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Why does a circular sweep self-polygonize? How best to avoid it?

Question asked by Gan Starling on Jul 9, 2018
Latest reply on Jul 13, 2018 by Paul Salvador

In modeling a bowline knot by sweeping a spline, and choosing circular pattern to sweep on that spline, the end result looks good to the eye, but only until I zoom in on either one of the ends. Then do I find, not a circle but instead a circular-looking polygon of many segments. And the problem with this, is that I need one of those ends to mate concentrically in an assembly.

Know that the circular pattern is not from a sketch, but from the sweep option itself. So can't be to do with my circle not being an actual circle. Know also that I did make a point of "relaxing" the spline prior to sweep. Doing that once seems all that's allowed, since afterwards the option is greyed out.

So my question is, what causes the undesirable polygonization? How to avoid it? How to fix it if it occurs?