IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v164y2019icp46-62.html
   My bibliography  Save this article

A C̃2 spline quasi-interpolant for fitting 3D data on the sphere and applications

Author

Listed:
  • Bouhiri, S.
  • Lamnii, A.
  • Lamnii, M.
  • Zidna, A.

Abstract

In this paper, a new local spline quasi-interpolant is constructed for fitting 3D data defined on a sphere-like surface S. After mapping the surface S to a rectangular domain, we use the tensor product of cubic polynomial B-splines and 2π-periodic uniform algebraic trigonometric B-splines (UAT B-splines) of order four for constructing a new quasi-interpolant T. The use of UAT B-splines allows us to obtain an approximating surface which is almost of class C2 and the approximation order is O(h4). We show that this method is particularly well designed to render 3D closed surfaces and it has been successfully applied to reconstruct human organs such as the lung and left ventricle of the heart.

Suggested Citation

  • Bouhiri, S. & Lamnii, A. & Lamnii, M. & Zidna, A., 2019. "A C̃2 spline quasi-interpolant for fitting 3D data on the sphere and applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 164(C), pages 46-62.
    • Handle: RePEc:eee:matcom:v:164:y:2019:i:c:p:46-62
    DOI: 10.1016/j.matcom.2018.06.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475418301666
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2018.06.009?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Lamnii, A. & Mraoui, H. & Sbibih, D. & Zidna, A., 2013. "Uniform tension algebraic trigonometric spline wavelets of class C2 and order four," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 87(C), pages 68-86.
    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. Theodosiou, T.C., 2021. "Derivative-orthogonal non-uniform B-Spline wavelets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 368-388.

    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:eee:matcom:v:164:y:2019:i:c:p:46-62. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.