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.