well in my opinion, elliptical geometry is slightly more “complex” than circular geometry, but by no means more “difficult”…
One of the traps that is easy to fall into is to assume that the parameter you refer to as “angle” corresponds to an actual angle on the drawing of the ellipse. It doesn’t, except in the degenerate case of a circle, where it is the angle from the horizontal axis to the point on the circle. In the formula you gave, “angle” is actually the ellipse’s eccentric anomaly. This detail can affect the drawing of the fan chart spokes. If we wish to locate spokes at intervals around the ellipse in order to have equal areas for the text, it’s not simply a matter of using equal increments of “angle” as it was in the case of the circle. For equal text areas, we would likely want roughly equal distances along the elliptic arc, and then back calculate the curve formula that would give the corresponding elliptic anomaly. This is trivial for circles. Unfortunately, there is no closed form formula to do this for ellipses.