How do I add a 3D border on all edges of a mesh? I would like to add a 3D border to all edges of a mesh, such that the border is a "cylinder" that wraps around the mesh. The effect would look something like this:



My object is very similar to the white-textured part of the above image, it is a fully 2D mesh. However, differently to this mesh, the object is entirely one face, so I just need this effect applied to all edges of the mesh, and there's no edges in the middle that could get in the way.
One simple way is to duplicate the object (press Shift D, then Esc), enter edit mode, select all and press X to delete Only faces, then add a skin modifier, set the size of the quad border with the "Mean radius" X and Y values of every vertex, then add a subsurf modifier to get the resolution and roundness you need.

Afetr applying all modifiers (always starting from the upper) you can rejoin the two meshes into one single object (Ctrl J).