A General Class of C¹ Smooth Rational Splines: Application to Construction of Exact Ellipses and Ellipsoids

In this paper, we describe a general class of C¹ smooth rational splines that enables, in particular, exact descriptions of ellipses and ellipsoids — some of the most important primitives for CAD and CAE. The univariate rational splines are assembled by transforming multiple sets of NURBS basis functions via so-called design...