Curvature computation for triangular meshes based on local parametrization

A local parametrization based curvature computation technique for triangular meshes is presented. The computation process starts with interpolating the region-of-interest of the given mesh with a Loop subdivision surface. The interpolation technique guarantees that the resulting surface reflects the local shape of the mesh, including features such as edges and corners; no data simplification is necessary. A blending technique is then applied to vicinities of extra-ordinary vertices to ensure continuity and boundedness of curvature at each extra-ordinary vertex. This blending process does not change the value of the surface at the extra-ordinary points. Curvatures for each given point are subsequently computed based on standard parametrization for Loop surfaces. Advantages of the new technique include that curvature can be computed in any direction for any point of the given mesh and higher accuracy of the computed results due to precise representation obtained by the interpolation process. Test results showing the effectiveness of the new technique are included.