Use "Shapely" or "sphere" for Astropy regions?

Should we use [Shapely](https://pypi.python.org/pypi/Shapely) and / or [Sphere](https://github.com/spacetelescope/sphere) and / or neither (i.e. re-implement or copy over things like polygon computations) as a dependency for this to-be `astropy.regions` package?

I don't remember if this important question was discussed in detail or decided at `PyAstro16`!?

Currently the API has `shapely` in many places, but nothing is really implemented and @astrofrog, I think it might just be the left-over of some API brainstorming a year or two ago?
https://github.com/astropy/regions/search?utf8=%E2%9C%93&q=shapely

@eteq @astrofrog @keflavich @larrybradley, all - thoughts?

Start by searching the repository for the existing `shapely` references mentioned in the issue and review how they appear in the `astropy.regions` API. Then investigate the Shapely and Sphere dependency options and the prior discussion around PyAstro16. Done means reaching and recording a decision on whether to use either dependency or neither, with the API direction aligned to that decision.

Written by the indexing model from the issue text.