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Mathematical Problems in Engineering
Volume 2013, Article ID 215614, 11 pages
Research Article

Cusps of Bishop Spherical Indicatrixes and Their Visualizations

1School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
2School of Science, Mudanjiang Normal University, Mudanjiang 157011, China

Received 15 October 2013; Accepted 9 December 2013

Academic Editor: Bo Shen

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 main result of this paper is using Bishop Frame and “Type-2 Bishop Frame” to study the cusps of Bishop spherical images and type-2 Bishop spherical images which are deeply related to a space curve and to make them visualized by computer. We find that the singular points of the Bishop spherical images and type-2 Bishop spherical images correspond to the point where Bishop curvatures and type-2 Bishop curvatures vanished and their derivatives are not equal to zero. As applications and illustration of the main results, two examples are given.