algorithmic modeling for Rhino
Can it tell whether it's elliptic?
I imagine three points are chosen on the original curve, a circle is fitted through these points, and then additional points on the curve are tested to see if they are near enough to the guide circle.
"Elliptical Curve" doesn't mean it's an Ellipse or a Circle. It can be, but it can be a part of it as well.
This just brings me back to my original question, how does Rhino "know"?
Could it be Rhino tries several "Tryget..." methods on the curve? There are for instance TryGetArc and TryGetEllipse methods (among others) for curves.
I don't know, and I never seem to be able to find answers to these kind of questions by digging through the Rhino source. I'm afraid you'll have to ask on the mcneel discourse forum where the Rhino programmers hang out.
The funny thing is, you can rebuild a circle or ellipse with enough points, regardless of degree, to resemble the original at practically an atomic level and it will still just reference as a "periodic planar curve", so they must be specified in some unique nurbistic manner.
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