* <tt>boundary_id</tt> that uniquely identifies which part of the
* boundary this face is on. If nothing is specified at creation time,
* each boundary face has a zero boundary id and each triangulation
- * object has an flat manifold id. On the other hand, the boundary
- * id of faces and the manifold id of objects can be set either at
+ * object has a flat_manifold_id. On the other hand, the boundary
+ * id of faces and the manifold_id of objects can be set either at
* creation time or later by looping over all cells and querying their
* faces.
*
* faces is ignored by Manifold objects, and Manifold descriptors can only be
* attached to manifold ids.
*
- * The behavior of the Triangulation class w.r.t. geometry descriptions is the
- * following: Triangulation::set_manifold() attaches a manifold descriptor to
- * the specified manifold id. The function expects a Manifold descriptor, and
- * you could describe both the interior and the boundary of the domain using the
- * same object.
+ * The behavior of the Triangulation class with respect to geometry descriptions
+ * is the following: Triangulation::set_manifold() attaches a manifold
+ * descriptor to the specified manifold_id. The function expects a Manifold
+ * descriptor, and you could describe both the interior and the boundary of the
+ * domain using the same object.
*
* Whenever a new vertex is needed in an object, the Triangulation queries the
* manifold_id of the object which needs refinement. If the query resulted in a
* number different from numbers::flat_manifold_id, then the Triangulation looks
* whether a previous call to Triangulation::set_manifold() was performed with
- * the given id, and if yes, it uses the stored object to obtain new vertices,
- * otherwise it uses a FlatManifold object.
+ * the given id. If it was, then the triangulation uses the stored object to
+ * obtain new vertices, otherwise it uses a FlatManifold object.
*
* @note This behavior is **not** backward compatible to that of deal.II
* versions prior to 9.0. If one ignores the manifold_id of an object (i.e., if
* thing to do. The classes derived from the Manifold base class therefore
* describe the geometry of a domain. One can then attach an object of a class
* derived from this base class to the Triangulation object using the
- * Triangulation::set_manifold() function associating it with a manifold id
- * (see types::manifold_id), use this manifold id on the cells, faces or edges
+ * Triangulation::set_manifold() function associating it with a manifold_id
+ * (see types::manifold_id), use this manifold_id on the cells, faces or edges
* of the triangulation that should be described by this manifold using the
* TriaAccessor::set_manifold_id() function, and then the Triangulation will
* ask the manifold object where a new vertex to be located on a cell, face or
* edge so attributed should be located upon mesh refinement. Several classes
* already exist to support the most common geometries, e.g.,
- * CylinderManifold, or PolarManifold, which represent respectively the
+ * CylindricalManifold, or PolarManifold, which represent respectively the
* geometry obtained when describing your space in cylindrical coordinates or
- * in polar coordinates, and by default, all curved geometries generated using
- * functions in the GridGenerator namespace attach by default the correct
- * Manifold object to the curved parts of the domain.
+ * in polar coordinates. By default, all curved geometries generated using
+ * functions in the GridGenerator namespace attach the correct Manifold object
+ * to the curved parts of the domain.
*
* <li> Integration: When using higher order finite element methods, it is
* often necessary to compute cell terms (like cell contributions to the