The area of geometric modeling is concerned with the creation of computationally efficient models of solid physical objects to facilitate their design, assembly, and analysis. In a geometric modeling system, a solid such as a robot hand or a coffee cup is modeled by a collection of points, curves, and surfaces. The sorting of points along an algebraic curve is an operation that arises frequently during the creation and manipulation of geometric models. This thesis presents a thorough investigation of sorting, including an evaluation of the two conventional methods of sorting and the presentation of a new and superior method.