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Digitization of Bézier Curves and Patches using Discrete Geometry

  • Oscar Figueiredo
  • Roger D. Hersch
  • Jean-Pierre Reveillès
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1568)

Abstract

Existing algorithms for rendering Bézier curves and surfaces fall into two categories: iterative evaluation of the parametric equations (generally using forward differencing techniques) or recursive subdivision. In the latter case, all the algorithms rely on an arbitrary precision constant (tolerance) whose appropriate choice is not clear and not linked to the geometry of the image grid. In this paper we show that discrete geometry can be used to improve the subdivision algorithm so as to avoid the need for any arbitrary value. The proposed approach extends well and we present its application in the case of 2D and 3D Bézier curves as well as Bézier triangle patches and tensor-product surface patches.

Keywords

Bézier curves Bézier surfaces De Casteljau subdivision polygonalization 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Oscar Figueiredo
    • 1
  • Roger D. Hersch
    • 1
  • Jean-Pierre Reveillès
    • 2
  1. 1.Ecole Polytechnique Fédérale de Lausanne EPFL/DI-LSPLausanneSwitzerland
  2. 2.LLAIC1, Computer Science Institute of TechnologyUniversité d’Auvergne Les CézeauxAubièreFrance

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