Integral of a vector dotted with unit normal over a triangulated surface

Dear All,

I have obtained a triangulated surface by isosurface function in three dimensional space. I am trying to perform an area integration over this surface. The integrand is a vector, defined on each grid of the isosurface, dotted with unit normal of the triangulated face. How can I convert the triangulation to another one which uses each grid as the face center? Because this way, integration would be easily done for each face.

Thanks,

Ahmad