LetιbeatriangulationofapolygonaldomainDR2withverticesV={v1:1≤i≤N,}andRSk(D,τ)={u∈Ck(D):(T∈τ,u|τisarationalfunction}.Thepurposeofthispaperistostudytheexist-enceandconstructionofCμ-rationalsplinefunctionsonanytriangulationτforCAGD.TheHermiteprob-lemHμ(V,U)={findu∈