Various embodiments of a system and methods for generating 3D surface patches from unconstrained 3D curves are described. The system may receive a set of unconstrained 3D wireframe curves that represent a 3D wireframe model. The 3D wireframe curves may be unorganized, may have inconsistent orientations, and may have an arbitrary number and type of curve intersections. The system may automatically generate the 3D surface patches, dependent on the 3D wireframe curves. The 3D surface patches may form a 3D surface that connects the 3D wireframe curves. The 3D surface patches may be generated from faces of the 3D wireframe model. The faces may be elementary cycles extracted from the 3D wireframe model. The system may receive user input which indicates changes to the 3D surface patches. A user may change, create, and/or delete 3D surface patches to achieve a desired 3D surface that represents the 3D wireframe model.