The application of Powell-Sabin's or Clough-Tocher's schemes to scatte
red data problems, as known requires the knowledge of the partial deri
vatives of first order at the vertices of an underlying triangulation.
We study a local method for generating partial derivatives based on t
he minimization of the energy functional on the star of triangles shar
ing a node that we called a cell. The functional is associated to some
piecewise polynomial function interpolating the points. The proposed
method combines the global Method II by Renka and Cline (cf. [16, pp.
230-231]) with the variational approach suggested by Alfeld (cf. [2])
with care to efficiency in the computations. The locality together wit
h some implementation strategies produces a method well suited for the
treatment of a big amount of data. An improvement of the estimates is
also proposed.