The reason it's easier to pack ellipses into a polygon is that there is an symbolic expression for the extent of an ellipse in any direction, which can be used for constructing the constraints that keep the ellipses inside the polygons. I haven't been able to come up the simple constraints to keep ellipses inside an ellipse, so I've used embedded Lagrange multipliers. However, that method doesn't work well, as the Lagrange multiplier equations can have 2 or 4 real solutions, depending on the circumstance.
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