import cv2
import numpy as np

# Rect: ((x,y), (width, height))
# RotatedRect: ((cx,cy), (width, height), angle)

def rotated_rect_corners(rotated_rect):
    center, size, angle = rotated_rect
    cx, cy = center
    width, height = size

    angle = np.radians(angle)
    b = np.cos(angle) * 0.5
    a = np.sin(angle) * 0.5

    p0 = (cx - a * height - b * width, cy + b * height - a * width)
    p1 = (cx + a * height - b * width, cy - b * height - a * width)
    p2 = (2 * cx - p0[0], 2 * cy - p0[1])
    p3 = (2 * cx - p1[0], 2 * cy - p1[1])

    return (p0, p1, p2, p3)

def rotated_rect_bbox_f(rotated_rect):
    corners = np.array(rotated_rect_corners(rotated_rect))
    min_xy = np.amin(corners, axis=0)
    max_xy = np.amax(corners, axis=0)
    size = max_xy - min_xy
    return (min_xy[0], min_xy[1], size[0], size[1])

points = np.array([[2,2],[1,3],[4,4],[3,5]])
rotated_rect = cv2.minAreaRect(points)

print rotated_rect
print rotated_rect_corners(rotated_rect)
print rotated_rect_bbox_f(rotated_rect)