Procedure for Converting a Wilson-Fowler Spline to a Cubic B-Spline with Double Knots

摘要

The Wilson-Fowler spline (WF-spline) has been used by the DOE Weapons Complex for over twenty years to represent point-defined smooth curves. Most modern CADCAM systems use parametric B-spline curves (or, more recently, rational B-splines) for this same purpose. The WF-spline is a parametric piecewise cubic curve. It has been shown that a WF-spline can be reparametrized so that its components are C sup 1 piecewise cubic functions (functions that are cubic polynomials on each parameter interval, joined so the function and first derivative are continuous). The purpose of these notes is to show explicitly how to convert a given WF-spline to a cubic B-spline with double knots. 7 refs. (ERA citation 13:035534)