Algorithm, how to fit a rectangle into a trapezoid?

Question

C++ / C#

Greetings!
With the help of OpenCV I get a lot of points of the figure, I filter it, and I get a trapezoid (that is, the coordinates of 4 vertices), there were no problems with this,
but now I would like to fit a rectangle parallel to the coordinate axes into it.
Tell me, please, is there a ready-made algorithm?

Answer 1

In general, the problem has no solution. In particular, when the base of the trapezoid is parallel to one of the axes, there are an infinite number of solutions.