Many of Boeing's products, including the new 787, make effective use of composite materials in their construction. These advanced materials offer superior weight and strength characteristics and are one of the principal reasons the 787 has become the fastest selling jetliner in aviation history. Building geometric models which enable the manufacture of these materials is non-trivial, however, and many ad hoc approaches are widely used. This talk will focus on a relatively new approach to the problem which makes use of a convolution operation to build empirical geometry models for these parts and the tools used to construct them. Insights into both the application and the underlying mathematics involved in the geometric modeling will be offered. Tom Grandine is a specialist in advanced geometric design and numerical analysis. His areas of expertise include curve and surface modeling, numerical approximation, splines, and multidisciplinary design optimization. He has extensive experience in computational methods for both engineering and manufacturing applications