# Bézier curve limits

Can be any curve of any shape (without sharp edges) described by Bézier curve with unlimited (but finite) number of control points?

The answer to the question above would probably be no, because I have already found out that circle cannot be described exactly by a Bézier curve. (http://en.wikipedia.org/wiki/B%C3%A9zier_curve)

But, are there any other limits of Bézier curve?

• Unlimited but finite number of control points, right? I'd say that there are many curves which cannot be exactly represented by (cubic) Bézier curves. Most cubic rational curves would fall in that class, and most curves of higher degree as well. You can approximate them, and given an arbitrary number of points you can probably approximate them arbitrary well, but it's still not exact. – MvG Apr 16 '14 at 7:28