Discrete curvatures and Gauss maps for polyhedral surfaces

The paper concerns the problem of correct curvatures estimates directly from polygonal meshes. We present a new algorithm that allows the construction of unambiguous Gauss maps for a large class of polyhedral surfaces, including surfaces of non-convex objects and even non-manifold surfaces. The resulting Gauss map provides shape recognition and curvature characterisation of the polyhedral surface (polygonal mesh) and can be used further for optimising the mesh or for developing subdivision schemes.