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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.

Linked References

  1. H. Shen, J. Fu, Z. Chen, and Y. Fan, “Generation of o set surface for tool path in nc machining through level set methods,” International Journal of Advanced Manufacturing Technology, vol. 46, no. 9–12, pp. 1043–1047, 2009. View at Publisher · View at Google Scholar
  2. R. Krasauskas and M. Peternell, “Rational offset surfaces and their modeling applications,” Nonlinear Computational Geometry, vol. 151, pp. 109–135, 2010. View at Google Scholar
  3. E. Brechner, “General tool offset curves and surfaces,” in Geometry Processing For Design and Manufacturing, SIAM, Philadelphia, Pa, USA, 1992. View at Google Scholar
  4. H. Pottmann, “General offset surfaces,” Neural Parallel and Scientific Computations, vol. 5, pp. 55–80, 1997. View at Google Scholar
  5. E. Arrondo, J. Sendra, and J. R. Sendra, “Genus formula for generalized offset curves,” Journal of Pure and Applied Algebra, vol. 136, no. 3, pp. 199–209, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  6. Q. Lin and J. G. Rokne, “Variable-radius offset curves and surfaces,” Mathematical and Computer Modelling, vol. 26, no. 7, pp. 97–108, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  7. J. R. Sendra and J. Sendra, “Algebraic analysis of offsets to hypersurfaces,” Mathematische Zeitschrift, vol. 234, no. 4, pp. 697–719, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. G. H. Georgiev, “Rational generalized offsets of rational surfaces,” Mathematical Problems in Engineering, vol. 2012, Article ID 618148, 15 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  9. R. E. Barnhill, “General tool offset curves and surfaces,” in Geometry Processing For Design and Manufacturing, SIAM, Philadelphia, Pa, USA, 1992. View at Google Scholar
  10. F. Anton, I. Emiris, B. Mourrain, and M. Teillaud, “The offset to an algebraic curve and an application to conics,” in Proceedings of the International Conference on Computational Science and Its Applications (ICCSA '05), pp. 683–696, May 2005. View at Scopus
  11. R. T. Farouki and C. A. Neff, “Algebraic properties of plane offset curves,” Computer Aided Geometric Design, vol. 7, no. 1–4, pp. 101–127, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  12. R. T. Farouki and C. A. Neff, “Analytic properties of plane offset curves,” Computer Aided Geometric Design, vol. 7, no. 1–4, pp. 83–99, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  13. F. Klok, “Two moving coordinate frames for sweeping along a 3D trajectory,” Computer Aided Geometric Design, vol. 3, no. 3, pp. 217–229, 1986. View at Google Scholar · View at Scopus
  14. E. Kreyszig, Differential Geometry, University of Toronto Press, 1959.
  15. R. P. Encheva and G. H. Georgiev, “Similar frenet curves,” Results in Mathematics, vol. 55, no. 3, pp. 359–372, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  16. T. F. Bancho, T. Gaffney, and C. McCrory, Cusps of Gauss Mappings Pitman, Research Notes in Mathematics, Pitman, London, UK, 1982.
  17. A. W. Nutbourne and R. R. Martin, Differential Geometry Applied To Curve and Surface Design, 1: Foundations, West Sussex, Chichester, UK; E. Horwood, New York, NY, USA, 1988.
  18. L. A. Piegl and W. Tiller, “Computing offsets of NURBS curves and surfaces,” CAD Computer Aided Design, vol. 31, no. 2, pp. 147–156, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus