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Mathematical Problems in Engineering
Volume 2013, Article ID 512020, 12 pages
Research Article

Singularities of a Space Curve according to the Relatively Parallel Adapted Frame and Its Visualization

1School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
2School of Science, Mudanjiang Normal University, Mudanjiang 15701, China

Received 21 October 2012; Accepted 26 December 2012

Academic Editor: Kue-Hong Chen

Copyright © 2013 Haiming Liu and Donghe Pei. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The relatively parallel adapted frame or Bishop frame is an alternative approach to define a moving frame that is well defined even when the curve has vanished second derivative, and it has been widely used in the areas of biology, engineering, and computer graphics. The main result of this paper is using the relatively parallel adapted frame for classification of singularity type of Bishop spherical Darboux image and Bishop dual which are deeply related with a space curve and making them visualized by computer.