An effective third-order local fitting patch and its application

In this paper, we extend Razdan and Bae´s second-order local fitting method to construct an effective third-order fitting patch. Compared to other estimation algorithms, this weighted bicubic Bezier patch more accurately obtains the normal vector and curvature estimation of a triangular mesh model. Furthermore, we define the principal geodesic torsion of each vertex on the mesh model and estimate it through this local fitting patch. In the end of this paper, we apply the third-order fitting patch for the mesh smoothing and hole-filling which can get the satisfactory results.