Analysis of uniform binary subdivision schemes for curve design

Nira Dyn*, John A. Gregory, David Levin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The paper analyses the convergence of sequences of control polygons produced by a binary subdivision scheme of the form {Mathematical expression} The convergence of the control polygons to a C° curve is analysed in terms of the convergence to zero of a derived scheme for the differences fi+1k-fik. The analysis of the smoothness of the limit curve is reduced to the convergence analysis of "differentiated" schemes which correspond to divided differences of fik:i∈ Z with respect to the diadic parametrization tik=i/2k. The inverse process of "integration" provides schemes with limit curves having additional orders of smoothness.

Original languageEnglish
Pages (from-to)127-147
Number of pages21
JournalConstructive Approximation
Issue number1
StatePublished - Dec 1991


  • AMS classification: 41A15, 65Q05, 68U05, 65D10
  • Control polygon
  • Curve design
  • Limit curve
  • Subdivision scheme


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