# Are there any cubic bezier curve that cannot imitate by multiple quadratic bezier curve?

I want to make a line curve system with bezier curve. And I want to use only quadratic bezier curve so it can be extend and control easily, it can add control point anywhere and more intuitive

But I'm curious that it might not be cover some kind of graph. At least I want it able to imitate cubic bezier curve

Is it any mathematically impossible? I have seen many system use cubic bezier curve over quadratic (System Font and Photoshop Path at least)

Are there any problem with quadratic bezier curve?

• It can approximate cubic Bezier curve, and I don't know what you means by "imitate". – user202729 May 26 '16 at 4:20
• @user202729 I mean not just approximate but really equal, by using less than four composite quadratic parts – Thaina May 26 '16 at 4:59

## 1 Answer

You can only approximate a cubic Bezier curve by multiple quadratic Bezier curves. They will not be equal as there will always be a small difference between them.

A cubic Bezier curve has the following advantages over quadratic Bezier curve: $C^2$ continuous, can have inflection point and can have separate control over the end slopes. These are the reason they are used much more widely than quadratic Bezier curves.