Abstract: With significant data missing in a point scan, reconstructing a complete surface with sufficient geometric and topological fidelity is highly challenging. We present an interactive technique for surface reconstruction from incomplete and sparse scans of 3D objects possessing sharp features. A fundamental premise of our interaction paradigm is that directly editing data in 3D is not only counterintuitive but also ineffective, while working with 1D entities (i.e., curves) is a lot more manageable. To this end, we factor 3D editing into two "orthogonal" interactions acting on skeletal and profile curves of the underlying shape, controlling its topology and geometric features, respectively. For surface completion, we introduce a novel skeleton-driven morph-to-fit, or morfit, scheme which reconstructs the shape as an ensemble of generalized cylinders. Morfit is a hybrid operator which optimally interpolates between adjacent curve profiles (the "morph") and snaps the surface to input points (the "fit"). The interactive reconstruction iterates between user edits and morfit to converge to a desired final surface. We demonstrate various interactive reconstructions from point scans with sharp features and significant missing data.