How to force mesh vertices to lay on a segment?

I would like to know if it's possible to have a little more freedom in creating a triangular mesh with geometryFromMesh and generateMesh: in particular, my geometry is a simple square, but I want to study conditions on the diagonal of such a square: for this reason, I'd like the vertices of the mesh's triangles to lay onto the said diagonal. Is there a way to do that?

[KSSV]

You may define the points inside the square along a diagonal. Did you try this?

[Mauro Giliberti]

How would I do that? The nodes used in geometryFromMesh aren't considered by generateMesh

[KSSV]

I actually use this: https://www.mathworks.com/matlabcentral/fileexchange/25555-mesh2d-delaunay-based-unstructured-mesh-generation . In this you need to specify the points and the specied region is meshed.