Curvature-sensitive splines and design with basic curves

This paper presents a non-uniform cubic C2C2 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 C2C2 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.

► Our non-uniform cubic C2C2 spline framework unifies treatment of basic curves.
► Basic curves, such as spirals and conics, are joined into the spline.
► The spline incorporates well-spaced samples, rational and non-rational basic curves.
► Focus is on transitions for strongly differing curvatures.
► A new form of curvature-sensitive averaging is introduced.