Mesh brep without adding new vertices on edges

I’m looking for a way to triangulate given brep using Grasshopper in a such way that no new vertices will be added along the outline of the brep. So far I can’t achieve result using standard MeshBrep or TriRemesh components. Any ideas will be appriciated.

Edit:
Seems that with this particular brep result can be achieved using TriRemesh and increasing Target edge lenght and iteration number. But I have hundreds of these breps and this approach fails for lot of them.
Brep_to_mesh_all_breps.gh (14.1 MB)

Brep_to_mesh.gh (68.9 KB)