In this paper we articulate a new modeling paradigm for both local and global editing on complicated point set surfaces of arbitrary topology. In essence, the proposed technique leads to a novel point-set methodology that can unify the topological advantage of the level-set methods and the simplicity of point-sampled surfaces. Any user-specified region of a point set surface in our system can be embedded into a grid-based level-set framework. The super-imposed grid structure enables both powerful local surface editing and global scalar-field free-form deformation anywhere across the point-sampled geometry. Furthermore, the underlying level-set representation, coupled with the concept of digital topology, greatly facilitates the topological modi- fication of the sculpted point-set geometry whenever necessary during shape deformation. We have developed a variety of editing toolkits that can allow users to directly manipulate the point-set surface through interactive sketching, smoothing, embossing, and global free-form deformations with ease. We demonstrate the usefulness and efficacy of our prototype system for the point-sampled geometry via many examples.