I have a lot of points lying in the same plane in 3D space.So I want to find 4 points among this set, which will be the most distant from each other. That is, the polygon built on these points will lie in this plane and will have the largest area. Haw can I do it? I am interested in the solution algorithm.
2026-04-01 23:28:04.1775086084
Finding 4 the most remote points described plane
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In your question are two conditions so we will follow with one of them. To build the polygon with four sides with vertices located at the giving points and with maximum area.
First calculate the convex hull closure.
Now depending on the number of points $n$ in the closure,
If $n$ < 4 then we include an interior point such that the triangle's area with the nearest side is minimum.
If $ n > 4$ we will prune the hull corners according to the minimum area triangles.