Abstract: We present a new 3D surface modeling approach that enables curve-based creation and modification of smooth surfaces by sketching. The key feature of the proposed methods is a two-way communication between the user-designed curve networks and the generated surfaces. A user-drawn curve network serves as a control cage, from which a subdivision surface is generated. The subdivision surface is updated to match the curve network while minimizing the curvature variation throughout the surface. Surface fairness is controlled independently to modify the curve network into suitable configurations that guarantee a smooth underlying surface. This approach enables a concurrent modeling of the curve network and the underlying surface, thus eliminating the need for a laborious, iterative adjustment of the curve network for smooth surface creation. We demonstrate our approach with example models, and evaluate it with a user study.