Mendel Leisk , Jun 24, 2007; 12:25 p.m.
Start with a petal hood designed so that at all points around it's circumference the outer edge is projecting as far as possible. To revise it to be circular all of the petals would have to be trimmed off, back to the low points.
Any time you have a square or rectangular picture the petals are more efficient. only with a round picture (say with a fisheye lens) would there be no advantage to the petals.