Spline Toolbox

Rational Splines

A rational spline is, by definition, any function that is the ratio of two splines:

This requires to be scalar-valued, but is often chosen to be vector-valued. Further, it is desirable that be not zero for any of interest.

Rational splines are popular because, in contrast to ordinary splines, they can be used to describe certain basic design shapes, like conic sections, exactly.

NURBS and Other Rational Splines

Example: Circle