The research was partly supported by Chinese 973 Program (2010CB328001) and Chinese 863 Program (2012AA040902). The second author was supported by the NSFC (61035002, 61272235). The fifth author was supported by the NSFC (61063029, 61173077).
Geometry (Session 2)
Polar NURBS Surface with Curvature Continuity
Article first published online: 25 NOV 2013
© 2013 The Author(s) Computer Graphics Forum © 2013 The Eurographics Association and John Wiley & Sons Ltd.
Computer Graphics Forum
Volume 32, Issue 7, pages 363–370, October 2013
How to Cite
Shi, K.-L., Yong, J.-H., Tang, L., Sun, J.-G. and Paul, J.-C. (2013), Polar NURBS Surface with Curvature Continuity. Computer Graphics Forum, 32: 363–370. doi: 10.1111/cgf.12244
- Issue published online: 25 NOV 2013
- Article first published online: 25 NOV 2013
- I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Curve, surface, solid, and object representations; Splines
Polar NURBS surface is a kind of periodic NURBS surface, one boundary of which shrinks to a degenerate polar point. The specific topology of its control-point mesh offers the ability to represent a cap-like surface, which is common in geometric modeling. However, there is a critical and challenging problem that hinders its application: curvature continuity at the extraordinary singular pole. We first propose a sufficient and necessary condition of curvature continuity at the pole. Then, we present constructive methods for the two key problems respectively: how to construct a polar NURBS surface with curvature continuity and how to reform an ordinary polar NURBS surface to curvature continuous. The algorithms only depend on the symbolic representation and operations of NURBS, and they introduce no restrictions on the degree or the knot vectors. Examples and comparisons demonstrate the applications of the curvature-continuous polar NURBS surface in hole-filling and free-shape modeling.