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An anisotropic smoothing algorithm for removing noise of triangular mesh models is proposed. First, the desirable normals of the triangles are approximated using our desirable normal computing schemes, and then each vertex is repositioned according to desirable normals of adjacent triangular faces. The desirable normals estimated by a weighted sum of normals at neighboring faces. If the face differs strongly from its neighboring face, the weight associated with that neighboring face is set small, and vice versa. We perform the anisotropic smoothing algorithm by controlling the magnitude of weight on estimation desirable normal of each triangular face. Many experimental results demonstrate the smoothing algorithm can not only efficiently remove the noise but also preserve original model's sharp features and avoid oversmoothing.