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// $Id: tria_boundary.h 19144 2009-07-30 20:12:08Z bangerth $
// Version: $Name$
//
// Copyright (C) 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 by the deal.II authors
//
// This file is subject to QPL and may not be distributed
// without copyright and license information. Please refer
// to the file deal.II/doc/license.html for the text and
// further information on this license.
//
//---------------------------------------------------------------------------
#ifndef __deal2__tria_boundary_h
#define __deal2__tria_boundary_h
/*---------------------------- boundary-function.h ---------------------------*/
#include <base/config.h>
#include <base/subscriptor.h>
#include <base/point.h>
#include <grid/tria.h>
DEAL_II_NAMESPACE_OPEN
template <int dim, int space_dim> class Triangulation;
/**
* This class is used to represent a boundary to a triangulation.
* When a triangulation creates a new vertex on the boundary of the
* domain, it determines the new vertex' coordinates through the
* following code (here in two dimensions):
* @verbatim
* ...
* Point<2> new_vertex = boundary.get_new_point_on_line (line);
* ...
* @endverbatim
* @p line denotes the line at the boundary that shall be refined
* and for which we seek the common point of the two child lines.
*
* In 3D, a new vertex may be placed on the middle of a line or on
* the middle of a side. Respectively, the library calls
* @verbatim
* ...
* Point<3> new_line_vertices[4]
* = { boundary.get_new_point_on_line (face->line(0)),
* boundary.get_new_point_on_line (face->line(1)),
* boundary.get_new_point_on_line (face->line(2)),
* boundary.get_new_point_on_line (face->line(3)) };
* ...
* @endverbatim
* to get the four midpoints of the lines bounding the quad at the
* boundary, and after that
* @verbatim
* ...
* Point<3> new_quad_vertex = boundary.get_new_point_on_quad (face);
* ...
* @endverbatim
* to get the midpoint of the face. It is guaranteed that this order
* (first lines, then faces) holds, so you can use information from
* the children of the four lines of a face, since these already exist
* at the time the midpoint of the face is to be computed.
*
* Since iterators are passed to the functions, you may use information
* about boundary indicators and the like, as well as all other information
* provided by these objects.
*
* There are specialisations, StraightBoundary, which places
* the new point right into the middle of the given points, and
* HyperBallBoundary creating a hyperball with given radius
* around a given center point.
*
* @ingroup boundary
* @author Wolfgang Bangerth, 1999, 2001, 2009, Ralf Hartmann, 2001, 2008
*/
template <int dim, int spacedim=dim>
class Boundary : public Subscriptor
{
public:
/**
* Type keeping information about
* the normals at the vertices of
* a face of a cell. Thus, there
* are
* <tt>GeometryInfo<dim>::vertices_per_face</tt>
* normal vectors, that define
* the tangent spaces of the
* boundary at the vertices. Note
* that the vectors stored in
* this object are not required
* to be normalized, nor to
* actually point outward, as one
* often will only want to check
* for orthogonality to define
* the tangent plane; if a
* function requires the normals
* to be normalized, then it must
* do so itself.
*
* For obvious reasons, this
* type is not useful in 1d.
*/
typedef Tensor<1,spacedim> FaceVertexNormals[GeometryInfo<dim>::vertices_per_face];
/**
* Destructor. Does nothing here, but
* needs to be declared to make it
* virtual.
*/
virtual ~Boundary ();
/**
* Return the point which shall
* become the new middle vertex
* of the two children of a
* regular line. In 2D, this line
* is a line at the boundary,
* while in 3d, it is bounding a
* face at the boundary (the
* lines therefore is also on the
* boundary).
*/
virtual Point<spacedim>
get_new_point_on_line (const typename Triangulation<dim,spacedim>::line_iterator &line) const = 0;
/**
* Return the point which shall
* become the common point of the
* four children of a quad at the
* boundary in three or more
* spatial dimensions. This
* function therefore is only
* useful in at least three
* dimensions and should not be
* called for lower dimensions.
*
* This function is called after
* the four lines bounding the
* given @p quad are refined, so
* you may want to use the
* information provided by
* <tt>quad->line(i)->child(j)</tt>,
* <tt>i=0...3</tt>, <tt>j=0,1</tt>.
*
* Because in 2D, this function
* is not needed, it is not made
* pure virtual, to avoid the
* need to overload it. The
* default implementation throws
* an error in any case, however.
*/
virtual Point<spacedim>
get_new_point_on_quad (const typename Triangulation<dim,spacedim>::quad_iterator &quad) const;
/**
* Depending on <tt>dim=2</tt> or
* <tt>dim=3</tt> this function
* calls the
* get_new_point_on_line or the
* get_new_point_on_quad
* function. It throws an
* exception for
* <tt>dim=1</tt>. This wrapper
* allows dimension independent
* programming.
*/
Point<spacedim>
get_new_point_on_face (const typename Triangulation<dim,spacedim>::face_iterator &face) const;
/**
* Return equally spaced
* intermediate points on a line.
*
* The number of points requested
* is given by the size of the
* vector @p points. It is the
* task of the derived classes to
* arrange the points in
* approximately equal distances.
*
* This function is called by the
* @p MappingQ class. This
* happens on each face line of a
* cells that has got at least
* one boundary line.
*
* As this function is not needed
* for @p MappingQ1, it is not
* made pure virtual, to avoid
* the need to overload it. The
* default implementation throws
* an error in any case, however.
*/
virtual void
get_intermediate_points_on_line (const typename Triangulation<dim,spacedim>::line_iterator &line,
std::vector<Point<spacedim> > &points) const;
/**
* Return equally spaced
* intermediate points on a
* boundary quad.
*
* The number of points requested
* is given by the size of the
* vector @p points. It is
* required that this number is a
* square of another integer,
* i.e. <tt>n=points.size()=m*m</tt>. It
* is the task of the derived
* classes to arrange the points
* such they split the quad into
* <tt>(m+1)(m+1)</tt> approximately
* equal-sized subquads.
*
* This function is called by the
* <tt>MappingQ<3></tt> class. This
* happens each face quad of
* cells in 3d that has got at
* least one boundary face quad.
*
* As this function is not needed
* for @p MappingQ1, it is not
* made pure virtual, to avoid
* the need to overload it. The
* default implementation throws
* an error in any case, however.
*/
virtual void
get_intermediate_points_on_quad (const typename Triangulation<dim,spacedim>::quad_iterator &quad,
std::vector<Point<spacedim> > &points) const;
/**
* Depending on <tt>dim=2</tt> or
* <tt>dim=3</tt> this function
* calls the
* get_intermediate_points_on_line
* or the
* get_intermediate_points_on_quad
* function. It throws an
* exception for
* <tt>dim=1</tt>. This wrapper
* allows dimension independent
* programming.
*/
void
get_intermediate_points_on_face (const typename Triangulation<dim,spacedim>::face_iterator &face,
std::vector<Point<spacedim> > &points) const;
/**
* Compute the normal vectors to
* the boundary at each vertex of
* the given face. It is not
* required that the normal
* vectors be normed
* somehow. Neither is it
* required that the normals
* actually point outward.
*
* This function is
* needed to compute data for C1
* mappings. The default
* implementation is to throw an
* error, so you need not
* overload this function in case
* you do not intend to use C1
* mappings.
*
* Note that when computing
* normal vectors at a vertex
* where the boundary is not
* differentiable, you have to
* make sure that you compute the
* one-sided limits, i.e. limit
* with respect to points inside
* the given face.
*/
virtual void
get_normals_at_vertices (const typename Triangulation<dim,spacedim>::face_iterator &face,
FaceVertexNormals &face_vertex_normals) const;
/**
* Given a candidate point and a
* line segment characterized by
* the iterator, return a point
* that lies on the surface
* described by this object. This
* function is used in some mesh
* smoothing algorithms that try
* to move around points in order
* to improve the mesh quality
* but need to ensure that points
* that were on the boundary
* remain on the boundary.
*
* If spacedim==1, then the line
* represented by the line
* iterator is the entire space
* (i.e. it is a cell, not a part
* of the boundary), and the
* returned point equals the
* given input point.
*
* Derived classes do not need to
* implement this function unless
* mesh smoothing algorithms are
* used with a particular
* boundary object. The default
* implementation of this
* function throws an exception
* of type ExcPureFunctionCalled.
*/
virtual
Point<spacedim>
project_to_surface (const typename Triangulation<dim,spacedim>::line_iterator &line,
const Point<spacedim> &candidate) const;
/**
* Same function as above but for
* a point that is to be
* projected onto the area
* characterized by the given
* quad.
*
* If spacedim<=2, then the surface
* represented by the quad
* iterator is the entire space
* (i.e. it is a cell, not a part
* of the boundary), and the
* returned point equals the
* given input point.
*/
virtual
Point<spacedim>
project_to_surface (const typename Triangulation<dim,spacedim>::quad_iterator &quad,
const Point<spacedim> &candidate) const;
/**
* Same function as above but for
* a point that is to be
* projected onto the area
* characterized by the given
* quad.
*
* If spacedim<=3, then the manifold
* represented by the hex
* iterator is the entire space
* (i.e. it is a cell, not a part
* of the boundary), and the
* returned point equals the
* given input point.
*/
virtual
Point<spacedim>
project_to_surface (const typename Triangulation<dim,spacedim>::hex_iterator &hex,
const Point<spacedim> &candidate) const;
};
/**
* Specialization of Boundary<dim,spacedim>, which places the new point
* right into the middle of the given points. The middle is defined
* as the arithmetic mean of the points.
*
* This class does not really describe a boundary in the usual
* sense. By placing new points in the middle of old ones, it rather
* assumes that the boundary of the domain is given by the
* polygon/polyhedron defined by the boundary of the initial coarse
* triangulation.
*
* @ingroup boundary
*
* @author Wolfgang Bangerth, 1998, 2001, Ralf Hartmann, 2001
*/
template <int dim, int spacedim=dim>
class StraightBoundary : public Boundary<dim,spacedim>
{
public:
/**
* Default constructor. Some
* compilers require this for
* some reasons.
*/
StraightBoundary ();
/**
* Let the new point be the
* arithmetic mean of the two
* vertices of the line.
*
* Refer to the general
* documentation of this class
* and the documentation of the
* base class for more
* information.
*/
virtual Point<spacedim>
get_new_point_on_line (const typename Triangulation<dim,spacedim>::line_iterator &line) const;
/**
* Let the new point be the
* arithmetic mean of the four
* vertices of this quad and the
* four midpoints of the lines,
* which are already created at
* the time of calling this
* function.
*
* Refer to the general
* documentation of this class
* and the documentation of the
* base class for more
* information.
*/
virtual Point<spacedim>
get_new_point_on_quad (const typename Triangulation<dim,spacedim>::quad_iterator &quad) const;
/**
* Gives <tt>n=points.size()</tt>
* points that splits the
* StraightBoundary line into
* $n+1$ partitions of equal
* lengths.
*
* Refer to the general
* documentation of this class
* and the documentation of the
* base class.
*/
virtual void
get_intermediate_points_on_line (const typename Triangulation<dim,spacedim>::line_iterator &line,
std::vector<Point<spacedim> > &points) const;
/**
* Gives <tt>n=points.size()=m*m</tt>
* points that splits the
* StraightBoundary quad into
* $(m+1)(m+1)$ subquads of equal
* size.
*
* Refer to the general
* documentation of this class
* and the documentation of the
* base class.
*/
virtual void
get_intermediate_points_on_quad (const typename Triangulation<dim,spacedim>::quad_iterator &quad,
std::vector<Point<spacedim> > &points) const;
/**
* Compute the normals to the
* boundary at the vertices of
* the given face.
*
* Refer to the general
* documentation of this class
* and the documentation of the
* base class.
*/
virtual void
get_normals_at_vertices (const typename Triangulation<dim,spacedim>::face_iterator &face,
typename Boundary<dim,spacedim>::FaceVertexNormals &face_vertex_normals) const;
/**
* Given a candidate point and a
* line segment characterized by
* the iterator, return a point
* that lies on the surface
* described by this object. This
* function is used in some mesh
* smoothing algorithms that try
* to move around points in order
* to improve the mesh quality
* but need to ensure that points
* that were on the boundary
* remain on the boundary.
*
* The point returned is the
* projection of the candidate
* point onto the line through
* the two vertices of the given
* line iterator.
*
* If spacedim==1, then the line
* represented by the line
* iterator is the entire space
* (i.e. it is a cell, not a part
* of the boundary), and the
* returned point equals the
* given input point.
*/
virtual
Point<spacedim>
project_to_surface (const typename Triangulation<dim,spacedim>::line_iterator &line,
const Point<spacedim> &candidate) const;
/**
* Same function as above but for
* a point that is to be
* projected onto the area
* characterized by the given
* quad.
*
* The point returned is the
* projection of the candidate
* point onto the bilinear
* surface spanned by the four
* vertices of the given quad
* iterator.
*
* If spacedim<=2, then the surface
* represented by the quad
* iterator is the entire space
* (i.e. it is a cell, not a part
* of the boundary), and the
* returned point equals the
* given input point.
*/
virtual
Point<spacedim>
project_to_surface (const typename Triangulation<dim,spacedim>::quad_iterator &quad,
const Point<spacedim> &candidate) const;
/**
* Same function as above but for
* a point that is to be
* projected onto the area
* characterized by the given
* quad.
*
* The point returned is the
* projection of the candidate
* point onto the trilinear
* manifold spanned by the eight
* vertices of the given hex
* iterator.
*
* If spacedim<=3, then the manifold
* represented by the hex
* iterator is the entire space
* (i.e. it is a cell, not a part
* of the boundary), and the
* returned point equals the
* given input point.
*/
virtual
Point<spacedim>
project_to_surface (const typename Triangulation<dim,spacedim>::hex_iterator &hex,
const Point<spacedim> &candidate) const;
};
/* -------------- declaration of explicit specializations ------------- */
#ifndef DOXYGEN
template <>
Point<1>
Boundary<1,1>::
get_new_point_on_face (const Triangulation<1,1>::face_iterator &) const;
template <>
void
Boundary<1,1>::
get_intermediate_points_on_face (const Triangulation<1,1>::face_iterator &,
std::vector<Point<1> > &) const;
template <>
Point<2>
Boundary<1,2>::
get_new_point_on_face (const Triangulation<1,2>::face_iterator &) const;
template <>
void
Boundary<1,2>::
get_intermediate_points_on_face (const Triangulation<1,2>::face_iterator &,
std::vector<Point<2> > &) const;
template <>
void
StraightBoundary<1,1>::
get_normals_at_vertices (const Triangulation<1,1>::face_iterator &,
Boundary<1,1>::FaceVertexNormals &) const;
template <>
void
StraightBoundary<2,2>::
get_normals_at_vertices (const Triangulation<2,2>::face_iterator &face,
Boundary<2,2>::FaceVertexNormals &face_vertex_normals) const;
template <>
void
StraightBoundary<3,3>::
get_normals_at_vertices (const Triangulation<3,3>::face_iterator &face,
Boundary<3,3>::FaceVertexNormals &face_vertex_normals) const;
template <>
Point<3>
StraightBoundary<3,3>::
get_new_point_on_quad (const Triangulation<3,3>::quad_iterator &quad) const;
template <>
void
StraightBoundary<1,1>::
get_intermediate_points_on_line (const Triangulation<1,1>::line_iterator &,
std::vector<Point<1> > &) const;
template <>
void
StraightBoundary<3,3>::
get_intermediate_points_on_quad (const Triangulation<3,3>::quad_iterator &quad,
std::vector<Point<3> > &points) const;
#endif // DOXYGEN
DEAL_II_NAMESPACE_CLOSE
#endif
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