Identification of C¹ and C² discontinuities for surface meshes in CAD

In computer-aided design and meshing, it is often important to identify the discontinuities (singularities) in coarse surface meshes. Due to the potential low resolution and noise, it is challenging to detect such features. We propose systematic characterizations of the edges, corners and curves at the singularities of a mesh and develop algorithms to identify these geometrical features. Our algorithms can detect C¹ discontinuities as well as typical C² discontinuities. We present the analysis of correctness of our method and demonstrate its effectiveness experimentally using stereolithographic (STL) meshes as well as coarse finite-element meshes of real-world objects.