Medial axis transform of a planar domain with infinite curvature boundary points

While rational curves are extensively used as a standard medium of representation in computer aided geometric design, their curvature may diverge where the tangent vector vanishes and the medial axis of the domain bounded by such curves develops peculiar behaviors. The approach of prior studies cannot be directly employed in this situation since the boundary curves cease to be real-analytic at those points. In addition to a careful re-examination of the properties of the medial axis still valid in the current setting, we present a detailed investigation of the medial axis near the points of infinite curvature that will serve as a theoretical foundation of future studies on its exact computation.

► We study the medial axis transform of a planar domain with rational boundary pieces.
► Such domains may contain points of infinite curvature on their boundary.
► The presence of infinite curvature points gives rise to new phenomena which need careful analysis.
► We obtain more or less parallel results with those in Choi et al. (1997a) for such domains.