Subdivision Algorithm for Bézier Curves

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

SNAPSHOTS

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

DETAILS

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 .
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 :
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.