Parametric Quadratic Splines with Minimal Curvature

Abstract

The concept of curvature-minimizing is extended to parametric polynomial splines of degree two. In contrast to the non-parametric case the resulting smooth curve is invariant under rotation of the co-ordinate system. Moreover, for a certain choice of the parameters (defining the functional to be minimized) it may be interpreted as a minimizer of the strain energy. For the case that the given data are points on a sufficiently smooth curve there is given an $O(h^2)$ error estimation ($h$ - steplength).