C1 and C2-continuous polynomial parametric Lp splines (p⩾1)

We introduce Lp (1⩽p⩽∞) piecewise polynomial parametric splines of degree 3 or 5 which smoothly interpolate data points. The coefficients of these polynomial splines are calculated by minimizing the Lp norm of the second derivative. It is demonstrated that the C1-continuous cubic (resp. G1-continuous cubic and C2-continuous quintic) Lp polynomial splines are unique for 1