Suppose you want a nice rounded box mesh. You know how to create a mesh for a tesselated box. You know how to get a nice sphere mesh from a tesselated box mesh - you just project the box's points to a sphere:

p' = normalize(p)

What about a rounded box? How can we take a tessellated box mesh and project it nicely to a rounded box? For a box spanning [-1, 1], with a rounding radius of r, you simply:

p_box = clamp(p, -vec3(1 - r), vec3(1 - r))
p' = p_box + r * normalize(p - p_box)

Clamp the point to a smaller box, project the remainder to a sphere, reconstruct. Note that, while I say 'vec3' here, it's good for 2D as well (or however many Ds you need).

I write this down both for myself, and since I didn't find anything by searching (yes, I'm a bit embarrassed that I tried searching this first...)