Moving parabolic approximation of point clouds

Using moving parabolic approximations (MPA), we reconstruct an improved point-based model of curve or surface represented as an unorganized point cloud, while also estimating the differential properties of the underlying smooth manifold. We present optimization algorithms to solve these MPA models, and examples which show that our reconstructions of the curve or surface, and estimates of the normals and curvature information, are accurate for precise point clouds and robust in the presence of noise.