Convex subdivision of a Bézier curve

Rachid Ait Haddou*, Walter Herzog

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Using the Walsh coincidence theorem, we show in this paper that the shape of the control polygon of a Bézier curve is closely related to the location of the complex roots of the corresponding polynomial. This explains why a convex polynomial over an interval does not necessarily produce a convex control polygon with respect to the same interval. Furthermore, our findings lead to an interesting algorithm of subdividing a Bézier curve into segments with convex control polygons.

Original languageEnglish (US)
Pages (from-to)663-671
Number of pages9
JournalComputer Aided Geometric Design
Volume19
Issue number8
DOIs
StatePublished - Oct 1 2002

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Geometry and Topology
  • Modeling and Simulation

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