* object (derived from Manifold). Notice that Triangulation uses only
* the Manifold interface, not the Boundary interface. Other tools,
* however, might need to compute exact normals at quadrature points,
- * and therefore a wrapper to query Boundary objects is provided.
+ * and therefore a wrapper to query Boundary objects is provided.
*
*
* <h3>An example</h3>
* const HyperShellBoundary<2> boundary_description(center);
* triangulation.set_boundary (0, boundary_description);
*
- * triangulation.refine_global (3);
+ * triangulation.refine_global (3);
* @endcode
* This code is better, producing the following mesh:
*
* cell = triangulation.begin_active(),
* endc = triangulation.end();
* for (; cell!=endc; ++cell)
- * cell->set_all_manifold_ids (0);
- *
+ * cell->set_all_manifold_ids (0);
+ *
* triangulation.refine_global (3);
* @endcode
* This leads to the following mesh:
* const HyperShellBoundary<2> boundary_description(center);
* triangulation.set_boundary (0, boundary_description);
*
- * triangulation.refine_global (3);
+ * triangulation.refine_global (3);
* @endcode
*
* @image html hypershell-boundary-only-4.png ""
* cell = triangulation.begin_active(),
* endc = triangulation.end();
* for (; cell!=endc; ++cell)
- * cell->set_all_manifold_ids (0);
- *
+ * cell->set_all_manifold_ids (0);
+ *
* triangulation.refine_global (3);
* @endcode
*
* in the context of what GridGenerator::hyper_shell() produces in 3d
* (see the documentation of this function). It is also germane to the
* cases discussed in the @ref GlossDistorted "glossary entry on distorted cells".
- *
+ *
+ * Another example where the manifold description not just at the boundary but
+ * also in the interior of the domain matters is for high-order methods. When
+ * using cubic or even higher degrees of the polynomials, full convergence is
+ * typically only obtained if a curved description at a boundary transitions
+ * into a straight description inside the domain (for example when meshing a
+ * ball including the origin) over a layer of finite thickness. This is
+ * realized by the class TransfiniteInterpolationManifold.
*
* @see @ref GlossManifoldIndicator "Glossary entry on manifold indicators"
*