A nodal basis of Cμ-rational spline functions on triangulations

Abstract

Let ρ be a triangulation of a polygonal domain D⊂R2 with vertices V={vi:l≤i≤Nv} and RSk(D, ρ)={u∈Ck(D): ≠ T∈ρ, u/T is a rational function}. The purpose of this paper is to study the existence and construction of Cμ-rational spline functions on any triangulation ρ for CAGD. The Hermite problem Hμ(V,U)={find u∈U: Dαu(vi)=Dαf(vi),|α|≤μ} is solved by the generalized wedge function method in rational spline function family, i.e. U=RSμ. this solution needs only the knowledge of partial derivatives of order≤μ at vi. The explicit repesentations of all Cμ-GWF(generalized wedge functions)and the interpolating operator with degree of precision at least 2μ+1 for any triangulation are given.