Tangentially cubic curves in euclidean spaces

Abstract

Curve design using splines is one of the most fundamental topics in CAGD. Using standard spline methods, variational curve design has been investigated in a large number of contributions. The minimizers of the L2 norm of the second derivative have cubic segments (vanishing fourth derivative), the corresponding splines on surfaces have segments with vanishing tangential componant of the fourth derivative. Such segments are called tangentially cubic. In this paper we study with the tangentially cubic curves (i.e. T.C-curves) in R n. We give necessary and sufficient conditions for k-type curves to be T.C-curves. Finally, we give some examples of finite type T.C-curves in E 3 .