which ensures that the obtained triangulations for S(1/3) space are nonsingular.