[Geometry Nodes] - Boolean based Mesh Cut Node

Geometry Nodes were developed in the first place for scattering objects on a surface and as such they perform really well. However doing specific operations on mesh components like vertices and edges it's not always easy or possible.

To improve this area of Geometry Nodes I want to propose a tool that can perform knife cut on base mesh with another mesh (cutter).

It's easy to spot similarities between this functionality and Mesh Boolean. The difference is that the cutter is not welded with base mesh, instead only the cut line is added.

This would allow for cutting and selecting intricate and non-trivial shapes that are impractical do to by hand.

Example usage:

Selection output Outside:

Selection output Inside:

Selection output Edge:

Different use cases. Extrude, solidify outside/inside, convert edge to curve.

Possible solutions for non-manifold geometry: