The picture you link to is a snood, a head covering, and the pattern is sort of a square. I understand that you want to use the same stitch pattern to make a mesh.
If you want one edge straight and the other inc to the center, then the inc edge decs look at the shawls in the links I posted above. They're very similar to what you want, and if you want purl rows on the WS instead of knit, they'll work with that. But pretty much, your ideas should work out.
When you're making your own pattern, sometimes it's better to figure it out by actually knitting it than to 'see' it in your head. So go ahead and try it, and if it doesn't work out as you've written, then see where you could make changes.
sue- knitting heretic