Inconsistent orientation of detected/generated ArUco and AprilTags

ArUco and AprilTag detection both uses a clockwise orientation, however, AprilTag corners start with bottom right while ArUco starts with upper left. See the example below:

Code:

import cv2


def draw_markers_with_corners(img, corners):
    for i, marker_corners in enumerate(corners):
        # Get the corners of the marker
        corner_points = marker_corners.reshape((4, 2))
        corner_points = corner_points.astype(int)

        # Draw each corner with its ordinal position
        for j, corner in enumerate(corner_points):
            # Draw corner point
            cv2.circle(img, tuple(corner), 5, (0, 0, 255), -1)
            # Label the corner with its ordinal position (0, 1, 2, 3)
            cv2.putText(
                img,
                str(j),
                (corner[0] + 10, corner[1] + 10),
                cv2.FONT_HERSHEY_SIMPLEX,
                0.5,
                (255, 0, 0),
                2,
            )

    return img


img = cv2.imread("markers.jpeg")

parameters = cv2.aruco.DetectorParameters()

april_dict = cv2.aruco.getPredefinedDictionary(cv2.aruco.DICT_APRILTAG_36h11)
april_detector = cv2.aruco.ArucoDetector(april_dict, parameters)
aruco_dict = cv2.aruco.getPredefinedDictionary(cv2.aruco.DICT_4X4_250)
aruco_detector = cv2.aruco.ArucoDetector(aruco_dict, parameters)

img_marked = img.copy()
april_corners, _, _ = april_detector.detectMarkers(img)
img_marked = draw_markers_with_corners(img_marked, april_corners)

aruco_corners, _, _ = aruco_detector.detectMarkers(img)
img_marked = draw_markers_with_corners(img_marked, aruco_corners)

cv2.imwrite("markers_detected.jpeg", img_marked)

The same issue persists (likely due to pre-defined dictionary configurations) for generation:

The generated AprilTag 36h11 - 0 (wrong orientation, see above)

The generated ArUco 4x4_250 - 0 (correct orientation, see above)

Code:

import cv2

april_dict = cv2.aruco.getPredefinedDictionary(cv2.aruco.DICT_APRILTAG_36h11)
aruco_dict = cv2.aruco.getPredefinedDictionary(cv2.aruco.DICT_4X4_250)

img = cv2.aruco.generateImageMarker(aruco_dict, 0, 200, borderBits=1)
cv2.imwrite("aruco.png", img)

img = cv2.aruco.generateImageMarker(april_dict, 0, 200, borderBits=1)
cv2.imwrite("april.png", img)

Start with the provided Python reproduction using ArucoDetector.detectMarkers and generateImageMarker for the AprilTag and ArUco dictionaries. Trace how each dictionary defines corner ordering and generated marker orientation; done means detection and generation use a consistent orientation for both marker families, with the reproduction confirming the corrected ordering.