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This article proposes a new modeling paradigm for local and global editing on point set surfaces. The technique unifies the topological advantage of implicitly defined surfaces, the strength of physics-based modeling techniques, and the simplicity of point-sampled surfaces. The implicit representation not only affords powerful local surface sculpting and global free-form deformation, but also enables users to easily modify the topology of the sculpted point-set. A variety of editing toolkits dynamically manipulates the implicitly defined point-set surface and performs global and local free-form deformations, interactive sketching, embossing, and smoothing. Experiments demonstrate that the proposed methodology augments current point-set-based modeling techniques with a new editing scheme.