Convexity Preservation of the Four-Point Interpolatory Subdivision Scheme

Nira Dyn, F. Kuijt, David Levin, Rudolf M.J. van Damme

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    In this note we examine the convexity preserving properties of the (linear) four-point interpolatory subdivision scheme of Dyn, Gregory and Levin when applied to functional univariate strictly convex data. Conditions on the tension parameter guaranteeing preservation of convexity are derived. These conditions depend on the initial data. The resulting scheme is the four-point scheme with tension parameter bounded from above by a bound smaller than 1/16. Thus the scheme generates C1 limit functions and has approximation order two.
    Original languageUndefined
    Pages (from-to)789-792
    Number of pages4
    JournalComputer aided geometric design
    Issue number16
    Publication statusPublished - 1999


    • Stationary subdivision schemes
    • METIS-140441
    • IR-74035
    • Convexity preservation

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