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We introduce a new technique for estimating the curvature tensor of a triangular mesh. The input of the algorithm is only a single triangle equipped with its (exact or estimated) vertex normals. This way we get a smooth function of the curvature tensor inside each triangle of the mesh. We show that the error of the new method is comparable with the error of a cubic fitting approach if the incorporated normals are estimated. If the exact normals of the underlying surface are available at the vertices, the error drops significantly. We demonstrate the applicability of the new estimation at a rather complex data set.