Monotonicity Preserving Interpolatory Subdivision Schemes

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    Abstract

    A class of local nonlinear stationary subdivision schemes that interpolate equidistant data and that preserve monotonicity in the data is examined. The limit function obtained after repeated application of these schemes exists and is monotone for arbitrary monotone initial data. Next a class of rational subdivision schemes is investigated. These schemes generate limit functions that are continuously differentiable for any strictly monotone data. The approximation order of the schemes is four. Some generalisations, such as preservation of piecewise monotonicity and application to homogeneous grid refinement, are briefly discussed.
    Original languageEnglish
    Pages (from-to)203-229
    Number of pages27
    JournalJournal of computational and applied mathematics
    Volume101
    Issue number1-2
    DOIs
    Publication statusPublished - 1999

    Keywords

    • Shape preservation
    • Subdivision
    • Computer aided geometric design
    • Interpolation
    • Monotonicity preservation

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