Detecting shapes from path points?

[rgartlan]

The PathItems object has utility functions for easily creating shapes like ellipses, rectangles, polygons, etc.  These functions return a PathItem.

I'm wondering whether it's possible (and perchance easy) to know by looking at an arbitrary PathItem or its PathPoints, whether it's one of these shapes.  The FXG export code knows how to do this, and I'm sure there's some fairly well-understood point analysis approaches to determining this by looking at each of the points (for instance, you know you have a rectangle if you have four points defining two parallel lines and equal diagonals).

But I'd like an easy way to get this information.  Any suggestions?

[CarlosCanto]

I don't think there's an easy way, you'll have to resort to math. FXG probably uses Math too.