Rational fixed radius rolling ball blends between natural quadrics

By applying results on canal surfaces, we study exact rational parametrizations of fixed radius rolling ball blends of pairs of natural quadrics. We classify all configurations where this kind of rational parametrization is possible, and describe a general algorithm for parametrizing fixed radius rolling ball blends. The algorithm is then applied to parametrize the fixed radius rolling ball blends of pairs of natural quadrics.

► Four pairs of natural quadrics have rational fixed radius rolling ball blends.
► Cone/plane, 2 cones with 1 or 2 touching points, cone/sphere with 1 touching point.
► We present minimal bi-degree rational parametrizations in these cases.
► A general algorithm for rational parametrizations of fixed radius blends is given.