Abstract: We present a general framework for performing geometry filtering through the solution of a screened Poisson equation. We show that this framework can be efficiently adapted to a changing Riemannian metric to support curvature-aware filtering and describe a parallel and streaming multigrid implementation for solving the system. We demonstrate the practicality of our approach by developing an interactive system for mesh editing that allows for exploration of a large family of curvature-guided, anisotropic filters.