C1 continuities detection in triangular meshes

The identification of C1 continuities is important in many applications involving point clouds or triangular meshes, such as surface segmentation, inspection and rendering. The methods in literature have some limitations which make them strongly dependent on some properties of the mesh (point typology, mesh resolution, uniformity of the shape of triangles and error in point location). Furthermore, some of them do not discriminate non-regular points from those that are inside a band around them.In this work, a new method for automatic detection of C1 continuities in triangular meshes is presented. The method introduces an original function, called sharpness indicator  , which enables us to evaluate properties related to surface smoothness. The performance of the new method is compared with that of four methods presented in literature as regards the recognition of C1 continuities both in synthetic and real meshes. Results are analysed and critically discussed.