_max_node_id = this->parallel_max_node_id();
  _max_elem_id = this->parallel_max_elem_id();

  _next_free_unpartitioned_elem_id =
    ((_max_elem_id-1) / (this->n_processors() + 1) + 1) *
    (this->n_processors() + 1) + this->n_processors();
  _next_free_local_elem_id =
    ((_max_elem_id + this->n_processors() - 1) / (this->n_processors() + 1) + 1) *
    (this->n_processors() + 1) + this->processor_id();

  _next_free_unpartitioned_node_id =
    ((_max_node_id-1) / (this->n_processors() + 1) + 1) *
    (this->n_processors() + 1) + this->n_processors();
  _next_free_local_node_id =
    ((_max_node_id + this->n_processors() - 1) / (this->n_processors() + 1) + 1) *
    (this->n_processors() + 1) + this->processor_id();

#ifdef LIBMESH_ENABLE_UNIQUE_ID
  _next_unique_id = this->parallel_max_unique_id();

    {
      ray_target = inside - Point(1);
      intersection_distances =
        this->find_ray_intersections(inside, ray_target);
    }

  // I'd make this an assert, but I'm not 100% confident we can't

  const unsigned int hon_begin = lo_elem.n_nodes();
  const unsigned int hon_end   = hi_elem->n_nodes();

  libmesh_assert_less (hon_begin, hon_end);
  libmesh_assert_less_equal
    (hon_end-hon_begin, max_new_nodes_per_elem);

  for (unsigned int hon=hon_begin; hon<hon_end; hon++)

   * The mesh should at least be consistent enough for us to add new
   * nodes consistently.
   */
  mesh.update_parallel_id_counts();

  /*
   * If the mesh is empty then we have nothing to do

   * completely-partitioned meshes (where we'll sync nodes later);
   * let's keep track to make sure we're not in any in-between state.
   */
  dof_id_type n_unpartitioned_elem = 0;

  /**
   * Loop over the elements in the given range.  If any are

          // We'd better be effectively serialized here.  In theory we
          // could support more complicated cases but for now we
          // only support "completely partitioned" and/or "serialized"
          if (mesh.is_serial())
            libmesh_assert(mesh.comm().verify(n_unpartitioned_elem));
          else
            libmesh_not_implemented();
        }