Minkowski Pythagorean hodographs Original Research Article

We introduce the Minkowski Pythagorean hodograph (MPH) curve as a polynomial curve whose speed measured under the Minkowski metric is polynomial. It is a generalization of the Pythagorean hodograph (PH) curve. The MPH curve is well adapted to the representation of the medial axis transform of a planar domain. In fact, if the smooth curve segment of the medial axis transform is written in the MPH form, the boundaries of the corresponding domain are easily computed as rational curves of the MPH curve parameter. Furthermore, just subtracting a constant value from the radius, the offset curves can be obtained as rational curves. We also give the characterization of MPH curves which is invariant under the Lorentz transform.