Drawing Euler Angles rotational model on a 2d image

Drawing Euler Angles rotational model on a 2d image

I'm currently attempting to draw a 3d representation of euler angles
within a 2d image (no opengl or 3d graphic windows). The image output can
be similar to as below.

Essentially I am looking for research or an algorithm which can take a
Rotation Matrix or a set of Euler angles and then output them onto a 2d
image, like above. This will be implemented in a C++ application that uses
OpenCV. It will be used to output annotation information on a OpenCV
window based on the state of the object.
I think I'm over thinking this because I should be able to decompose the
unit vectors from a rotation matrix and then extract their x,y components
and draw a line in cartesian space from (0,0). Am i correct in this
thinking?
Any help would be appreciated.
Thanks,