Pythagorean-hodograph (PH) curves offer many important computational advantages over the "ordinary" Bezier/B-spline representations commonly used in CAD/CAM applications. Among the attributes that distinguish PH curves from the latter are: exact rectification in terms of a polynomial arc-length function; exact rational representations of their offsets; a closed-form expression, suitable for purposes of optimization, for their elastic bending energies; and a propensity to yield fairer loci --- exhibiting a smoother curver distribution --- in the interpolation of discrete data. Moreover, existing CAD systems can readily take advantage of these properties, since the PH curves are entirely compatible with the Bezier/B-spline representation. This project investigates outstanding theoretical and algorithmic issues concerning the construction and manipulation of PH curves. Their solution will permit the full potential of PH curves to be realized in applications such as rapid prototyping and NC milling. These issues encompass trimming procedures for PH curve offsets; real-time CNC interpolators for PH curves; optimal shape design with PH curves; algorithms for efficient construction of C2 PH splines; and alternate algebraic formulations for PH space curves. ***
