  We propose a variational functional and fast algorithms to reconstruct
implicit surface from point cloud data with a curvature constraint. The
minimizing functional balances the distance function from the point cloud and
the mean curvature term. Only the point location is used, without any local
normal or curvature estimation at each point. With the added curvature
constraint, the computation becomes particularly challenging. To enhance the
computational efficiency, we solve the problem by a novel operator splitting
scheme. It replaces the original high-order PDEs by a decoupled PDE system,
which is solved by a semi-implicit method. We also discuss approach using an
augmented Lagrangian method. The proposed method shows robustness against
noise, and recovers concave features and sharp corners better compared to
models without curvature constraint. Numerical experiments in two and three
dimensional data sets, noisy and sparse data are presented to validate the
model.
