• DocumentCode
    2863151
  • Title

    The fractal nature of Bezier curves

  • Author

    Goldman, Ron

  • Author_Institution
    Dept. of Comput. Sci., Rice Univ., Houston, TX, USA
  • fYear
    2004
  • fDate
    2004
  • Firstpage
    3
  • Lastpage
    11
  • Abstract
    Fractals are attractors - fixed points of iterated function systems. Bezier curves are polynomials - linear combinations of Bernstein basis functions. The de Casteljau subdivision algorithm is used here to show that Bezier curves are also attractors. Thus, somewhat surprisingly, Bezier curves are fractals. This fractal nature of Bezier curves is exploited to derive a new rendering algorithm for Bezier curves.
  • Keywords
    computational geometry; curve fitting; fractals; iterative methods; polynomials; rendering (computer graphics); Bernstein basis functions; Bezier curves; de Casteljau subdivision algorithm; fixed points; fractal nature; iterated function systems; linear combinations; polynomials; Computer science; Convergence; Fractals; Gaskets; Polynomials; Solid modeling;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    Geometric Modeling and Processing, 2004. Proceedings
  • Print_ISBN
    0-7695-2078-2
  • Type

    conf

  • DOI
    10.1109/GMAP.2004.1290020
  • Filename
    1290020
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=2863151