Tracing back centroids to the triangle (incenter)

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Let's say we have a triangular mesh defined as
TR = triangulation (F,P);
where F is Nx3 and represents the faces while P is Nx3 and represents 3D coordinates.
We then use the following line to get the centroid of each triangle:
centroid = incenter(TR);
Next we find the nearest pairs of centroids:
[Idx] =knnsearch (centroid,centroid,'K',2, 'Distance',"euclidean");
And get the coordinates of the second nearest centroid (first one is the original centroid itself):
centroid2 = centroid(Idx (:,2),:);
Now I want to go back and check which triangles, centroid and centroid2 correspond to in TR.
Why do I need this? Because I want to:
1) Check if the two triangles are parallel but not in the same plane
2) If not, search for K=3 and so on
3) If yes, project the centroid onto the parallel triangle and see if it is within that triangle
4) If not, go back to step 2
5) If yes, return the distance,

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