Medial axis transform and offset curves by Minkowski Pythagorean hodographcurves

We present a new approach to medial axis transform and offset curve computa tion. Our algorithm is based on the domain decomposition scheme which reduc es a complicated domain into a union of simple subdomains each of which is very easy to handle. This domain decomposition approach gives rise to the d ecomposition of the corresponding medial axis transform which is regarded a s a geometric graph in the three dimensional Minkowski space R-2,R-1. Each simple piece of the domain, called the fundamental domain, corresponds to a space-like curve in R-2,R-1. Then using the new spline, called the Minkows ki Pythagorean hodograph curve which was recently introduced, we approximat e within the desired degree of accuracy the curve part of the medial axis t ransform with a G(1) cubic spline of Minkowski Pythagorean hodograph. This curve has the property of enabling us to write all offset curves as rationa l curves. Further, this Minkowski Pythagorean hodograph curve representatio n together with the domain decomposition lemma mal;es the trimming process essentially trivial. We give a simple procedure to obtain the trimmed offse t curves in terms of the radius function of the MPH curve representing the medial axis transform. (C) 1999 Elsevier Science Limited. All rights reserv ed.