Try opening the Vertex panel while in edit mode, and clicking Smooth, or by or pressing Ctrl + V, Smooth Vertex.
You could also try using Relax.
Hope you find a solution!
@ExcessEnergy The op already pointed out that smooth shading didn’t work.
What you could do instead is do loopcuts or go overkill and apply a subdivision modifier. (you’ll probs have to decimate it of course)
Or just manually take the knife tool and slash at it creating more vertices.
Or a normal subdivide.
I wasn’t referring to anything shading related. I was referring to the blender functions that smooth out all of the vertices, and makes them look more even and relaxed.
https://docs.blender.org/manual/en/latest/modeling/meshes/editing/vertex/smooth_vertices.html
https://docs.blender.org/manual/en/latest/addons/mesh/relax.html
Yeah, it’s rather unforunately that Blender has “Smooth Vertices” as both a normals shading thing and a vertex position thing, especially because adding them to your quick access menu makes it impossible to know which is which!
That said, the OP might not find that even the correct “smooth vertices” from vertex menu does a whole lot, simply because the curve is already quite smooth for the number of verts it has. The only way for it to be less faceted is to subdivide all those edges. When you do edge->subdivide, you get an adjustable parameter for smoothing as part of the operation, or you can smooth the vertices after subdividing.
I didn’t take into account how close to perfect the smoothness of the curve already is. It’s not a matter of making it less rugged, but a matter of making it a more precise curve.
I think this is going to be the best solution.
I would recommend using the Bevel modifier