  To definite and compute differential invariants, like curvatures, for
triangular meshes (or polyhedral surfaces) is a key problem in CAGD and the
computer vision. The Gaussian curvature and the mean curvature are determined
by the differential of the Gauss map of the underlying surface. The Gauss map
assigns to each point in the surface the unit normal vector of the tangent
plane to the surface at this point. We follow the ideas developed in Chen and
Wu \cite{Chen2}(2004) and Wu, Chen and Chi\cite{Wu}(2005) to describe a new and
simple approach to estimate the differential of the Gauss map and curvatures
from the viewpoint of the gradient and the centroid weights. This will give us
a much better estimation of curvatures than Taubin's algorithm \cite{Taubin}
(1995).
