Curvature-sensitive splines and design with basic curves

This paper presents a non-uniform cubic C spline framework that unifies three scenarios for incorporating data from basic curves, such as spirals and conics. In the first scenario, no parameterization of the basic curves is available, only well-spaced samples; in the second, a parameterization is available but cannot be used directly in a spline framework; only in the third scenario can pieces of basic curves be exactly re-represented and included into the spline. In all three cases the output is a cubic C spline suitable for standard CAD downstream processing. A key challenge in constructing the spline is to cope with transitions in the presence of strongly differing curvatures. Here we introduce a new form of curvature-sensitive averaging.