BIT Numerical Mathematics

, Volume 55, Issue 3, pp 751–779 | Cite as

Shape preserving \(HC^2\) interpolatory subdivision

  • Davide Lettieri
  • Carla ManniEmail author
  • Francesca Pelosi
  • Hendrik Speleers


A subdivision procedure is developed to solve a \(C^2\) Hermite interpolation problem with the further request of preserving the shape of the initial data. We consider a specific non-stationary and non-uniform variant of the Merrien \(HC^2\) subdivision family, and we provide a data dependent strategy to select the related parameters which ensures convergence and shape preservation for any set of initial monotone and/or convex data. Each step of the proposed subdivision procedure can be regarded as the midpoint evaluation of an interpolating function—and of its first and second derivatives—in a suitable space of \(C^2\) functions of dimension \(6\) which has tension properties. The limit function of the subdivision procedure is a \(C^2\) piecewise quintic polynomial interpolant.


Subdivision Hermite interpolation Shape preservation Bézier form 

Mathematics Subject Classification

65D05 65D17 


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Davide Lettieri
    • 1
  • Carla Manni
    • 1
    Email author
  • Francesca Pelosi
    • 1
  • Hendrik Speleers
    • 1
  1. 1.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomeItaly

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