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

Abdul Majeed, Muhammad Abbas and Kenjiro T. Miura
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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

Mathematics, 2022, vol. 10, issue 8, 1-16

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.

Keywords: Ball curves; parametric continuity; geometric continuity; B-spline curves; NURBS curves; craniofacial fracture reconstruction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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