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// $Id: mapping_c1.h 30450 2013-08-23 15:48:29Z kronbichler $
//
// Copyright (C) 2001 - 2013 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------
#ifndef __deal2__mapping_c1_h
#define __deal2__mapping_c1_h
#include <deal.II/base/config.h>
#include <deal.II/fe/mapping_q.h>
DEAL_II_NAMESPACE_OPEN
/*!@addtogroup mapping */
/*@{*/
/**
* Mapping class that uses C1 (continuously differentiable) cubic
* mappings of the boundary. This class is built atop of
* MappingQ by simply determining the interpolation points for a
* cubic mapping of the boundary differently: MappingQ chooses
* them such that they interpolate the boundary, while this class
* chooses them such that the discretized boundary is globally
* continuously differentiable.
*
* To use this class, make sure that the
* Boundary::@p get_normals_at_vertices function is implemented
* for the user's boundary object.
*
* For more information about the <tt>spacedim</tt> template parameter
* check the documentation of FiniteElement or the one of
* Triangulation.
*
* @author Wolfgang Bangerth, 2001
*/
template<int dim, int spacedim=dim>
class MappingC1 : public MappingQ<dim,spacedim>
{
public:
/**
* Constructor. Pass the fixed degree @p 3 down to the base class, as a
* cubic mapping suffices to generate a continuous mapping of the boundary.
*/
MappingC1 ();
/**
* Return a pointer to a copy of the present object. The caller of this copy
* then assumes ownership of it.
*/
virtual
Mapping<dim,spacedim> *clone () const;
protected:
/**
* For <tt>dim=2,3</tt>. Append the support points of all shape functions
* located on bounding lines to the vector @p a. Points located on the line
* but on vertices are not included.
*
* Needed by the <tt>compute_support_points_simple(laplace)</tt>
* functions. For <tt>dim=1</tt> this function is empty.
*
* This function chooses the respective points not such that they are
* interpolating the boundary (as does the base class), but rather such that
* the resulting cubic mapping is a continuous one.
*/
virtual void
add_line_support_points (const typename Triangulation<dim>::cell_iterator &cell,
std::vector<Point<dim> > &a) const;
/**
* For <tt>dim=3</tt>. Append the support points of all shape functions
* located on bounding faces (quads in 3d) to the vector @p a. Points
* located on the line but on vertices are not included.
*
* Needed by the @p compute_support_points_laplace function. For
* <tt>dim=1</tt> and 2 this function is empty.
*
* This function chooses the respective points not such that they are
* interpolating the boundary (as does the base class), but rather such that
* the resulting cubic mapping is a continuous one.
*/
virtual void
add_quad_support_points(const typename Triangulation<dim>::cell_iterator &cell,
std::vector<Point<dim> > &a) const;
};
/*@}*/
/* -------------- declaration of explicit specializations ------------- */
#ifndef DOXYGEN
template <> void MappingC1<1>::add_line_support_points (
const Triangulation<1>::cell_iterator &,
std::vector<Point<1> > &) const;
template <> void MappingC1<2>::add_line_support_points (
const Triangulation<2>::cell_iterator &cell,
std::vector<Point<2> > &a) const;
template <> void MappingC1<1>::add_quad_support_points (
const Triangulation<1>::cell_iterator &,
std::vector<Point<1> > &) const;
template <> void MappingC1<2>::add_quad_support_points (
const Triangulation<2>::cell_iterator &,
std::vector<Point<2> > &) const;
#endif // DOXYGEN
DEAL_II_NAMESPACE_CLOSE
#endif
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