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A geometric approach for Hermite subdivision

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Abstract

We present a non-stationary, non-uniform scheme for two-point Hermite subdivision. The novelty of this approach relies on a geometric interpretation of the subdivision steps—related to generalized Bernstein bases—which permits to overcome the usually unavoidable analytical difficulties. The main advantages consist in extra smoothness conditions, which in turn produce highly regular limit curves, and in an elegant structure of the subdivision—described by three de Casteljau type matrices. As a by-product, the scheme is inherently shape preserving.

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Authors and Affiliations

  1. Dipartimento di Scienze Matematiche ed Informatiche, Università di Siena, Siena, Italy

    Paolo Costantini

  2. Dipartimento di Matematica, Università di Roma “Tor Vergata”, Rome, Italy

    Carla Manni

Authors
  1. Paolo Costantini
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  2. Carla Manni
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Correspondence to Paolo Costantini.

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Costantini, P., Manni, C. A geometric approach for Hermite subdivision. Numer. Math. 115, 333–369 (2010). https://doi.org/10.1007/s00211-009-0280-0

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  • DOI: https://doi.org/10.1007/s00211-009-0280-0

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