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Mathematical Problems in Engineering
Volume 2014, Article ID 504610, 16 pages
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.


Curves are the building blocks of shapes and designs in computer aided geometric design (CAGD). It is important to ensure these curves are both visually and geometrically aesthetic to meet the high aesthetic need for successful product marketing. Recently, magnetic curves that have been proposed for computer graphics purposes are a particle tracing technique that generates a wide variety of curves and spirals under the influence of a magnetic field. The contributions of this paper are threefold, where the first part reformulates magnetic curves in the form of log-aesthetic curve (LAC) denoting it as log-aesthetic magnetic curves (LMC) and log-aesthetic magnetic space curves (LMSC), the second part elucidates vital properties of LMCs, and the final part proposes G2 LMC design for CAD applications. The final section shows two examples of LMC surface generation along with its zebra maps. LMC holds great potential in overcoming the weaknesses found in current interactive LAC mechanism where matching a single segment with G2 Hermite data is still a cumbersome task.