Incense, candle smoke and cigarette smoke often exhibit smoke flows with a surface-like appearance. Although delving into well-known computational fluid dynamics may provide a solution to create such an appearance, we propose a much efficient alternative that combines a low-resolution fluid simulation with explicit geometry provided by NURBS surfaces. Among a wide spectrum of fluid simulation, our algorithm specifically tailors to reproduce the semi-transparent surface look and motion of the smoke. The main idea is that we follow the traces called streaklines created by the advected particles from a simulation and reconstruct NURBS surfaces passing through them. Then, we render the surfaces by applying an opacity map to each surface, where the opacity map is created by utilizing the smoke density and the characteristics of the surface contour. Augmenting the results from low-resolution simulations such a way requires a low computational cost and memory usage by design.