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The class Manifold_with_boundary_tag is a tag class used to monitor the surface meshing algorithm. When instantiated with the tag Manifold_with_boundary_tag, the function template make_surface_mesh ensures that the output mesh is a manifold surface but it may have boundaries.
#include <CGAL/make_surface_mesh.h>
make_surface_mesh
Manifold_tag
Non_manifold_tag