G1 Hermite interpolation by Minkowski Pythagorean hodograph cubics

As observed by Choi et al. (1999), curves in Minkowski space R2,1 are very well suited to describe the medial axis transform (MAT) of a planar domain, and Minkowski Pythagorean hodograph (MPH) curves correspond to domains, where both the boundaries and their offsets are rational curves (Moon, 1999). Based on these earlier results, we give a thorough discussion of G1 Hermite interpolation by MPH cubics, focusing on solvability and approximation order. Among other results, it is shown that any analytic space–like curve without isolated inflections can be approximately converted into a G1 spline curve composed of MPH cubics with the approximation order being equal to four. The theoretical results are illustrated by several examples. In addition, we show how the curvature of a curve in Minkowski space is related to the boundaries of the associated planar domain.