Some remarks on \(V^ 2\)-splines
Let X(t) be a plane curve. Differentiation with respect to arc length will be denoted by a prime ' while differentiation with respect to an arbitrary parameter will be denoted by a dot \({}^.\). It is shown that X(t) is visually \(C^ 2\) if and only if there is a function v(t) depending on the parameterization t(s) such that \(\ddot X(t+)-\ddot X(t- )=v(t)\dot X(t).\) This is applied to derive the defining equations of the interpolatory \(\nu\)-splines introduced by G. Nielson. Some piecewise polynomial alternatives to splines under tension, in: \textit{R. E. Barnhill} and \textit{R. F. Riesenfeld}, eds., ''Computer aided geometric design'' (1974; Zbl 0316.68006).
scientific article; zbMATH DE number 3964611