Geometric Hermite interpolation with maximal order and smoothness Original Research Article

We conjecture that, under suitable assumptions, splines of degree ⩽n can interpolate points on a smooth curve in Rm with order of contact k − 1 = n − 1 + [(n − 1)(m − 1)] at every nth knot. Moreover, this Geometric Hermite Interpolant (GHI) has the optimal approximation order k + 1. We give a proof of this conjecture for planar quadratic spline curves and describe a simple construction of curvature continuous quadratic splines from control polygons.