At http://www.equipped.org/tarp-shelters.htm you'll find numerous ideas for folding square and rectangular tarps into some form of shelter. Look it over for ideas to see if adding a floor and webbing to any might be a start.

You mentioned the bilgy so here's an idea for a variation. Broaden the front and support it with 2 poles. Sort of like this...
http://www.equipped.org/graphics/tarps/image132.jpg

but keeping the overall bilgy design. You'd wind up with a bilgy that has a triangle roof. Good luck.