This Small Grant for Exploratory Research (SGER) project will investigate a novel approach to driving CNC machines directly from the analytic descriptions of paths based on the use of Pythagorean-hodograph (PH) curves. The principal goal of this exploratory study is to give a practical demonstration of the advantages of PH curve interpolator algorithms by implementing and testing them within the framework of a commercial open-architecture CNC software product. The MDSI OpenCNC system will be used for this purpose. The performance of the PH curve CNC interpolators in terms of positional accuracy, feedrate smoothness, continuously-variable feedrate capability, and other characteristics will be compared with both linear/circular G code part programs and approximate Bezier/B-spline interpolation algorithms. The PH curves incorporate a special algebraic structure, which renders them well suited to real-time processing by open-architecture CNC interpolators and controllers. In addition to bypassing the need for intermediate linear/circular tool path approximations, PH curves offer a new ability to drive CNC machines at continuously-varying feedrates. This project offers the potential for very significant performance improvements in CNC machines.