Paper Info
Title
Rational parametric representation of parabolic cyclide: formulation and applications
Abstract
The Dupin cyclide is a quartic surface with several interesting properties such as circular lines of curvature and rational parametric representation. Non-degenerate forms of the Dupin cyclide have been used for applications such as surface composition, variable radius blending and free space representation. The parabolic cyclide, a cubic surface, is a degenerate form of the Dupin cyclide with a pair of skew lines of curvature on its surface. The parabolic cyclide patch is attractive for geometric design applications due to its lower algebraic degree and (degenerate) straight lines of curvature, which can be used to provide smooth transition from planar to curved surfaces. The parametric representations available for the general Dupin cyclide cannot, in general, be extended to the parabolic cyclide. In this paper, we derive a new rational biquadratic and corresponding NURBS representation for a parabolic cyclide patch. We also discuss the practical issues involved in using these parametric representations and provide examples of applications of this patch.
Year
DOI
Venue
1995
10.1016/0167-8396(95)00032-2
Computer Aided Geometric Design
Keywords
DocType
Volume
parabolic cyclide,rational parametric representation,dupin cycle,nurbs representation
Journal
12
Issue
ISSN
Citations 
6
Computer Aided Geometric Design
8
PageRank 
References 
Authors
0.99
4
2
Name
Order
Citations
PageRank
Y.L. Srinivas1333.90
Debashish Dutta2283.42