# Approximating Bezier curves

I would like to approximate one cubic Bezier curve with two quadratic ones. In other words, I would like to split a cubic curve at some parameter t and approximate the resulting halves with a quadratic Bezier each.

(cubic -> split at t -> two cubics -> two quadratics)

Obviously, it is possible to split the original curve very badly, say by choosing t closely to 0 or 1, if the curve looks like a simple arch.

• how to choose good t? With regards to the original cubic curve coordinates? If I knew what "badness" is, would it be possible to choose such t that the resulting quadratic splits would be equally "bad", i.e. to how to fairly split the original curve?
Or minimise $\int_0^1 (B_{cubic}-B_{quad})^2\,d\,t$. –  Daryl Oct 26 '12 at 20:49