Ready for review.

I've still got more comments to write, including the docstring.interp trick.

I decided to do all the tools at once (and add the paint tool), because it will better inform what the base class should look like. I'll also add a UAT notebook.

@pelson @tacaswell, I propose the following:
The Rectangle and Ellipse tools each get three resize handles and one rotation handle. The RegularPolygon tool gets a resize handle and a rotation handle.
The Lasso Tool gets no handles.
All tools are moved by picking on the patch and not on a handle.

Closing in favor of implemented the Painter widget only in #7411. I bit off more than I can chew with this one.