C2 Hermite interpolation by Minkowski Pythagorean hodograph curves and medial axis transform approximation

We describe and fully analyze an algorithm for C2 Hermite interpolation by Pythagorean hodograph curves of degree 9 in Minkowski space R2,1. We show that for any data there exists a four-parameter system of interpolants and we identify the one which preserves symmetry and planarity of the input data and which has the optimal approximation degree. The new algorithm is applied to an efficient approximation of segments of the medial axis transform of a planar domain leading to rational parameterizations of the offsets of the domain boundaries with a high order of approximation.