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This seems to work:
In [1]: import cv2
In [2]: objectPoints = np.random.random((10,3,1))
In [3]: imagePoints = np.random.random((10,2,1))
In [4]: cameraMatrix = np.eye(3)
In [5]: distCoeffs = np.zeros((5,1))
In [6]: cv2.solvePnP(objectPoints, imagePoints, cameraMatrix, distCoeffs)
Out[6]:
(True, array([[ 0.15797798], [ 0.48352235], [-0.25566527]]), array([[ 0.36711979], [ 1.02124737], [ 1.83962556]]))
Image points of shape (N, 1, 2) and object points of shape (N,1,3) also works (your case number 2) for me. Perhaps you had a bad shape for distCoeffs?
