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There are some online materials on how to get the intersection between two great circles (e.g. link1, link2).

However, I couldn't find any material on how to get the intersection of multiple (more than 2) great circles.

Any help would be much appreciated.

====Edit====

To clarify, I have a bunch of great circle created from some measurements. Ideally all the great circles would pass two antipodal points on a sphere. However, due to noise from the measurments the great circles do not pass through the same points on the sphere.

So what would be the best estimate or best fit intersection points on the sphere of the great circles.

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  • $\begingroup$ Are you expecting an answer that is a bunch of points or a bunch of regions? $\endgroup$ Commented Jul 17, 2024 at 13:22
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    $\begingroup$ If you have three distinct great circles $C_1$, $C_2$, $C_3$, then $C_1 \cap C_2$ will always be a pair of antipodal points, and $C_1 \cap C_2 \cap C_3$ will either be the same two points or the empty set (depending on whether $C_3$ also passes through those two points). Why are you interested in the intersection of more than two great circles, and what do you think it would be? $\endgroup$ Commented Jul 17, 2024 at 13:33
  • $\begingroup$ Thanks for pointing out the confusion. I hope I clarified my question (see above) $\endgroup$ Commented Jul 18, 2024 at 6:41
  • $\begingroup$ So you have what is known in old-fashioned navigation as a "cocked hat" and you want to make the best estimate of the true location. I don't know the answer, but it's a good question. $\endgroup$ Commented Jul 18, 2024 at 23:49

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