Processing cv::RotatedRect width and height

Question

I need to define a rotated rectangle from its 4 corners. The rotated rectangle is defined by a center point, a size couple (width, height), and an angle.

How is it decided which size is the height, and which one is the width?

The width is not the length of the most horizontal edge, is it? E.g. if the angle is bigger than 90°, does it swap?

Answer 1

height should be the largest side, width is the other one, and angle is the rotation angle (in degrees) in a clockwise direction.

Otherwise, you can get an equivalent rectangle with height and width swapped, rotated by 90 degrees.

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You can use minAreaRect to find a RotatedRect:

vector<Point> pts = {pt1, pt2, pt3, pt4}

RotatedRect box = minAreaRect(pts);

// Be sure that largest side is the height
if (box.size.width > box.size.height)
{
    swap(box.size.width, box.size.height);
    box.angle += 90.f;
}

Answer 2

Ok, with Miki's help, and with some tests, I got it clearer...

It seems that the rotated rectangle is an upright rectangle (width and height are clearly defined, then)... that is rotated!

In image coords, y is directed to the bottom, the angle is given clockwise. In usual math coords (y to the top), the angle is given counter-clockwise. Then, it fits with c++ <math.h> included atan2(y,x) function for example (except that it returns radians).

Then, to summarize, if we consider one given edge of the rectangle (two corners), its length can be considered as the width if we retrieve the angle with atan2 on its y difference and x difference. Something like:

 Point pt1, pt2, pt3, pt4;
 RotatedRect rect;

 rect.center = (pt1 + pt2 + pt3 + pt4)/4;

 // assuming the points are already sorted
 rect.size.width = distance(pt1, pt2); // sqrt(...)
 rect.size.height = distance(pt2, pt3);

 rect.angle = atan2(pt2.y-pt1.y, pt2.x-pt1.x);

and this can be improved with width being the mean value of dist(pt1,pt2) and dist(pt3,pt4) for example. The same for height.

angle can also be calculated as being the mean value of atan for (pt1, pt2) and atan for (pt3, pt4).