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.
| Original language | English |
|---|---|
| Pages (from-to) | 281-295 |
| Number of pages | 15 |
| Journal | Computer Aided Geometric Design |
| Volume | 29 |
| Issue number | 6 |
| DOIs | |
| State | Published - Aug 2012 |
Bibliographical note
Funding Information:✩ This paper has been recommended for acceptance by B. Juettler. * Corresponding author. E-mail address: [email protected] (S.-H. Kwon). 1 The author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (2011-0005756). 2 This work was supported by the Catholic University of Korea, Research Fund, 2011. 3 Supported in part by WCU-SNU, 2009. The author also holds joint appointment in the Research Institute of Mathematics, Seoul National University.
Keywords
- Exact computation
- Medial axis transform
- Point of infinite curvature
- Rational boundary curve
- Real-analytic curve