Tracing back centroids to the triangle (incenter)

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,