How to do a Constrained Delaunay tetrahedralization within a constrained volume without using the vertices defining that volume

Question

I am currently using the python library Tetgen in order to perform a constrained Delaunay tetrahedralization on a set of vertices and faces. Those vertices have been generated within a constrained volume.

I try to apply Delaunay only on the vertices that have been generated and not the vertices defining the volume, but in order to keep them constrained I also have to include the vertices defining the volume when doing the tetrahedralization.

Here for instance we have vertices that define the shape of the mesh and its constraint. The vertices in the volume are the ones I want to perform Delaunay on but without using the vertices used to define the volume. So far the only solution has been to remove the unwanted segment and vertices once the tetrahedralization was performed but this technique is not suitable for other problems and so far I have not been able to find another way to do it.