How to retrieve path from point A to point B (geometry)

Check is the ShrotestPathFinder transformer works for you: https://www.safe.com/transformers/shortest-path-finder/

Yes, in an AttributeManager you can enable "adjacent features", giving you access to the attributes of e.g. the previous feature. You can create a new attribute, fill it with the value of the previous feature's ID_EXT_B and then use a TestFilter to see if it matches ID_EXT_A.

Put X and Y values in attributes and send everything to both ports of a FeatureMerger set up with Accumulation Mode: Merge Supplier and Conflict Resolution: Use Supplier. You can even generate a list if this doesn't bring X and Y from joined features.

Join on ID_EXT_A to ID_EXT_B.

Send merged port to a VertexCreator with mode Add Point and X and Y to X and Y attributes.

Following my question, I am trying to use loops for it, but it seems to block.

As a reminder my data is as follows:

ID_ELEMENT ID_EXT_A ID_EXT_B

4 A B

6 B C1

7 B C2

11 C2 D1

13 C1 D2

14 D2 E

I know my last point is E, so I need to climb my way back to A. Leaving me with the path: E -> D2 -> C1 -> B -> A

I am very new to FME and I obviously keep my developer's background, so I am trying to loop: here is what I did:

I put the previous node's ID in the variable. And each time it runs though, i check for the line where ID_EXT_A = Variable.

Maybe you see what I am doing wrong ?

A new day, a new idea.

You can 'hide' the loop in a recursive SQL query in an InlineQuerier, working back from the end nodes, and only keeping the paths that begin at a starting point.

This works with paths of all depths, with more than one starting point in your data set, and even with paths that split and rejoin.

The magic occurs in the InlineQuerier:

WITH RECURSIVE Links_CTE(ID_EXT_A,Path) AS
    (
        -- initial select statement to get started
        -- this is only executed once
        -- in this case we are starting at the end nodes and working back
        SELECT "ID_EXT_A","ID_EXT_A"||','||"ID_EXT_B" FROM "Links" WHERE "EndNode" = 'Yes'
 
        -- merge those results with the following query
        UNION ALL
 
        -- recursive select statement
        -- executed repeatedly until there are no more results
        SELECT "Links"."ID_EXT_A","Links"."ID_EXT_A"||','||"Links_CTE"."Path"
            FROM "Links"
            JOIN "Links_CTE" ON "Links"."ID_EXT_B"= "Links_CTE"."ID_EXT_A"
    )
 
    -- now query the Links_CTE to produce results
    SELECT "Path" from "Links_CTE" where "ID_EXT_A" in (select "ID_EXT_A" from "Links" where "StartNode" = 'Yes')

Also see the attached workspace.