This thesis presents a comprehensive set of algorithms, techniques, and accompanying diagrams for the geometric description of turbomachinery blades. Many of the techniques presented are new and cannot be found in the literature. The geometry construction process is broken into several steps. Each of these steps has variations that constrain different design parameters, enabling design-specific constraints to be met. The process of mapping curves from two-dimensional space to three-dimensional space is described in detail. All the algorithms are designed to work with B-spline curves (and in some cases NURBS curves) and produce a B-spline surface for the blade.