Help with curved groove on curved surface Been struggling with this for awhile, and finally decided to ask for help from the experts.

I have a cylinder onto which I'd like a groove at goes across it diagonally and also vertically down the cylinder. I'm having trouble visualizing how to do it, and still have good topology.

I've tried knife, knife project, moving individual verts, etc. Something tells me there is an easier and cleaner way to do it, so that I have clean topology and no shading artifacts. Am I right?

I've added two pictures of this scenario for reference.
As your shape is a cylinder, you could greatly simplify your work if you use a Simple Deform modifier:


Just create your shape as a flat map, avoid any ngons, make a topology that will allow you to add some edge loops when you'll need to sharp the angles.
Extrude what needs to be extruded.
Give it a Simple Deform modifier/Bend mode, with a Deform Angle of 360°.
Give it a Subdivision Surface modifier and a Smooth Shading.
To make the joint at the 360° junction, you'll need to apply the Simple Deform and then W > Remove Doubles.