Correctly filling a convex and concave mesh from curves I need to make curving concave and convex meshes, while at the same time, expressing the mesh data as only quads. (Quad meshes work well with subdivision, smooth shading, and bevel, but triangular or n-gonal meshes don't work with all 3.)

The nature of being both concave and convex thwarts making quads going completely vertically or horizontally and similarly messes with the almighty grid fill. I had no luck converting this mesh from a filled 2d curve, since the curve is filled with triangles that cause shading artifacts. So I tried manual work, revealing it is indeed impossible to fill with quads in a purely vertices/horizontal manner. An n-gon fill doesn't work, and the last image shows that grid fill has issues even at its best. I also tried smoothing vertices on all methods, and it got the grid fill method pretty close.

I could use workarounds, like using flat shading on the flat side of the axe with an autosmooth modifier, but I want subdivision and smooth shading.

(When extruded out) how can I fill this mesh in a way that doesn't cause smooth shading artifacts?
You should retopolgize this mesh. It is pretty simple with method I will present (if this kind a mesh will suite you).

First of all you should make a plane and position it at the bottom of the blade.

Then extrude it all the way up.

Select loop and extrude to the end of axe scaling down each loop.


This gif shows the retopo flow:

If you need more detailed description, let me know in comment what do you need.
Edit: