Those are pretty!
What you're looking for are splines
, and Wolfram supports a huge number of them. One of the tricky things about splines is that the curve doesn't go through all of the points, and there's quite an art to choosing control points and “tensions” in the curve sections. Certain types of splines (Catmull-Rom being one) go through all control points, but you've still got to mind some parameters for good results.
Where splines can be really useful is in reducing the number of control points. Most vector graphics packages approximate a circle with four spline quadrants between four control points at the extrema. It's not a perfect circle, but visually good enough. With some judicious spline fits, you might be able to get your thousands of points down to a few hundred.
If you're concerned about the straight line segments making your figures look jaggy, see if you can alter the join between segments from mitre or bevel to round. I find it makes for a cleaner plot.
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