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Log-Aesthetic Magnetic Curves and Their Application for CAD Systems

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  • Mei Seen Wo
  • R. U. Gobithaasan
  • Kenjiro T. Miura

Abstract

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 G 2 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 G 2 Hermite data is still a cumbersome task.

Suggested Citation

  • Mei Seen Wo & R. U. Gobithaasan & Kenjiro T. Miura, 2014. "Log-Aesthetic Magnetic Curves and Their Application for CAD Systems," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-16, October.
    • Handle: RePEc:hin:jnlmpe:504610
    DOI: 10.1155/2014/504610
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    Cited by:

    1. Valery Ochkov & Inna Vasileva & Ekaterina Borovinskaya & Wladimir Reschetilowski, 2021. "Approximation of Generalized Ovals and Lemniscates towards Geometric Modeling," Mathematics, MDPI, vol. 9(24), pages 1-17, December.

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