On interpolation by Planar cubic $G^2$ pythagorean-hodograph spline curves

In this paper, the geometric interpolation of planar data points and boundary tangent directions by a cubic $G^2$ Pythagorean-hodograph (PH) spline curve is studied. It is shown that such an interpolant exists under some natural assumptions on the data. The construction of the spline is based upon the solution of a tridiagonal system of nonlinear equations. The asymptotic approximation order 4 is confirmed.