Reference documentation for deal.II version 8.4.1

#include <deal.II/grid/tria_boundary.h>
Public Types  
typedef Tensor< 1, spacedim >  FaceVertexNormals[GeometryInfo< dim >::vertices_per_face] 
Public Member Functions  
virtual  ~Boundary () 
virtual void  get_intermediate_points_on_line (const typename Triangulation< dim, spacedim >::line_iterator &line, std::vector< Point< spacedim > > &points) const 
virtual void  get_intermediate_points_on_quad (const typename Triangulation< dim, spacedim >::quad_iterator &quad, std::vector< Point< spacedim > > &points) const 
void  get_intermediate_points_on_face (const typename Triangulation< dim, spacedim >::face_iterator &face, std::vector< Point< spacedim > > &points) const 
virtual Tensor< 1, spacedim >  normal_vector (const typename Triangulation< dim, spacedim >::face_iterator &face, const Point< spacedim > &p) const 
virtual void  get_normals_at_vertices (const typename Triangulation< dim, spacedim >::face_iterator &face, FaceVertexNormals &face_vertex_normals) const 
virtual Point< spacedim >  project_to_surface (const typename Triangulation< dim, spacedim >::line_iterator &line, const Point< spacedim > &candidate) const 
virtual Point< spacedim >  project_to_surface (const typename Triangulation< dim, spacedim >::quad_iterator &quad, const Point< spacedim > &candidate) const 
virtual Point< spacedim >  project_to_surface (const typename Triangulation< dim, spacedim >::hex_iterator &hex, const Point< spacedim > &candidate) const 
Public Member Functions inherited from FlatManifold< dim, spacedim >  
FlatManifold (const Point< spacedim > periodicity=Point< spacedim >(), const double tolerance=1e10)  
virtual Point< spacedim >  get_new_point (const Quadrature< spacedim > &quad) const 
virtual Point< spacedim >  project_to_manifold (const std::vector< Point< spacedim > > &points, const Point< spacedim > &candidate) const 
Public Member Functions inherited from Manifold< dim, spacedim >  
virtual  ~Manifold () 
virtual Point< spacedim >  get_new_point_on_line (const typename Triangulation< dim, spacedim >::line_iterator &line) const 
virtual Point< spacedim >  get_new_point_on_quad (const typename Triangulation< dim, spacedim >::quad_iterator &quad) const 
virtual Point< spacedim >  get_new_point_on_hex (const typename Triangulation< dim, spacedim >::hex_iterator &hex) const 
Point< spacedim >  get_new_point_on_face (const typename Triangulation< dim, spacedim >::face_iterator &face) const 
Point< spacedim >  get_new_point_on_cell (const typename Triangulation< dim, spacedim >::cell_iterator &cell) const 
Public Member Functions inherited from Subscriptor  
Subscriptor ()  
Subscriptor (const Subscriptor &)  
virtual  ~Subscriptor () 
Subscriptor &  operator= (const Subscriptor &) 
void  subscribe (const char *identifier=0) const 
void  unsubscribe (const char *identifier=0) const 
unsigned int  n_subscriptions () const 
void  list_subscribers () const 
DeclException3 (ExcInUse, int, char *, std::string &,<< "Object of class "<< arg2<< " is still used by "<< arg1<< " other objects."<< "\n\n"<< "(Additional information: "<< arg3<< ")\n\n"<< "See the entry in the Frequently Asked Questions of "<< "deal.II (linked to from http://www.dealii.org/) for "<< "a lot more information on what this error means and "<< "how to fix programs in which it happens.")  
DeclException2 (ExcNoSubscriber, char *, char *,<< "No subscriber with identifier <"<< arg2<< "> subscribes to this object of class "<< arg1<< ". Consequently, it cannot be unsubscribed.")  
template<class Archive >  
void  serialize (Archive &ar, const unsigned int version) 
Protected Member Functions  
const std::vector< Point< 1 > > &  get_line_support_points (const unsigned int n_intermediate_points) const 
Private Attributes  
std::vector< std_cxx11::shared_ptr< QGaussLobatto< 1 > > >  points 
Threads::Mutex  mutex 
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):
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
to get the four midpoints of the lines bounding the quad at the boundary, and after that
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 specializations, 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.
typedef Tensor<1,spacedim> Boundary< dim, spacedim >::FaceVertexNormals[GeometryInfo< dim >::vertices_per_face] 
Type keeping information about the normals at the vertices of a face of a cell. Thus, there are GeometryInfo<dim>::vertices_per_face
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.
Definition at line 100 of file tria_boundary.h.
Destructor. Does nothing here, but needs to be declared to make it virtual.
Definition at line 32 of file tria_boundary.cc.

virtual 
Return intermediate points on a line spaced according to the interior support points of the 1D GaussLobatto quadrature formula.
The number of points requested is given by the size of the vector points
. It is the task of derived classes to arrange the points in approximately equal distances along the length of the line segment on the boundary bounded by the vertices of the first argument.
Among other places in the library, this function is called by the Mapping classes, for example the MappingQGeneric
class. On the other hand, not all mapping classes actually require intermediate points on lines (for example, \(Q_1\) mappings do not). Consequently this function is not made pure virtual, to allow users to define their own boundary classes without having to overload this function. However, the default implementation throws an error in any case and can, consequently, not be used if you use a mapping that does need the information provided by this function.
Reimplemented in TorusBoundary< dim, spacedim >, HyperBallBoundary< dim, spacedim >, StraightBoundary< dim, spacedim >, StraightBoundary< dim, dim >, and CylinderBoundary< dim, spacedim >.
Definition at line 39 of file tria_boundary.cc.

virtual 
Return intermediate points on a line spaced according to the tensor product of the interior support points of the 1D GaussLobatto quadrature formula.
The number of points requested is given by the size of the vector points
. It is required that this number is a square of another integer, i.e. n=points.size()=m*m
. It is the task of the derived classes to arrange the points such they split the quad into (m+1)(m+1)
approximately equalsized subquads.
Among other places in the library, this function is called by the Mapping classes, for example the MappingQGeneric
class. On the other hand, not all mapping classes actually require intermediate points on quads (for example, \(Q_1\) mappings do not). Consequently this function is not made pure virtual, to allow users to define their own boundary classes without having to overload this function. However, the default implementation throws an error in any case and can, consequently, not be used if you use a mapping that does need the information provided by this function.
Reimplemented in TorusBoundary< dim, spacedim >, HyperBallBoundary< dim, spacedim >, StraightBoundary< dim, spacedim >, StraightBoundary< dim, dim >, and CylinderBoundary< dim, spacedim >.
Definition at line 50 of file tria_boundary.cc.
void Boundary< dim, spacedim >::get_intermediate_points_on_face  (  const typename Triangulation< dim, spacedim >::face_iterator &  face, 
std::vector< Point< spacedim > > &  points  
)  const 
Depending on dim=2
or dim=3
this function calls the get_intermediate_points_on_line or the get_intermediate_points_on_quad function. It throws an exception for dim=1
. This wrapper allows dimension independent programming.
Definition at line 60 of file tria_boundary.cc.

virtual 
Return the normal vector to the surface at the point p. If p is not in fact on the surface, but only closeby, try to return something reasonable, for example the normal vector at the surface point closest to p. (The point p will in fact not normally lie on the actual surface, but rather be a quadrature point mapped by some polynomial mapping; the mapped surface, however, will not usually coincide with the actual surface.)
The face iterator gives an indication which face this function is supposed to compute the normal vector for. This is useful if the boundary of the domain is composed of different nondifferential pieces (for example when using the StraightBoundary class to approximate a geometry that is completely described by the coarse mesh, with piecewise (bi)linear components between the vertices, but where the boundary may have a kink at the vertices itself).
Reimplemented in HyperBallBoundary< dim, spacedim >, StraightBoundary< dim, spacedim >, and StraightBoundary< dim, dim >.
Definition at line 114 of file tria_boundary.cc.

virtual 
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 onesided limits, i.e. limit with respect to points inside the given face.
Definition at line 126 of file tria_boundary.cc.

virtual 
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.
Reimplemented in StraightBoundary< dim, spacedim >, and StraightBoundary< dim, dim >.
Definition at line 137 of file tria_boundary.cc.

virtual 
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.
Reimplemented in StraightBoundary< dim, spacedim >, and StraightBoundary< dim, dim >.
Definition at line 154 of file tria_boundary.cc.

virtual 
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.
Reimplemented in StraightBoundary< dim, spacedim >, and StraightBoundary< dim, dim >.
Definition at line 171 of file tria_boundary.cc.

protected 
Returns the support points of the GaussLobatto quadrature formula used for intermediate points.
Definition at line 188 of file tria_boundary.cc.

mutableprivate 
Point generator for the intermediate points on a boundary.
Definition at line 275 of file tria_boundary.h.

mutableprivate 
Mutex for protecting the points array.
Definition at line 280 of file tria_boundary.h.