details of Jacobian computed from OpenCV’s projectPoints function

The Jacobian initialization part of cv::projectPoints is as the above. So the the “OutputArray _Jacobian” of the function

is matrix of [2 x # of points] by [10 + # of distortion coeff.]. Here “2” is for the 2D image point (that is x and y coordinates), 10 is in order for
1. rotation component x
2. rotation component y
3. rotation component z
4. translation component x
5. translation component y
6. translation component z
7. focal length component x
8. focal length component y
9. principal point component x
10. principal point component y

When the distortion model is that of the most common whose elements are k1, k2, p1, p2, k3, the # of columns of _Jacobian matrix becomes 15, where 11 to 15th are as following
11. k1
12. k2
13. p1
14. p2
15. k3