C-2 Hermite interpolants obtained by subdivision

We propose a two point subdivision scheme with parameters to draw curves th at satisfy Hermite conditions at both ends of [a,b]. We build three functio ns f,p and s on dyadic numbers and, using infinite products of matrices, we prove that, under assumptions on the parameters, these functions can be ex tended by continuity on [a, b], with f' = p and f " = s.