An algorithm to find bounding box of closed bezier curves?

Question

I'm looking for an algorithm to find bounding box (max/min points) of a closed quadratic bezier curve in Cartesian axis:

input: C (a closed bezier curve)
output: A B C D points

Note: above image shows a smooth curve. it could be not smooth. (have corners)

Answer 1

Well, I would say you start by adding all endpoints to your bounding box. Then, you go through all the bezier elements. I assume the formula in question is this one:

From this extract two formulas for X, and Y respectively. Test both for extrema by taking the derivative (zero crossings). Then add the corresponding points to your bounding box as well.

Answer 2

I believe that the control points of a Bezier curve form a convex hull that encloses the curve. If you just want a axis-aligned bounding box, I think you need to find the min and max of each (x, y) for each control point of all the segments.

I suppose that might not be a tight box. That is, the box might be slightly larger than it needs to be, but it's simple and fast to compute. I guess it depends on your requirements.