* Given an input triangulation @p in_tria, this function makes a new flat
* triangulation @p out_tria which contains a single level with all active
* cells of the input triangulation. If @p spacedim1 and @p spacedim2 are
- * different, only the smallest spacedim components of the vertices are
+ * different, only the first few components of the vertex coordinates are
* copied over. This is useful to create a Triangulation<2,3> out of a
* Triangulation<2,2>, or to project a Triangulation<2,3> into a
- * Triangulation<2,2>, by neglecting the z components of the vertices.
+ * Triangulation<2,2>, by neglecting the $z$ components of the vertices.
*
* No internal checks are performed on the vertices, which are assumed to
* make sense topologically in the target @p spacedim2 dimensional space. If
* this is not the case, you will encounter problems when using the
* triangulation later on.
*
- * All information about cell manifold_ids and material ids are copied from
- * one triangulation to the other, and only the boundary manifold_ids and
- * boundary_ids are copied over from the faces of @p in_tria to the faces of
- * @p out_tria. If you need to specify manifold ids on interior faces, they
- * have to be specified manually after the triangulation is created.
+ * All information about cell
+ * @ref GlossManifoldIndicator "manifold indicators" and
+ * @ref GlossMaterialId "material indicators" are copied from
+ * one triangulation to the other. However, only manifold and
+ * boundary indicators of faces are copied over for faces that
+ * are located at the boundary of the triangulation. If you need
+ * to specify manifold ids on interior faces, they
+ * have to be re-set manually after the triangulation is created.
*
* This function will fail if the input Triangulation is of type
* parallel::distributed::Triangulation, as well as when the input
- * Triangulation contains hanging nodes.
+ * Triangulation contains hanging nodes. In other words, this function
+ * only works for globally refined triangulations.
*
* @param[in] in_tria The base input for a new flat triangulation.
* @param[out] out_tria The desired flattened triangulation constructed from
* the in_tria.
*
- * @note Since @p input and @p output have different spatial dimensions no
+ * @note Since @p input and @p output have different spatial dimensions, no
* manifold objects are copied by this function: you must attach new
* manifold objects to @p out_tria.
*/