Fitting smooth surfaces to scattered 3D data using piecewise quadratic approximation

The approximation of surfaces to scattered data is an important problem encountered in a variety of scientific applications, such as reverse engineering, computer vision, computer graphics, and terrain modeling. This paper describes an automatic method for constructing smooth surfaces defined as a network of curved triangular patches. The method starts with a coarse mesh approximating the surface through triangular elements covering the boundary of the domain, then iteratively adds new points from the data set until a specified error tolerance is achieved. The resulting surface over the triangular mesh is represented by piecewise polynomial patches possessing C¹ continuity. The method has been implemented and tested on a number of real data sets.