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The Problem

I am working on a problem of clustering for mobile nodes.

Initially, I though of clustering the nodes based on their angle of movement (relative to the x-axis). However this situation would fail in case that we have two groups of nodes moving on the same direction but on two parallel tracks. Their angle of movement would be the same, as such my approach would place both groups on the same cluster, which would be wrong (see grey nodes in the fig).

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Besides the angle of direction, also the (x,y,z) components of the nodes are known. Their distance from the origin can be computed as well.

The Question

What type of math/trigonometry/geometry calculations can be used to make a reasonable clustering scheme here?

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