Trying to figure out if a curved path can constitute a portion of a perfect circle

[Eduard Buta]

Hello community,

I've been trying to use scripting to find out if a user-selected curved path (formed from two anchor points) can be part of a perfect circle, and if so, draw the circle with the appropriate circumference on the artboard.

It's a pretty complex topic that (in my mind) requires some mathematical knowledge to figure out. I've found the following article that does a pretty good job explaining how a circle can be approximated based on a cubic Bezier curve. However, I got stuck pretty early on because I didn't know exactly how to translate the two anchor point path I have on the screen into the four control points that form a cubic Bezier curve. Especially when it comes to referencing such coordinates via scripting.

Hoping that some of your bright minds might want to jump in on the challenge!

[m1b]

Haha, excellent @Jacob Bugge you are right of course. I wonder if, in the case of H1 length = H2 length, that the difference between RM and (R1 or R2) could be used to calculate an ellipse? @femkeblanco might know. 🙂

[Jacob Bugge]

It certainly can, Mark, directly by the ratio of RM to R1 (or R2), which are termed a and b in connexion with ellipses,

https://duckduckgo.com/?t=ftsa&q=ellipse&atb=v320-1&ia=web

and the ellipticity is (R1-RM)/R1 or (a-b)/a as the (first) flattening, and then some more.

https://duckduckgo.com/?t=ftsa&q=ellipticity&atb=v320-1&ia=web

[m1b]

Hi @Jacob Bugge, I had a bit of a look at the possibility of adjusting the script to detect bezier segments that were part of an ellipse (and the circle being a limit), but it got very hard for my poor maths skill. The problem is that, if you imagine a basic Illustrator-style ellipse of say 100 x 50, and then cut out a section from between two arbitrary points on one of the four bezier segments, then that curve can be different depending on where on the segment it came from. I just couldn't work out how to analyse it.

- Mark

[Jacob Bugge]

Mark,

Without symmetry as in H1 = H2,  even with an efficient(ly) customized programme/script, I believe it would be a long wait for the answer, which might be smoke (and maybe fire) filling the room.

[m1b]

Yes I suspect you are right, Jacob. Truly the project has now lost much of its appeal. Haha.