Bézier curve


last updated: 2005-01-18

Given a set of n+1 control points Pi the Bézier curve is written in terms of Bernstein polynomials:

The curve has the following properties:

  • there is no line that has more intersections with a Bézier curve than with the curve composed by the line segments through the points.
  • the curve can be translated and rotated by performing these operations on the control points.
  • a numerical instability for large numbers of control points.
  • moving a single control point changes the global shape of the curve.
    This can be avoided by smoothly patching together low-order Bézier curves.

The rational Bézier curve is a generalization of the curve:


Another generalization of the curve is the B-spline.