Algorithm to find the minimum-area-rectangle for given points in order to compute the major and minor axis length

Question

I have a set of points (black dots in geographic coordinate value) derived from the convex hull (blue) of a polygon (red). see Figure:

Answer 1

OpenCV has this. See this:

http://docs.opencv.org/trunk/dd/d49/tutorial_py_contour_features.html

7.b. Rotated Rectangle

With

cv2.minAreaRect(cnt)

You can get the length and width of the rectangle as well as its angle. You can also compute the corners if you wish to draw it.