If the 3 control points of the quadratic Bézier curve are known, how do you calculate algebraically the equation of that curve (which is an y=f(x) function)? Let's say I have..
- P0 (x,y) - startPoint
- P1 (x,y) - controlPoint
- P2 (x,y) - endPoint
and I want to get implicit equation for that, something like that:
f(x) = −0.5x^2 + 3.5x − 1 (for example).
Although all quadric Bezier curve is part of a certain parabola, not all parabola can be represented as f(x)=ax2+bx+c. So, the first thing you need to do is check if x2=x1+x32. If this check fails, then your quadratic Bezier curve is not a segment of f(x)=ax2+bx+c.
Ok, but if check fails how can I find its equation?
Another article about cubic Bezier is http://www.moshplant.com/direct-or/bezier/math.html Is there any approach for quadratic?