Minkowski Pythagorean hodographs

We introduce the Minkowski Pythagorean hodograph (MPH) curve as a polynomia l curve whose speed measured under the Minkowski metric is polynomial. It i s a generalization of the Pythagorean hodograph (PH) curve. The MPH curve i s well adapted to the representation of the medial axis transform of a plan ar domain. In fact, if the smooth curve segment of the medial axis transfor m is written in the MPH form, the boundaries of the corresponding domain ar e easily computed as rational curves of the MPH curve parameter. Furthermor e, just subtracting a constant value from the radius, the offset curves can be obtained as rational curves. We also give the characterization of MPH c urves which is invariant under the Lorentz transform. (C) 1999 Elsevier Sci ence B.V. All rights reserved.