How to emit particles at intersection of faces (Scan animation) I want to make an animation that explains laser scanning. It will consist of two videos.
One of the videos is rotating duck with a laser on it. 
You can see the animation here. The animation is by me and the first of the two videos is already done.


https://media.giphy.com/media/iDJOi8TmgXrHKRQuoA/giphy.gif

The other is supposed to be a sort of point cloud that is generated by the scanning laser from the first video. So wherever the laser hits the rotating duck, there should spawn points.

What I have tried so far:
I tried to make the point cloud with a particle system. It worked well except that I could only generate points over the entire duck faces and not only at the "laser line". Ideal would be to have an emitter that is the intersection between the rotating duck and a face. 

I hope I stated my question clearly.
Thanks
Material
Dot pattern texture with appearance controled by Radial Blend texture.



Laser line is shrinkwrapped line, just for illustration, you will use your laser :)
Particles
They looks better, since there is not a deformation on surface curvature. I wanted to use the same Radial blend texture as factor for Emission, but I had some dificulties to get it work for particle system. So here is a version with particles emited from Shrinkwrapped line of vertices suggested by Rich Sedman
Works nice like real one in term - light string follows surface and keeps empty places where light cant touch surface (like in tail part).
Issue is distribution. I wasnt able to set even release particles from vertices.