In this work, a survey of several curvature estimation methods for surface meshes was conducted, and a comparison of two types of curvature estimation techniques was conducted based on convergence studies. As a result of this work, a new and improved method was proposed as an extension of one of the surveyed methods. The new method robustly estimates normals, principal curvatures, mean curvatures and Gaussian curvatures at vertices of general unstructured triangulations. The method has been tested on complex meshes and has provided good results.