Linear methods for G 1, G 2, and G 3 - Multi-degree reduction of Bézier curves

Abedallah Rababah, Stephen Mann

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)


In this paper, linear methods to find the multi-degree reduction of Bézier curves with G 1-, G 2-, and G 3-continuity at the end points of the curves are derived. This is a significant improvement over existing geometric continuity degree reduction methods. The general equations for G 2- and G 3-multi-degree reduction schemes are non-linear; we were able to simplify these non-linear equations to linear ones by requiring C 1-continuity. Our linear solution is given in an explicit, non-iterative form, and thus has lower computational costs than existing methods which were either non-linear or iterative. Further, there are no other existing G 3-methods for multi-degree reduction. We give some examples and figures to demonstrate the efficiency, simplicity, and stability of our methods.

Original languageEnglish
Pages (from-to)405-414
Number of pages10
JournalCAD Computer Aided Design
Issue number2
Publication statusPublished - Feb 2013
Externally publishedYes


  • Bézier curves
  • Geometric continuity
  • Multiple degree reduction

ASJC Scopus subject areas

  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering


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