That's the point I was making.  By (x,y)->x  I mean that you'd just use the x (cosine table) for example.  The easiest projection is to throw away axes :)

If you're making shapes as repeated paths in 2-D, then taking a projection (along an axis  x y or any rotation of x,y) will generate a signal that makes sense and generalizes, creating simple sinusoids for circles and complex tones for different shapes.

The pitch would vary by how fast the path is repeated, and the timbre would vary according to the shape.  The amplitude would vary by the size of the shape.  Those are simple rules--and may not be what you're interested in--but it would be consistent.  For example, using a square in it's normal rotation and projecting along x or y alone, you'd get a "square wave".

If you want to use a contribution from both of your axes, you can just sum them together.  (x+y)*sqrt(2)/2 is just a projection along the line x-y=0