On Monday, May 18, 2015 at 1:34:15 PM UTC-7, J. Nieuwenhuize wrote:
If we go back to theory, the perfect wing is a double super-ellipse (Lamé curve):
http://en.wikipedia.org/wiki/Superellipse

Both the top view and the dihedral of the wing should have the shape of a super-ellipse for lowest induced drag for a given bending moment (structural weight) and wetted area (profile drag at high speeds). Both the A350 and the Dreamliner are very close to this ideal:
wallpaperswide.com/download/boeing_787_dreamliner-wallpaper-1920x1200.jpg

Another plus compared to a wing without dihedral and winglets is that the interference drag between the winglet and the wing is much reduced.

Such a gradually curved wing is impossible to build because all the control surfaces would have a bend in them. The wing with sections progressively canted more and more (polyhedral) is a good compromise.

It also helps with flutter apparantly. The Vortex shedding frequency of the various sections make the critical flutter speed for such a wing higher, allowing either a higher VNE, or a less stiff and thus lighter wing structure.
h

Elliptical polyhedral is not part of any drag theory I ever learned studying aerodynamics. The wing planform, airfoils, twist and the use of winglets are used together to optimize the tradeoff between parasitic and induced drag while maintaining desirable handling and stall characteristics. My sense is that use of dihedral (or polyhedral) is mostly motivated by handling (and perhaps ground clearance) considerations rather than performance considerations. They may also think it looks cool.

9B