Well.. to problem of texturemapping a cylinder to point camera, we have few things known:
1. U-coordinate of each vertex never change, so we only need to count 1 value; V-coordinate.
BUT
2. If we think about how texture behaves if model stands still and only texture-coordinates change, we know that the animation and the general looks would be different depending on angle. Sort of distortion/ripples happen. So we can skip step 1 and rotate the cylinder along its center, so we still have only 1 value to calculate and that is rotation angle.
3. What values we have to use? We can use glGet on GL_MODELVIEW_MATRIX to get all 3 rotation vectors that camera uses. And we can count normal vector to cylinder when it is at 0 degree rotation (which is completely free to choose along the surface of cylinder).
4. That all known, we should better draw some picture to get a good overview on what vectors we are comparing, or analyze them realtime in program... and that goes way beyond a simple forum post