Curve fairing

A method is presented to fair cubic spline curves. A cubic spline curve is fair if its curvature plot is continuous and, it has at most R inflection points and S bulges with the specific signs of curvature values at the end points, where R is specified by designers and S is derived from the fairing procedure. Each segment of a cubic spline curve within two neighboring data points is shown to be a fair curve; however, it is not true for cubic parametric spline curves. Thus the fairing method concentrates on the whole shape of several neighboring spline segments and checks whether the whole curve has redundant inflection points and bulges. The proposed algorithm recursively removes the redundant inflection points and eliminates the surplus bulges based on the fairness definition and fairness criterion. It has been successfully applied to many practical examples in mathematical ship lofting. The experimental results show that the method is powerful and effective for fairing cubic splines.