Date of Award
Doctor of Philosophy (PhD)
A rational interpolating cubic curve which implicitly maintains first order geometric continuity in splines has been developed. The curve is formed by blending two rational quadratic curves. Since the blending method used was originally introduced by Overhauser, this curve is referred to as the Rational Overhauser (Rover) curve. The curve formulation utilizes four shape factors to provide control of the curve. A geometrical and analytical interpretation of these shape factors and their relationship to each other is discussed. Procedures for representing conic sections using the rational Overhauser curve are presented. Also included are techniques for mapping between the Rover curve and rational forms of the Hermite, Bezier, and B-Spline curves.
Jortner, Jeffrey Neil, "The Rational Overhauser: an Interpolating Rational Cubic Curve." (1987). LSU Historical Dissertations and Theses. 4363.