Point Nemo, search for the most distant point on the sphere

Hello Guys

please tell me how can I find the most distant point from other points lying on the sphere?

I tried to solve this problem, but for some positions of the points I think the result is not right

this task has geographical interpretation

point nemo.gh (9.5 KB)

FarthestPt.gh (13.9 KB)
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I guess I get you wrong.

FarthestPairOfPoints.gh (14.7 KB)


thank you very much for your reply
this method in principle works well, but for example, in the cases below it gives a result with reference to a group of points, but in fact the point farthest from this group of points lies on the other end of the sphere?

pointnemo ex.gh (9.5 KB)

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You need to either Internalise your Geometry, or upload the .3dm file you referenced your geometry from.

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I apologize did not add the file

pointnemo ex.gh (9.0 KB)
point nemo.3dm (89.1 KB)

IsolatedPoint.gh (20.7 KB)

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Mahdiyar, thank you very much for your reply
Now your definition is looking for the most remote in the group of given points
I probably didn’t exactly put it
you need to find the most distant point from this group of points, those should have a little shovel on a new sphere that is maximally remote from each of these points

Below is an approximate point and definition, but it does not quite work correctly

point nemo.3dm (33.7 KB)
IsolatedPoint 2.gh (25.8 KB)

More distant point based on what? are there geometries on the sphere?

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seghierkhaled, yes, the distance between the points must be determined by the sphere, not by a straight line there is a group of points lying on the sphere, you need to find (generate) the most distant point from this group of points on the sphere

I am not sure if i understand

pointnemo ex2.gh (17.2 KB)

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I will try to explain
the red dot should be as far as possible from all other points on the sphere
it must be calculated / built geometrically it is not there initially
initially there is a sphere and a group of points lies on it, you need to build such a point that would be removed as far as possible from the existing group of points on the sphere, the distance must be measured over the sphere

Check the file again, i find the same point using two methods, but maybe i am wrong

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Pt_Nemo.gh (14.7 KB)
Here’s my attempt.
I believe pt nemo is coincident with one of the edges sharing 3 cells on the 3d voronoi… can’t counter-test so i’m not sure.

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Quite the same approach, the furthest point is surely related with the convex hull of the points.

I am not sure of the robustness of my method to sort the planes. But it gives the same resul as Riccardo

Pt_Nemo_LD.gh (23.8 KB)