How to calculate rotation angle from rectangle points?

Question

I have 4 points 1,2,3,4 that closes a rectangle.

The points are in a array in this following way: x1

Answer 1

The center of the rectangle is right between two opposite corners:

cx = (x1 + x3) / 2
cy = (y1 + y3) / 2

The size of the rectangle is the distance between two points:

w = sqrt(pow(x2-x1, 2) + pow(y2-y1, 2))
h = sqrt(pow(x3-x2, 2) + pow(y3-y2, 2))

The corners of the gray rectangle can be calculated from the center and the size, for example the top left corner:

x = cx - w / 2
y = cy - h / 2

The angle is the arctangent of a side of the square:

a = arctan2(y4 - y1, x4 - x1)

(I'm not sure exactly which angle it returns, or what angle you expect for that matter, so you get to test a bit.)