de Casteljau's Algorithm Revisited

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    Abstract

    It is demonstrated how all the basic properties of Bezier curves can be derived swiftly and efficiently without any reference to the Bernstein polynomials and essentially with only geometric arguments. This is achieved by viewing one step in de Casteljau's algorithm as an operator (the de Casteljau operator) acting on a sequence of points, producing a sequence with one point less. The properties of Bezier curves are then derived by analysing de Casteljau's operator.
    Original languageEnglish
    Title of host publicationMathematical Methods for Curves and Surfaces II
    Place of PublicationNashville
    PublisherVanderbilt University Press
    Publication date1998
    Pages221-228
    ISBN (Print)0-8265-1315-8
    Publication statusPublished - 1998
    EventInternational Conference on Mathematical Methods for Curves and Surfaces - Lillehammer, Norway
    Duration: 3 Jul 19978 Jul 1997

    Conference

    ConferenceInternational Conference on Mathematical Methods for Curves and Surfaces
    CountryNorway
    CityLillehammer
    Period03/07/199708/07/1997
    SponsorSINTEF, The Research Council of Norway, University of Oslo
    SeriesINNOVATIONS IN APPLIED MATHEMATICS

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