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 error estimation ( - steplength).
Cite this article
Gerhard Maess, Kurt Frischmuth, Parametric Quadratic Splines with Minimal Curvature. Z. Anal. Anwend. 10 (1991), no. 2, pp. 255–262DOI 10.4171/ZAA/449