[WIP] Path Mapping Barycenters

[floWetzels]

This PR adds the path mapping distance to the MergeTreeBarycenter, MergeTreeClustering and MergeTreeTemporalReduction modules. Furthermore, the PlanarGraphLayout has been adapted to also enable a "path based layout" for merge trees. It also contains some bug fixes, additions and minor refactorings for other modules related to merge tree edit distances, e.g. when using BDIEDs in MergeTreeDistanceMatrix, it is now possible to apply the preprocessing steps also available for other distances.

In essence, this PR adds the code for the VIS23 paper "Merge Tree Geodesics and Barycenters with Path Mappings" and further related adaptations.

Some further changes are still pending and will be added by @MatPont soon. So please don't merge until they are finished.

An accompanying ttk-data PR will come soon, too.

[julien-tierny]

Wonderful, thanks a lot Florian!
Could you please:

• fix the issues raised by the continuous integration? (warnings)
• submit a PR to ttk-data with new examples using the path mapping distance capabilities, for instance by adapting the examples covered by the Wasserstein distance (https://topology-tool-kit.github.io/examples/mergeTreeClustering/, https://topology-tool-kit.github.io/examples/mergeTreeFeatureTracking/, https://topology-tool-kit.github.io/examples/mergeTreeTemporalReduction/). This aspect is important, to make sure we can test your contribution in the future and make sure there's no regression.
  Thanks!

[floWetzels]

Yes, I'm on it!

[floWetzels]

@julien-tierny If the CI runs through, please remember to wait for the remaining changes by @MatPont to be pushed before merging into dev.
I'm working on the ttk-data example.

[floWetzels]

I created the accompanying ttk-data PR: topology-tool-kit/ttk-data#162

[julien-tierny]

work in progress, see topology-tool-kit/ttk-data#162

[floWetzels]

I think all issues are fixed now. Can you have another look, @julien-tierny?

Also, there seems to be a problem with the macos builds in the CI. Is this a problem from our side or an issue of the CI?

[floWetzels]

Anything new on this, @julien-tierny? The CI issues seem to be fixed.

[julien-tierny]

sorry for my late reply. I'm behind on the TTK PRs these days. I'll try to take care of that as soon as possible.
thanks!

[floWetzels]

Hi @julien-tierny, a quick reminder for this PR.
I have another PR in the pipeline that branches from this branch, so it would be great to have this one done before the new one.
It contains the source code of this paper: https://doi.ieeecomputersociety.org/10.1109/TVCG.2025.3567120