I've been playing with small tarps to find how little I can get away with, depending on the weather -- currently variations on a 5'x10' rectangular tarp.
This idea has probably come up before but it's new to me and I call it a Pseudo-Cat, for lack of imagination. It's basically a 3 segment piecewise linear approximation of a catenary along the bottom edge. The overall tarp gets hexified in the process.
Basically, you cut triangular wings off the ends of the rectangle
and reattach them at the bottom corners, like so:
Here it is pitched:
I was surprised at how much the pitch tightened up compared to a plain rectangle. Also, the corner ripples are interesting:
I'm thinking they point along the lines of force, which would be interesting information for modeling what's happening with the fabric.
Anyway, I'm going to explore the idea a bit and thought I'd toss it out there for anyone interested.