Bounding the distance between 2D parametric Bézier curves and their control polygon

M. I. Karavelas, P. D. Kaklis, K. V. Kostas

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


Employing the techniques presented by Nairn, Peters and Lutterkort in [1], sharp bounds are firstly derived for the distance between a planar parametric Bézier curve and a parameterization of its control polygon based on the Greville abscissae. Several of the norms appearing in these bounds are orientation dependent. We next present algorithms for finding the optimal orientation angle for which two of these norms become minimal. The use of these bounds and algorithms for constructing polygonal envelopes of planar polynomial curves, is illustrated for an open and a closed composite Bézier curve.

Original languageEnglish
Pages (from-to)117-128
Number of pages12
JournalComputing (Vienna/New York)
Issue number1-2
Publication statusPublished - Jan 1 2004


  • Bounding region
  • Collision detection
  • Control polygon
  • Optimal-orientation bounds
  • Parametric Bézier curves
  • Polygonal envelopes

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Computational Mathematics


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