Ellipse Empiricism

Spent some hours trying to figure out if I could figure this out with math.  I could not.
The several ellipses I'm building are to have the wood oriented pointing somewhat toward the center point.  It would be easy to do the arithmetic of the angles needed if the arc was a portion of a circle but an ellipse is way above my pay grade to calculate.

So I did it like anybody with a pencil and a straight edge would do it.  Laid out the wood and sort of made lines until it looked about right and cut each angle by eye so to speak.

Thought I would do the old big/small configuration.  A large piece followed by a narrower wedge followed by a large.  I think it was a real nice solution.  I also think it will play well with what Ken has planned for the front of the cabinet.  Laid out the large ones somewhat pointing toward center, placed narrower piece on top and eyeballed where to draw a pencil line.
You can also see a contraption Mike made to draw the correct ellipse(s).

First three pieces cut and fitted.

Then took the marked up wood over to my interpretation of a taper jig.  Since I have a large sliding table, the jig rides on that.  Most jigs I've seen slide against the fence of the saw.

Here's the jig with a marked up piece of walnut in it.  I can vary the angle with the arm that rotates.  The square of plywood that's against the fence accomplished two things.  One is since it's parallel to the blade I rotate the arm until the pencil line is aligned with the inside edge of the plywood.  The plywood also sits exactly inline with where the blade will cut so I slide the jig left or right until my cut line is under the plywood.

One of the narrower tapers.

Went very well, even had time to bake some bread.

I'll glue up tomorrow and somehow take it over to Ken's to see how it fits on the counter.