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A family of ternary subdivision schemes for curves

Author

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  • Rehan, Kashif
  • Siddiqi, Shahid S.

Abstract

A family of ternary 3-point subdivision schemes is introduced and has a degree of smoothness C1 continuity. A family of ternary 4-point subdivision schemes is derived and has degrees of smoothness C1 and C2 continuities. Also a ternary 4-point approximating subdivision scheme is proposed that generates the limiting curve of C3 continuity. The eigenvalue analysis and generating function formalism are used to analyze the continuity properties of these subdivision schemes. Also these subdivision schemes are compared with the established subdivision schemes.

Suggested Citation

  • Rehan, Kashif & Siddiqi, Shahid S., 2015. "A family of ternary subdivision schemes for curves," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 114-123.
    • Handle: RePEc:eee:apmaco:v:270:y:2015:i:c:p:114-123
    DOI: 10.1016/j.amc.2015.08.024
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    Citations

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    Cited by:

    1. Pakeeza Ashraf & Abdul Ghaffar & Dumitru Baleanu & Irem Sehar & Kottakkaran Sooppy Nisar & Faheem Khan, 2020. "Shape-Preserving Properties of a Relaxed Four-Point Interpolating Subdivision Scheme," Mathematics, MDPI, vol. 8(5), pages 1-14, May.
    2. Amat, S. & Choutri, A. & Ruiz, J. & Zouaoui, S., 2018. "On a nonlinear 4-point ternary and non-interpolatory subdivision scheme eliminating the Gibbs phenomenon," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 16-26.
    3. Sofiane Zouaoui & Sergio Amat & Sonia Busquier & Mª José Legaz, 2022. "Some New n -Point Ternary Subdivision Schemes without the Gibbs Phenomenon," Mathematics, MDPI, vol. 10(15), pages 1-22, July.
    4. Sardar Muhammad Hussain & Aziz Ur Rehman & Dumitru Baleanu & Kottakkaran Sooppy Nisar & Abdul Ghaffar & Samsul Ariffin Abdul Karim, 2020. "Generalized 5-Point Approximating Subdivision Scheme of Varying Arity," Mathematics, MDPI, vol. 8(4), pages 1-25, March.

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