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This is not the same question as Geometrynodes Curve Intersections - or at least not how the answers interpreted it. That question solicited answers dealing entirely with two straight line segments, whereas I'm dealing with multi-point Bezier curves. As a result I'm not sure how to generalize any of the solutions (or if I need another approach entirely).

Two semi-circular splines, labeled A and B. The intersecting point is circled, and a text annotation reads "Curve factor = 0.33 or whatever".

My goal at the moment is to truncate Curve A at the intersection with Curve B, and vice versa, to create a Gothic-arch-style shape. A generalized solution for testing if two arbitrary splines intersect (and where) would be very useful, but I don't know if we have tools for that yet.

Because I'll be truncating, the most useful final output would be the curve Factor at the point, because I have no idea how to go from a Location on a curve to a Factor.

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  • $\begingroup$ The answer by Tobias Einarsson at the question you linked will work with any kind of splines, curved or straight (provided there is one and only one intersection.) $\endgroup$ Commented Aug 25, 2023 at 13:40
  • $\begingroup$ "This is not the same question as Geometrynodes Curve Intersections - or at least not how the answers interpreted it. That question solicited answers[…]" - a question is not defined by its answers, your question is a duplicate. If you modify your question to show how you tried some answer from there and failed, then perhaps the question will become correct. BTW, throughout the industry, measuring things related to bezier length is done by subdividing the bezier into straight segments, and then you can isolate the closest segments, and then all the answers there work. $\endgroup$ Commented Aug 25, 2023 at 14:04
  • $\begingroup$ Also if you rephrase your question to be a more specific scenario (not too specific…) like "find intersection between two half-circles"… But maybe math exchange is a better place to ask it, as it seems there could be a mathematical solution… $\endgroup$ Commented Aug 25, 2023 at 14:06
  • $\begingroup$ Thanks for the advice, I'll have a look at how I can rework the question more appropriately, and recheck the solutions from the other question. $\endgroup$ Commented Aug 25, 2023 at 16:53
  • $\begingroup$ Regards to isolating "the closest segments" - wouldn't that require already knowing which ones are the closest segments to the point in interest? $\endgroup$ Commented Aug 25, 2023 at 16:54

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I'm not sure if I understand your problem, but if you want to input the $r$ radius of circles and $d$ distance between them and get the arc made of intersection of both (in your case just the top part):

Then you can use the red triangle, which is a right triangle, with its base (side adjacent to the $α$ angle) equal to $d\over2$, allowing you to calculate the angle - with an assumption $r = 1$ it's just $α = \arccos\left(\frac{d}{2}\right)$, otherwise just scale the argument to $\arccos$ accordingly: $α = \arccos\left(\frac{d}{2r}\right)$

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