In product design, designers often create a multitude of concept sketches as part of the ideation and exploration process. Transforming such sketches to 3D digital models requires special expertise due to a lack of intuitive computer aided design (CAD) tools suitable for rapid modeling. Recent advances in sketch-based user interfaces and immersive environments have introduced novel curve design methods that facilitate the transformation of such sketches into 3D digital models. However, rapid surfacing of such data remains an open challenge. Based on the observation that a sparse network of curves is reasonably sufficient to convey the intended geometric shape, we propose a new method for creating approximate surfaces on curve clouds automatically. A notable property of our method is that it relieves many topological and geometric restrictions of 3D conventional networks such as the curves do not need to be connected to one another or gently drawn. Our method calculates a 3D guidance vector field in the space that the curve cloud appears. This guidance vector field helps drive a deformable closed surface onto the curves. During this deformation, surface smoothness is controlled through a set of surface smoothing and subdivision operations. The resulting surface can be further beautified by the user manually using selective surface modification and fairing operations. We demonstrate the effectiveness of our approach on several case examples. Our studies have shown that the proposed technique can be particularly useful for rapid visualization.