Domes made with lengths of hoop-shaped PVC pipes have become popular for shade structures because of the ease with which plastic pipe can be cut, joined, transported, and assembled. This structural idiom has long been used by nomadic peoples, who would arch flexible branches to form a dome and cover it with hide or weavings.
These domes gain stability by weaving long, arched PVC pipes in an inverted bowl shape. Firmly staking the ends of each pipe length to the ground creates a bowed arch. Lacing a number of arched pipes together in a circular plan using rope lashings or bungie cords creates a stable dome, if you have enough of the pipes crossing such that you create a network of 3- to 6-foot triangles. Typical nominal PVC pipe size for a strong, moderate sized dome (20- to 30-foot dia.) are 1-1/2" for primary members, and 1" for bracing members; minimum grade, Schedule 40, although some people go with lighter irrigation pipe. Some camps at Burning Man have gone to 2" pipe for larger domes.
PVC domes can be dimensioned such that parachutes will readily conform to the hemispherical shape. Camouflage netting is even more conformable, and will not catch the wind as much, but will not shed a light rain. Polypropylene shade cloth, which typically comes six feet wide, can be laced over a PVC dome and attached with ties.
The Cultural Worker's Union of Santa Cruz is one camp that has been building and improving their dome design since 1996. Improvements made in 1998 included the addition of a reinforcing center ring (photo above and info from Aaron Ferrucci & Jeremy Lutes). The Space Lounge group designed single domes for Checkpoint Salon and the Earth Guardians, and a more free-form PVC pipe dome structure for Media Mecca in 1998; since then they have used geodesic domes.
PVC pipe is a great material for portable structures if its limitations are recognized. It has low strength; brittleness; and is prone to deterioration from exposure to sunlight over time. It typically comes in white or gray, but orange, blue, and purple conduit can be found at plumbing and electrical suppliers. Common sizes can be bought anywhere; it's as maleable and versatile as TinkerToys or popsicle sticks; very lightweight; and easy to cut and drill with hand tools.
Camp Siestah's plan used a parachute strung from a single pole (LeeDogg's site is inaccessible, unfortunately), resulting in a cone or wide teepee shape rather than a dome. A central 3-inch PVC pipe pole was the only rigid support, from which twenty guy lines spoke out to 48-inch capped steel stakes arrayed in a circle equal in size to the diameter of the parachute (the pole length is equal to half the nominal diameter of the parachute, plus one or two feet for burial).
Also see Argyre Patras' parachute plan for another simple setup, which uses a PVC pipe hoop around the parachute perimeter.