Design and manipulation of curves and surfaces are required in many different areas of technology, for example in the definition of products such as cars and the casings for electrical devices. Fourier methods have long been used in image processing but have seen much less use in computer aided design (CAD). This paper suggests the use of Fourier methods for the generation of blends, which provide smooth transitions between model surfaces, and fairings, which smooth large regions of the surface of an object. A description is given of the use of Fourier methods to allow predictable and simple control over curved shape in a two- dimensional system, and results of the system are presented and analyzed. This allows informed assertions to be made regarding the extension to a surface smoothing system, which, at the time of writing, has not been developed. In particular we note that under certain circumstances the Fourier smoothing methods reduce to spline production, and the connection with spline theory is made clear where applicable.