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

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• 作者：Chang Yong Han^a ; ¹ ; Song-Hwa Kwon^b ; ² ; ^{skwon@catholic.ac.kr} ; Hyeong In Choi^c ; ³
• 关键词：Medial axis transform ; Rational boundary curve ; Point of infinite curvature ; Real-analytic curve ; Exact computation
• 刊名：Computer Aided Geometric Design
• 出版年：2012
• 期刊代码：20_01678396
• 类别：cp
• 出版时间：August, 2012
• 卷：29
• 期：6
• 页码：281-295
• 文件大小：426 K

摘要

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.