Generating tetrahedral mesh from nodes

I have a series of nodes in space and I want to generate a tetrahedral mesh from them.

This is how the accurate geometry looks like when I use generateMesh with the stl file.

I take the nodes from mesh and reposition them within the same space using my algorithm. Now I need to rebuild the mesh using these new nodes. When I use delaunayTriangulation, the geometry is not preserved at all.