O. Aichholzer, W. Aigner, T. Hackl, and N. Wolpert
We propose a method to compute the algebraically correct medial axis for simply
connected planar domains which are given by boundary representations composed
of rational circular arcs. The algorithmic approach is based on the
Divide-and-Conquer paradigm. However, we show how to avoid inaccuracies in
the medial axis computations arising from a non-algebraic biarc construction
of the boundary. To this end we introduce the Exact Circular Arc Boundary
representation (ECAB), which allows algebraically exact calculation of
bisector curves. Fractions of these bisector curves are then used to
construct the exact medial axis. We finally show that all necessary
computations can be performed over the fild of rational numbers with a small
number of adjoint square-roots.
