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Journal of Applied Mathematics
Volume 2014, Article ID 124240, 13 pages
http://dx.doi.org/10.1155/2014/124240
Research Article

Properties of Generalized Offset Curves and Surfaces

1School of Science, Jimei University, Xiamen 361021, China
2School of Mathematical Science, Xiamen University, Xiamen 361005, China

Received 25 October 2013; Accepted 11 March 2014; Published 21 May 2014

Academic Editor: Jacek Rokicki

Copyright © 2014 Xuejuan Chen and Qun Lin. 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.

Abstract

This paper proposes a definition of generalized offsets for curves and surfaces, which have the variable offset distance and direction, by using the local coordinate system. Based on this definition, some analytic properties and theorems of generalized offsets are put forward. The regularity and the topological property of generalized offsets are simply given by representing the generalized offset as the standard offset. Some examples are provided as well to show the applications of generalized offsets. The conclusions in this paper can be taken as the foundation for further study on extending the standard offset.