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Minimal energy Cr-surfaces on uniform Powell-Sabin type meshes

Author

Listed:
  • Barrera, D.
  • Fortes, M.A.
  • González, P.
  • Pasadas, M.

Abstract

In this paper we present a method to obtain a Cr-surface (r≥1) on a polygonal domain which approximates a Lagrange data set and minimizes an “energy functional”. The minimization space is formed by bivariate spline functions constructed on a uniform Powell-Sabin type triangulation of the domain. We prove a convergence result and we present a method for the estimation of the smoothing parameters involved in the functional. We finish with some numerical and graphical examples.

Suggested Citation

  • Barrera, D. & Fortes, M.A. & González, P. & Pasadas, M., 2008. "Minimal energy Cr-surfaces on uniform Powell-Sabin type meshes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(2), pages 161-169.
    • Handle: RePEc:eee:matcom:v:77:y:2008:i:2:p:161-169
    DOI: 10.1016/j.matcom.2007.08.020
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    Cited by:

    1. Kouibia, A. & Pasadas, M., 2014. "Optimization of the parameters of surfaces by interpolating variational bicubic splines," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 102(C), pages 76-89.
    2. Fortes, M.A. & González, P. & Palomares, A. & Rodríguez, M.L., 2019. "Filling holes using a mesh of filled curves," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 164(C), pages 78-93.
    3. Fortes, M.A. & Medina, E., 2022. "Fitting missing data by means of adaptive meshes of Bézier curves," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 33-48.
    4. Fortes, M.A. & González, P. & Palomares, A. & Pasadas, M., 2015. "Filling holes with shape preserving conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 118(C), pages 198-212.
    5. Fortes, M.A. & Pasadas, M. & Sbibih, D. & Serghini, A. & Tijini, A., 2011. "Variational trivariate fitting using Worsey–Piper macro elements on tetrahedral partitions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(10), pages 2161-2173.
    6. Fortes, M.A. & González, P. & Pasadas, M. & Rodríguez, M.L., 2011. "A hole filling method for surfaces by using C1-Powell–Sabin splines. Estimation of the smoothing parameters," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(10), pages 2150-2160.

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