Error-controllable Feature-aware Subdivision Surfaces Fitting

With the rapid development of 3D acquisition technology, the 3D digital geometry model has become a common digital media. Because the 3D object obtained by the 3D scanning technology is generally in the form of large-scale scattered points or polygonal mesh, it is inconvenient for the subsequent application. It becomes an important issue to fit an optimal and concise surface to approximate the dense data. Subdivision surface fitting occurred for easier surface modeling. Compared with the parametric curve and surface method, subdivision surface fitting is applicable to surface with arbitrary topology and it is unnecessary to split surface in surface modeling. Most of the previous subdivision surface fitting techniques exploit mesh simplification methods to acquiring the base mesh of fitting surface. However, the research based on feature is rare and this kind of method has advantage in feature aligning. This paper introduces an errorcontrollable subdivision surface fitting framework based on features of mesh.In the first phase, we approximate the discrete differential properties of mesh and extract the ridges and umbilicus. These features can describe the shape of the model well. After features extraction, filtering and sampling processes are performed and the base mesh is acquired by geodesic distance transform algorithm. In order to avoid large amount of computation of solving equations in the procedure of calculating the control mesh, we employ a kind of progressive interpolation-like method to acquire the control mesh. During subdivision surface fitting, we adopt loop evaluation technique and adaptive subdivision method for error control.According to the experimental results, the framework proposed in this paper can be used to reconstruct the original mesh model with good quality under certain reconstruction error.