Draw a quadratic Bézier curve through three given points

Question

I have three points in 2D and I want to draw a quadratic Bézier curve passing through them. How do I calculate the middle control point (x1 and y1

Answer 1

If you don't want the exact middle point, rather you want any value for t (0 to 1), the equation is:

controlX = pointToPassThroughX/t - startX*t - endX*t;
controlY = pointToPassThroughY/t - startY*t - endY*t;

Of course, this will also work for the mid point, just set t to be 0.5. Simple! :-)