Geometric construction of quintic parametric B-splines

The aim of this paper is to present a new class of B-spline-like functions with tension properties. The main feature of these basis functions consists in possessing C 3 or even C 4 continuity and, at the same time, being endowed by shape parameters that can be easily handled. Therefore they constitute a useful tool for the construction of curves satisfying some prescribed shape constraints. The construction is based on a geometric approach which uses parametric curves with piecewise quintic components.