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C1 cubic splines on Powell–Sabin triangulations

Author

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  • Grošelj, Jan
  • Krajnc, Marjeta

Abstract

A bivariate C1 cubic spline space on a triangulation with Powell–Sabin refinement which extends the well-known C1 quadratic spline space and has a nested structure is introduced. A construction of a locally supported basis that forms a partition of unity is presented based on choosing particular triangles and line segments in the domain. Further, it is shown how these objects can be determined in order to obtain nonnegative basis functions under a natural restriction on the Powell–Sabin refinement. Geometrically intuitive B-spline representation is proposed which makes these splines a useful tool for CAGD applications.

Suggested Citation

  • Grošelj, Jan & Krajnc, Marjeta, 2016. "C1 cubic splines on Powell–Sabin triangulations," Applied Mathematics and Computation, Elsevier, vol. 272(P1), pages 114-126.
    • Handle: RePEc:eee:apmaco:v:272:y:2016:i:p1:p:114-126
    DOI: 10.1016/j.amc.2015.07.013
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    References listed on IDEAS

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    1. Lamnii, M. & Mraoui, H. & Tijini, A. & Zidna, A., 2014. "A normalized basis for C1 cubic super spline space on Powell–Sabin triangulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 99(C), pages 108-124.
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    Cited by:

    1. Salah Eddargani & María José Ibáñez & Abdellah Lamnii & Mohamed Lamnii & Domingo Barrera, 2021. "Quasi-Interpolation in a Space of C 2 Sextic Splines over Powell–Sabin Triangulations," Mathematics, MDPI, vol. 9(18), pages 1-22, September.

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    1. Salah Eddargani & María José Ibáñez & Abdellah Lamnii & Mohamed Lamnii & Domingo Barrera, 2021. "Quasi-Interpolation in a Space of C 2 Sextic Splines over Powell–Sabin Triangulations," Mathematics, MDPI, vol. 9(18), pages 1-22, September.
    2. Serghini, A., 2021. "A construction of a bivariate C2 spline approximant with minimal degree on arbitrary triangulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 358-371.

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