For some specific purposes (and thereafter for fun) I wrote the PatternCreator for Glyphs.
When doing so, two questions arose and I can’t figure out an answer:

Creating a perfect circle happens when the handles are 55% between zero and the intersection-point of the handles. (And a little bit % more I see when drawing a circle with the Circle tool in Glyphs.)
What is the logic, where can I find information about how the curve is related to the position of the handles? I would like to know how the curve is calculated.

If I want to fill in an existing letterform with a pattern, is there still no other option than the one I found on How do I intersect two shapes? ? Because it would be a lot of work to get this ready. For example the glyph ‘o’: make a pattern, make intersections, select all parts of the pattern that lies outside the original shape, then doing the same for the inner circle of the ‘o’, while making sure that pattern-parts which have no intersections with the ‘o’ at all are also erased…

If there is no other option I will do it this way, but how is the code of Glyphs doing this when the user presses the button ‘intersect?’

Just mentioning random fact I know about circle and Bezier. Circle in bezier is, no matter how hard you try, is only an approximation (0.027% different at biggest, and tends to be slightly larger. Very close, but mathematically impossible nonetheless). And the ideal handle length is approximately 55.1915024494…%, so it’s okay to be tad longer sometimes.

I seem to remember other approximations with 56 and 57 point something. But since I cannot find anything about it anymore, perhaps I am remembering wrong. But it is to be expected that you get different results depending on what exactly you want to approximate: area, circumference, number of points touching the circle, approximate it from outside or inside, etc.