The thought process being that the circle WILL be a PITA to sew, but will reduce the likelihood of a concentration of force on a few stitches, like would happen with the points on a square or rectangle.
The lines bisecting the circle across the center provide a straight pull against the force of the attached line... sort of like the post about sewing webbing with straight, lengthwise lines instead of a box and x pattern.
Funny how none of us seem to even consider hand-sewing the attachment points.
I wonder if that is the better alternative, as it would eliminate the hassle of managing a whole tarp worth of material on the machine.
Oh, another random thought... I just had the mental image of my tarp rolled/folded and clipped on 4 sides around the work area. The whole thing folds up so small if we fold up everything but the area needed to attach the pull out, then it shouldn't be that much of a hassle to maneuver it in the machine.
Clear as mud?
BTW, Tim. I'm not ignoring your silicone attachment method. I just don't trust adhesives by themselves for stuff I'll take into the field. However, from what I've read about the stuff you make, I'm inclined to give your method a try at some point.