Abstract: We present a reverse engineering method for constructing a surface approximation scheme whose input is a set of unorganized noisy points in space and whose output is a set of quadric patches. The local surface properties, necessary for the subsequent segmentation, are estimated directly from the data using a simple and efficient data structure—the neighborhood graph. Our segmentation scheme, based on principal curvatures, constructs initial point subsets, which may be enlarged or further subdivided based on associated approximation error estimates obtained through approximation of the initial segments by quadric surfaces. Our method is highly efficient and produces a high-quality piecewise quadric surface approximation of engineering objects, which we demonstrate for several simple and complex example data sets.