Abstract The three-dimensional reconstruction of scenes from multiple views has made impressive strides in recent years, chiefly by methods correlating isolated feature points, intensities, or curvilinear structure. In the general setting, i.e., without requiring controlled acquisition, limited number of objects, abundant patterns on objects, or object curves to follow particular models, the majority of these methods produce unorganized point clouds, meshes, or voxel representations of the reconstructed scene, with some exceptions producing 3D drawings as networks of curves. Many applications, e.g., robotics, urban planning, industrial design, and hard surface modeling, however, require structured representations which make explicit 3D curves, surfaces, and their spatial relationships. Reconstructing surface representations can now be constrained by the 3D drawing acting like a scaffold to hang on the computed representations, leading to increased robustness and quality of reconstruction. This paper presents one way of completing such 3D drawings with surface reconstructions, by exploring occlusion reasoning through lofting algorithms.