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Mathematical Problems in Engineering
Volume 2014, Article ID 504610, 16 pages
http://dx.doi.org/10.1155/2014/504610
Research Article

Log-Aesthetic Magnetic Curves and Their Application for CAD Systems

1School of Informatics & Applied Mathematics, University Malaysia Terengganu, 21030 Kuala Terengganu, Malaysia
2Graduate School of Science & Technology, Shizuoka University, Shizuoka 432-8561, Japan

Received 9 April 2014; Revised 1 September 2014; Accepted 6 September 2014; Published 27 October 2014

Academic Editor: Dan Simon

Copyright © 2014 Mei Seen Wo et al. 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. J. Ruskin, The Elements of Drawing, Dover Publications, New York, NY, USA, 1971.
  2. R. U. Gobithaasan and K. T. Miura, “Logarithmic curvature graph as a shape interrogation tool,” Applied Mathematical Sciences, vol. 8, no. 16, pp. 755–765, 2014. View at Publisher · View at Google Scholar · View at Scopus
  3. T. Harada, F. Yoshimoto, and M. Moriyama, “An aesthetic curve in the field of industrial design,” in Proceedings of the IEEE Symposium on Visual Languages, pp. 38–47, 1999. View at Publisher · View at Google Scholar
  4. K. T. Miura, “A general equation of aesthetic curves and its self-affinity,” Computer-Aided Design and Applications, vol. 3, no. 1–4, pp. 457–464, 2006. View at Publisher · View at Google Scholar · View at Scopus
  5. N. Yoshida and T. Saito, “Interactive aesthetic curve segments,” The Visual Computer, vol. 22, no. 9–11, pp. 896–905, 2006. View at Publisher · View at Google Scholar · View at Scopus
  6. R. U. Gobithaasan and K. T. Miura, “Aesthetic spiral for design,” Sains Malaysiana, vol. 40, no. 11, pp. 1301–1305, 2011. View at Google Scholar · View at Scopus
  7. R. U. Gobithaasan, R. Karpagavalli, and K. T. Miura, “Drawable region of the generalized log aesthetic curves,” Journal of Applied Mathematics, vol. 2013, Article ID 732457, 7 pages, 2013. View at Publisher · View at Google Scholar · View at Scopus
  8. R. U. Gobithaasan, R. Karpagavalli, and K. T. Miura, “Shape analysis of generalized log-aesthetic curves,” International Journal of Mathematical Analysis, vol. 7, no. 36, pp. 1751–1759, 2013. View at Publisher · View at Google Scholar · View at Scopus
  9. R. U. Gobithaasan, Y. M. Teh, A. R. M. Piah, and K. T. Miura, “Generation of Log-aesthetic curves using adaptive Runge–Kutta methods,” Applied Mathematics and Computation, vol. 246, pp. 257–262, 2014. View at Publisher · View at Google Scholar
  10. K. T. Miura, D. Shibuya, R. U. Gobithaasan, and S. Usuki, “Designing log-aesthetic splines with G2 continuity,” Computer-Aided Design and Applications, vol. 10, no. 6, pp. 1021–1032, 2013. View at Publisher · View at Google Scholar · View at Scopus
  11. N. Yoshida and T. Saito, “Quasi-aesthetic curves in rational cubic Bézier forms,” Computer-Aided Design and Applications, vol. 4, no. 1–4, pp. 477–486, 2007. View at Publisher · View at Google Scholar · View at Scopus
  12. G. Farin, “Class A Bézier curves,” Computer Aided Geometric Design, vol. 23, no. 7, pp. 573–581, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. R. I. Nabiyev and R. Ziatdinov, “A mathematical design and evaluation of Bernstein-Bézier curves’ shape features using the laws of technical aesthetics,” Mathematical Design & Technical Aesthetics, vol. 2, no. 1, pp. 6–13, 2014. View at Google Scholar
  14. R. Levien and C. H. Séquin, “Interpolating splines: which is the fairest of them all?” Computer-Aided Design and Applications, vol. 6, no. 1, pp. 91–102, 2009. View at Publisher · View at Google Scholar · View at Scopus
  15. K. T. Miura and R. U. Gobithaasan, “Aesthetic curves and surfaces in computer aided geometric design,” International Journal of Automation Technology, vol. 8, no. 3, pp. 304–316, 2014. View at Google Scholar · View at Scopus
  16. J. D. Jackson, Classical Electrodynamics, Wiley, New York, NY, USA, 1962. View at MathSciNet
  17. J. Bittencourt, “Charged particle motion in constant and uniform electromagnetic fields,” in Fundamentals of Plasma Physics, pp. 33–58, Springer, New York, NY, USA, 2004. View at Google Scholar
  18. L. Xu and D. Mould, “Magnetic curves: curvature-controlled aesthetic curves using magnetic fields,” in Proceedings of the 5th Eurographics conference on Computationals, Visualization and Imaging Aesthetics in Graphic, pp. 1–8, 2009.
  19. R. U. Gobithaasan and K. T. Miura, “Logarithmic curvature graph as a shape interrogation tool,” Applied Mathematical Sciences, vol. 8, no. 13–16, pp. 755–765, 2014. View at Publisher · View at Google Scholar · View at Scopus
  20. G. Harary and A. Tal, “3D Euler spirals for 3D curve completion,” Computational Geometry, vol. 45, no. 3, pp. 115–126, 2012. View at Publisher · View at Google Scholar · View at Scopus
  21. R. Brent, Algorithms for Minimization without Drivatives, Prentice Hall, Englewood Cliffs, NJ, USA, 1972. View at MathSciNet