To definite and compute differential invariants, like curvatures, fortriangular meshes (or polyhedral surfaces) is a key problem in CAGD and thecomputer vision. The Gaussian curvature and the mean curvature are determinedby the differential of the Gauss map of the underlying surface. The Gauss mapassigns to each point in the surface the unit normal vector of the tangentplane to the surface at this point. We follow the ideas developed in Chen andWu \cite{Chen2}(2004) and Wu, Chen and Chi\cite{Wu}(2005) to describe a new andsimple approach to estimate the differential of the Gauss map and curvaturesfrom the viewpoint of the gradient and the centroid weights. This will give usa much better estimation of curvatures than Taubin's algorithm \cite{Taubin}(1995).
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