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Surface Modeling from 2D Contours with an Application to Craniofacial Fracture Construction

Author

Listed:
  • Abdul Majeed

    (Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan)

  • Muhammad Abbas

    (Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City 70000, Vietnam
    Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 70000, Vietnam)

  • Kenjiro T. Miura

    (Department of Mechanical Engineering, Shizuoka University, Hamamatsu, Shizuoka 432-8011, Japan)

  • Mohsin Kamran

    (Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan)

  • Tahir Nazir

    (Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan)

Abstract

Treating trauma to the cranio-maxillofacial region is a great challenge and requires expert clinical skills and sophisticated radiological imaging. The aim of reconstruction of the facial fractures is to rehabilitate the patient both functionally and aesthetically. Bio-modeling is an important tool for constructing surfaces using 2D cross sections. The aim of this manuscript was to show 3D construction using 2D CT scan contours. The fractured part of the cranial vault were constructed using a Ball curve with two shape parameters, later the 2D contours were flipped into 3D with an equidistant z component. The surface created was represented by a bi-cubic rational Ball surface with C 2 continuity. At the end of this article, we present two real cases, in which we had constructed the frontal and parietal bone fractures using a bi-cubic rational Ball surface. The proposed method was validated by constructing the non-fractured part.

Suggested Citation

  • Abdul Majeed & Muhammad Abbas & Kenjiro T. Miura & Mohsin Kamran & Tahir Nazir, 2020. "Surface Modeling from 2D Contours with an Application to Craniofacial Fracture Construction," Mathematics, MDPI, vol. 8(8), pages 1-16, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1246-:d:392237
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    References listed on IDEAS

    as
    1. Majeed, Abdul & Mt Piah, Abd Rahni & Rafique, Muhammad & Abdullah, Johari Yap & Rajion, Zainul Ahmad, 2017. "NURBS curves with the application of multiple bones fracture reconstruction," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 70-84.
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    Cited by:

    1. Abdul Majeed & Muhammad Abbas & Kenjiro T. Miura, 2022. "A Comparative Study of Different Schemes Based on Bézier-like Functions with an Application of Craniofacial Fractures Reconstruction," Mathematics, MDPI, vol. 10(8), pages 1-16, April.
    2. Abdul Majeed & Mehwish Naureen & Muhammad Abbas & Kenjiro T. Miura, 2022. "Construction of Cubic Trigonometric Curves with an Application of Curve Modelling," Mathematics, MDPI, vol. 10(7), pages 1-22, March.

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    1. Abdul Majeed & Mehwish Naureen & Muhammad Abbas & Kenjiro T. Miura, 2022. "Construction of Cubic Trigonometric Curves with an Application of Curve Modelling," Mathematics, MDPI, vol. 10(7), pages 1-22, March.
    2. Abdul Majeed & Muhammad Abbas & Kenjiro T. Miura, 2022. "A Comparative Study of Different Schemes Based on Bézier-like Functions with an Application of Craniofacial Fractures Reconstruction," Mathematics, MDPI, vol. 10(8), pages 1-16, April.

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