Subdivision Algorithm for Bézier Curves

This Demonstration illustrates the convergence of the de Casteljau-based subdivision algorithm for Bézier curves.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


The subdivision algorithm follows from the de Casteljau algorithm that calculates a current point , for , of a polynomial Bézier curve , for , where are the control points, by applying the following recurrence formula:
for .
For any value of between and , we have
The subdivision algorithm associates to the polygon the two polygons and . They constitute the control polygons of the two parts of the curve , respectively for in and :
When , varies over and varies over .
This Demonstration illustrates repeated application of the above procedure (the control "k" denotes the number of iterations). Obviously, the resulting polygon sequence converges very quickly to the curve .
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+