Beta-bezier curves

Fuhua Cheng, Anastasia N. Kazadi, Alice J. Lin

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


A new definition of Beta-Bezier curves which include classic Bezier curves as a special case is given. With the new definition, the functions of Beta-Bezier curves are easier to study. It shows that Beta-Bezier curves not only have all the basic properties of Bezier curves such as convex hull property, recursive subdivision, B-spline conversion and C2 interpolation, but also the capability of modifying the shape a Bezier curve segment or a C2-continuous, composite cubic Bezier curve without changing the control points of the curve. This is because in the cubic case a Beta-Bezier curve is actually also a Bezier curve. Hence, we have a curve design technique more general than Bezier curves. Since C2-continuous, composite cubic Bezier curves are equivalent to uniform B-spline curves, this means the new curve design technique is more general than uniform B-spline curves as well.

Original languageEnglish
Pages (from-to)1265-1278
Number of pages14
JournalComputer-Aided Design and Applications
Issue number6
StatePublished - 2021

Bibliographical note

Funding Information:
This work is supported by NNSFC (Grant No. 61572020).

Publisher Copyright:
© 2021 CAD Solutions, LLC.


  • Beta-Bernstein basis function
  • Beta-Bezier curve
  • Bezier curve
  • Shape parameter

ASJC Scopus subject areas

  • Computational Mechanics
  • Computer Graphics and Computer-Aided Design
  • Computational Mathematics


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