Complex Bézier curves and the geometry of polygons

Rachid Ait-Haddou*, Walter Herzog, Taishin Nomura

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


In this paper, we associate to every planar polygon a complex polynomial, in which the blossom of the polynomial function captures the process in which linear transformations applied to the polygon lead to regular structures. In particular, we prove, in a purely algebraic way several well-known theorems on polygons such as the Napoleon-Barlotti Theorem, the Petr-Douglas-Neumann Theorem, and the Fundamental Decomposition Theorem of polygons to regular polygons.

Original languageEnglish (US)
Pages (from-to)525-537
Number of pages13
JournalComputer Aided Geometric Design
Issue number7
StatePublished - Oct 2010
Externally publishedYes


  • Bézier curve
  • Discrete Fourier transform
  • Geometry of polygons
  • Napoleon-Barlotti Theorem
  • Petr-Douglas-Neumann Theorem
  • Polar forms

ASJC Scopus subject areas

  • Modeling and Simulation
  • Automotive Engineering
  • Aerospace Engineering
  • Computer Graphics and Computer-Aided Design


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