IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i8p1269-d791525.html
   My bibliography  Save this article

A Comparative Study of Different Schemes Based on Bézier-like Functions with an Application of Craniofacial Fractures Reconstruction

Author

Listed:
  • Abdul Majeed

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

  • Muhammad Abbas

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

  • Kenjiro T. Miura

    (Department of Mechanical Engineering, Shizuoka University, Hamamatsu 432-8561, Shizuoka, Japan)

Abstract

Cranial implants, especially custom made implants, are complex, important and necessary in craniofacial fracture restoration surgery. However, the classical procedure of the manual design of the implant is time consuming and complicated. Different computer-based techniques proposed by different researchers, including CAD/CAM, mirroring, reference skull, thin plate spline and radial basis functions have been used for cranial implant restoration. Computer Aided Geometric Design (CAGD) has also been used in bio-modeling and specifically for the restoration of cranial defects in form of different spline curves, namely C 1 , C 2 , G C 1 G C 2 , rational curves, B-spline and Non-Uniform Rational B-Spline (NURBS) curves. This paper gives an in-depth comparison of existing techniques by highlighting the limitations and advantage in different contexts. The construction of craniofacial fractures is made using different Bézier-like functions (Ball, Bernstein and Timmer basis functions) and is analyzed in detail. The C 1 , G C 1 and G C 2 cubic Ball curves are performed well for construction of the small fractured part. Any form of fracture is constructed using this approach and it has been effectively applied to frontal and parietal bone fractures. However, B-spline and NURBS curves can be used for any type of fractured parts and are more friendly user.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1269-:d:791525
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/8/1269/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/8/1269/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Abdul Majeed & Muhammad Abbas & Faiza Qayyum & Kenjiro T. Miura & Md Yushalify Misro & Tahir Nazir, 2020. "Geometric Modeling Using New Cubic Trigonometric B-Spline Functions with Shape Parameter," Mathematics, MDPI, vol. 8(12), pages 1-25, November.
    2. 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.
    3. 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.
    4. Abdul Majeed & Abd Rahni Mt Piah & R U Gobithaasan & Zainor Ridzuan Yahya, 2015. "Craniofacial Reconstruction Using Rational Cubic Ball Curves," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-14, April.
    5. Abdul Majeed & Abd Rahni Mt Piah & Zainor Ridzuan Yahya, 2016. "Surface Reconstruction from Parallel Curves with Application to Parietal Bone Fracture Reconstruction," PLOS ONE, Public Library of Science, vol. 11(3), pages 1-16, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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 & Faiza Qayyum & Kenjiro T. Miura & Md Yushalify Misro & Tahir Nazir, 2020. "Geometric Modeling Using New Cubic Trigonometric B-Spline Functions with Shape Parameter," Mathematics, MDPI, vol. 8(12), pages 1-25, November.
    3. 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.
    4. Nur Atiqah Binti Zulkifli & Samsul Ariffin Abdul Karim & A’fza Binti Shafie & Muhammad Sarfraz & Abdul Ghaffar & Kottakkaran Sooppy Nisar, 2019. "Image Interpolation Using a Rational Bi-Cubic Ball," Mathematics, MDPI, vol. 7(11), pages 1-18, November.
    5. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1269-:d:791525. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.