Exact medial axis computation for circular arc boundaries

Authors:
Oswin Aichholzer;Wolfgang Aigner;Thomas Hackl;Nicola Wolpert
Affiliations:
Institute for Software Technology, Graz University of Technology, Austria;Institute for Software Technology, Graz University of Technology, Austria;Institute for Software Technology, Graz University of Technology, Austria;Faculty Geomatics, Computer Science and Mathematics, Stuttgart University of Applied Sciences, Germany
Venue:
Proceedings of the 7th international conference on Curves and Surfaces
Year:
2010

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Abstract

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-&-Conquer paradigm, as used in [12]. 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 field of rational numbers with a small number of adjoint square-roots.