Opening this PR as a draft since it's still in progress. The core implementation is in place but it still needs more tests and documentation, and possibly some small code improvements. And it is also meant to allow early feedback on the chosen approach and related aspects.

I didn't look at the code yet, but the extension conceptually makes sense, and the implementation via a closed parameter seems reasonable. 👍

Thanks for the feedback!

When starting the implementation we were actually leaning towards the third approach mentioned

Introduce an internal _PolygonalChainSelector base class to provide common functionality for the existing PolygonSelector and a new OpenPolygonalChainSelector.

Although it would make the PR a bit more complex, we believe it would be worthwhile since it would centralize the shared logic and provide a cleaner architecture with clearer semantics for both cases. We also believe the level of difficulty would still be appropriate for us.

We ended up going with the current approach because it seemed like the simplest and least invasive starting point, but we are very interested in hearing thoughts about this alternative approach as well.

More tests have been added along with new documentation. A small note on the documentation is that we intentionally kept changes to the API docstring minimal to avoid potential semantic confusion and to keep the focus on the primary polygon selection behavior.

The PR is now ready for review.

And as an additional note, I also explored the alternative approach

Introduce an internal _PolygonalChainSelector base class to provide common functionality for the existing PolygonSelector and a new OpenPolygonalChainSelector.

implementing a working prototype (main...lucaznch:matplotlib:polyline). It follows a template-method-like pattern, refactoring the current PolygonSelector(..., closed) into a shared _PolygonalChainSelector base class.

From my point of view this approach has advantages. It provides a clearar separation of semantics between closed polygons and open polygonal chains, while also isolating shared and specialized functionality more explicitly, making it easier to extend I believe.

For example, the bounding box functionality is currently specific to closed polygons. If one wanted to add similar functionality for open polygonal chains (e.g., a "bounding" curve), it would be easier to incorporate in this structure.

That said, I am unsure whether the additional abstraction is beneficial in practice, or whether it perhaps introduces a bit more complexity.

In the meantime, we decided to adjust the implementation and move to what we believe is a cleaner and more maintainable architectural approach for this feature.

The previous implementation extended PolygonSelector with a closed parameter controlling whether the polygonal chain was open or closed. This introduced a slight semantic mismatch, as PolygonSelector would support both closed and open polygonal chains, while also making the class somewhat more difficult to maintain.

The new implementation introduces two new classes: PolylineSelector, a new public widget class dedicated to open polygonal chains, and _PolygonalSelector, a new internal base class providing the core structure and behavior for polygonal chain selector widgets.

PolygonSelector now inherits from _PolygonalSelector (instead of _SelectorWidget) while preserving its original API, semantics, and behavior for closed polygonal regions.

Starting from the previous implementation (fully in 870d2e6), we analyzed which parts were common to polygonal chains and which were specific to closed or open chains, and then extracted the shared structure and behavior into _PolygonalSelector, while allowing subclasses to implement or override specialized behavior where appropriate.