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For example on an object like a banana, a snake or a C shaped object.

Is there a way to find the 2 "endpoints" or the 2 vertices that are furthest apart using geometry nodes?

muckyu
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  • Important to clarify your metric: furthest apart in 3D space, or the longest route through the geometry? – Robin Betts Feb 21 '24 at 08:45
  • Preferrably longest route through the geometry. – muckyu Feb 21 '24 at 11:20
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    @muckyu can you make some example meshes, manually position the points that are further apart and explain the algorithm (e.g. draw a path from one to another) on why they are considered to be the furthest apart? That would make it a good question. For example, a "shortest path" could be used to get all possible paths through edges, and then pick the longest, but it's still not really "the longest path", because you could make it shorter by going through diagonals of the faces, and then shorter still by just arbitrarily traveling through the mesh. – Markus von Broady Feb 21 '24 at 11:34

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This is the most efficient way I could find: rather than measuring distances between each pair of points, I'm making a copy (copying has to be done in order to iterate on every possible pair - and a repeat zone is in general much slower than the old ways) and moving chosen point to the origin. Now the distance to this point is just the length of the position vector:

You can use this group like so:

Robin Betts' convex hull optimization:

Markus von Broady
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    Not sure... Could you reduce this to the same method on the convex hull? – Robin Betts Feb 21 '24 at 12:29
  • @RobinBetts good question! I think you're correct, this could be optimized by the convex hull. The simple proof being, that convex hull never creates (does it?) new points. – Markus von Broady Feb 21 '24 at 13:49
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    @RobinBetts ...And for any point it's always another point that is the furthest, because if 2 points building in edge are in equal distance, than the edge is inside the sphere defined by this distance. The same goes for 3 points and a triangle. And if any point disappeared in convex hull, then that point was closer than some points on the hull... I think so but I'm still making some tests – Markus von Broady Feb 21 '24 at 13:58
  • Thanks - this worked quite well!

    One question - for the convex hull method you mentioned. Do you mean I just add the convex hull node at the beginning before the "mesh to points" node?

     – muckyu Feb 22 '24 at 08:20
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    @muckyu see edit. – Markus von Broady Feb 22 '24 at 09:33
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    +1 clever solution!! – Chris Feb 23 '24 at 08:44