How to flips some inverted normals

Hello,
The mesh has some inverted triangles (black). How can I proceed to flip these normals in order to have the correct cells orientations locally?
I try this but it doesn’t work.

vtkNew<vtkPolyDataNormals> normals;
normals->SetInputData(fillholefilter->GetOutput());
normals->SetConsistency(1);
normals->FlipNormalsOff();
normals->ComputePointNormalsOff();
normals->ComputeCellNormalsOn();
normals->SplittingOff();
normals->SetAutoOrientNormals(1);
normals->Update();

Could it be that the surface has a fold, like a the letter z followed by a punch with a hammer on top of the letter?

Hello,

Check whether your mesh is manifold. That is, whether it can be unfolded into a 2D surface like those paper polyhedra we made during the school years. Being able to be unfolded, it allows to make all normals point into the same direction. Please, take a look at this: Remove faces in contact with non-manifold edges

best,

PC