I'm using these function calls:
glEnable(GL_BLEND)
glEnable(GL_POLYGON_SMOOTH)
glBlendFunc(GL_SRC_ALPHA_SATURATE, GL_ONE)
It doesn't work and won't render.
glEnable(GL_BLEND)
glEnable(GL_POLYGON_SMOOTH)
glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA)
It doesn't anti-alias.
Try glHint(GL_POLYGON_SMOOTH_HINT, GL_NICEST)
This is a mundane answer.. but if you want rounded corners, you'll probably want to use more more vertices at the corners and place them for a more rounded shape. You could also look into doing this procedurally.. but if you're doing a game and you want to get it finish, I'd usually recommend that you have the final vertex position in the data (unless you have a compelling reason to make it dynamic).
Alternatively, you can use a texture with a rounded appearance near the corners. This is gradually becoming less popular as video hardware becomes more powerful, but is still quite effective.