A nodal basis of Cμ-rational spline functions on triangulations

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