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

Authors:
Chang Yong Han;Song-Hwa Kwon;Hyeong In Choi
Affiliations:
Department of Applied Mathematics, Kyung Hee University, Yongin, Gyeonggi 446-701, Republic of Korea;Department of Mathematics, The Catholic University of Korea, Bucheon 420-743, Republic of Korea;Department of Mathematics, Seoul National University, Seoul 151-747, Republic of Korea
Venue:
Computer Aided Geometric Design
Year:
2012

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Abstract

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.