Poisson surface reconstruction creates watertight surfaces from oriented

point sets. In this work we extend the technique to explicitly incorporate

the points as interpolation constraints. The extension can be interpreted as

a generalization of the underlying mathematical framework to a screened

Poisson equation. In contrast to other image and geometry processing

techniques, the screening term is defined over a sparse set of points rather

than over the full domain. We show that these sparse constraints can

nonetheless be integrated efficiently. Because the modified linear system

retains the same finite-element discretization, the sparsity structure is

unchanged, and the system can still be solved using a multigrid approach.

Moreover we present several algorithmic improvements that together

reduce the time complexity of the solver to linear in the number of points,

thereby enabling faster, higher-quality surface reconstructions.