Constructing parametric quadratic curves

Constructing a parametric spline curve to pass through a set of data points requires assigning a knot to each data point. In this paper we discuss the construction of parametric quadratic splines and present a method to assign knots to a set of planar data points. The assigned knots are invariant under affine transformations of the data points, and can be used to construct a parametric quadratic spline which reproduces parametric quadratic polynomials. Results of comparisons of the new method with several known methods are included.