Abstract: 3D sketching is an appealing approach for creating concept shapes in the early stages of design. While curve networks alone can convey shape, surfacing the network can dramatically help with visualization and interaction. Unfortunately, surfacing a curve network is an inherently ambiguous problem, and even if the correct surface patches are identified, they can have an arbitrarily complex 3D geometry, making it challenging to produce a reasonable tessellation. In this paper we address the problem of creating light-weight surface tessellations on the fly. Our approach is to identify potential patches in the curve network, and then break complicated patches into simpler ones which can be tessellated using any simple algorithm. Our surfacing approach relies on the observation that breaking a complicated patch into a set of nearly planar ones with small total area seems to create a simple, natural-looking surfaces. We demonstrate our approach on curve networks generated by two different 3D sketching systems.