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Reference documentation for deal.II version 9.6.0
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Reference documentation for deal.II version 9.6.0
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#include <deal.II/grid/manifold_lib.h>
Public Types | |
| using | FaceVertexNormals |
Public Member Functions | |
| SphericalManifold (const Point< spacedim > center=Point< spacedim >()) | |
| virtual std::unique_ptr< Manifold< dim, spacedim > > | clone () const override |
| virtual Point< spacedim > | get_intermediate_point (const Point< spacedim > &p1, const Point< spacedim > &p2, const double w) const override |
| virtual Tensor< 1, spacedim > | get_tangent_vector (const Point< spacedim > &x1, const Point< spacedim > &x2) const override |
| virtual Tensor< 1, spacedim > | normal_vector (const typename Triangulation< dim, spacedim >::face_iterator &face, const Point< spacedim > &p) const override |
| virtual void | get_normals_at_vertices (const typename Triangulation< dim, spacedim >::face_iterator &face, typename Manifold< dim, spacedim >::FaceVertexNormals &face_vertex_normals) const override |
| virtual void | get_new_points (const ArrayView< const Point< spacedim > > &surrounding_points, const Table< 2, double > &weights, ArrayView< Point< spacedim > > new_points) const override |
| virtual Point< spacedim > | get_new_point (const ArrayView< const Point< spacedim > > &vertices, const ArrayView< const double > &weights) const override |
| const Point< spacedim > & | get_center () const |
| void | get_normals_at_vertices (const Triangulation< 1 >::face_iterator &, Manifold< 1, 1 >::FaceVertexNormals &) const |
| void | get_normals_at_vertices (const Triangulation< 1, 2 >::face_iterator &, Manifold< 1, 2 >::FaceVertexNormals &) const |
| template<class Archive > | |
| void | serialize (Archive &ar, const unsigned int version) |
Computing the location of points. | |
| virtual Point< spacedim > | project_to_manifold (const ArrayView< const Point< spacedim > > &surrounding_points, const Point< spacedim > &candidate) const |
| 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 |
Computing normal vectors | |
| virtual void | get_normals_at_vertices (const typename Triangulation< dim, spacedim >::face_iterator &face, FaceVertexNormals &face_vertex_normals) const |
Subscriptor functionality | |
Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class. | |
| void | subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const |
| void | unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const |
| unsigned int | n_subscriptions () const |
| template<typename StreamType > | |
| void | list_subscribers (StreamType &stream) const |
| void | list_subscribers () const |
Static Public Member Functions | |
| static ::ExceptionBase & | ExcInUse (int arg1, std::string arg2, std::string arg3) |
| static ::ExceptionBase & | ExcNoSubscriber (std::string arg1, std::string arg2) |
Public Attributes | |
| const Point< spacedim > | center |
Private Types | |
| using | map_value_type = decltype(counter_map)::value_type |
| using | map_iterator = decltype(counter_map)::iterator |
Private Member Functions | |
| std::pair< double, Tensor< 1, spacedim > > | guess_new_point (const ArrayView< const Tensor< 1, spacedim > > &directions, const ArrayView< const double > &distances, const ArrayView< const double > &weights) const |
| void | do_get_new_points (const ArrayView< const Point< spacedim > > &surrounding_points, const ArrayView< const double > &weights, ArrayView< Point< spacedim > > new_points) const |
| void | check_no_subscribers () const noexcept |
Private Attributes | |
| const Point< spacedim > | p_center |
| const PolarManifold< spacedim > | polar_manifold |
| std::atomic< unsigned int > | counter |
| std::map< std::string, unsigned int > | counter_map |
| std::vector< std::atomic< bool > * > | validity_pointers |
| const std::type_info * | object_info |
Static Private Attributes | |
| static std::mutex | mutex |
Manifold description for a spherical space coordinate system.
You can use this Manifold object to describe any sphere, circle, hypersphere or hyperdisc in two or three dimensions. This manifold can be used as a co-dimension one manifold descriptor of a spherical surface embedded in a higher dimensional space, or as a co-dimension zero manifold descriptor for a body with positive volume, provided that the center of the spherical space is excluded from the domain. An example for the use of this function would be in the description of a hyper-shell or hyper-ball geometry, for example after creating a coarse mesh using GridGenerator::hyper_ball(). (However, it is worth mentioning that generating a good mesh for a disk or ball is complicated and requires addition steps. See the "Possibilities for extensions" section of step-6 for an extensive discussion of how one would construct such meshes and what one needs to do for it.)
The two template arguments match the meaning of the two template arguments in Triangulation<dim, spacedim>, however this Manifold can be used to describe both thin and thick objects, and the behavior is identical when dim <= spacedim, i.e., the functionality of SphericalManifold<2,3> is identical to SphericalManifold<3,3>.
While PolarManifold reflects the usual notion of polar coordinates, it may not be suitable for domains that contain either the north or south poles. Consider for instance the pair of points \(x_1=(1,\pi/3,0)\) and \(x_2=(1,\pi/3,\pi)\) in polar coordinates (lying on the surface of a sphere with radius one, on a parallel at height \(\pi/3\)). In this case connecting the points with a straight line in polar coordinates would take the long road around the globe, without passing through the north pole.
These two points would be connected (using a PolarManifold) by the curve
\begin{align*} s: [0,1] & \rightarrow & \mathbb S^3 \\ t & \mapsto & (1,\pi/3,0) + (0,0,t\pi) \end{align*}
This curve is not a geodesic on the sphere, and it is not how we would connect those two points. A better curve, would be the one passing through the North pole:
\[ s(t) = x_1 \cos(\alpha(t)) + \kappa \times x_1 \sin(\alpha(t)) + \kappa ( \kappa \cdot x_1) (1-\cos(\alpha(t))). \]
where \(\kappa = \frac{x_1 \times x_2}{\Vert x_1 \times x_2 \Vert}\) and \(\alpha(t) = t \cdot \arccos(x_1 \cdot x_2)\) for \(t\in[0,1]\). Indeed, this is a geodesic, and it is the natural choice when connecting points on the surface of the sphere. In the examples above, the PolarManifold class implements the first way of connecting two points on the surface of a sphere, while SphericalManifold implements the second way, i.e., this Manifold connects points using geodesics. If more than two points are involved through a SphericalManifold::get_new_points() call, a so-called spherical average is used where the final point minimizes the weighted distance to all other points via geodesics.
In particular, this class implements a Manifold that joins any two points in space by first projecting them onto the surface of a sphere with unit radius, then connecting them with a geodesic, and finally rescaling the final radius so that the resulting one is the weighted average of the starting radii. This Manifold is identical to PolarManifold in dimension two, while for dimension three it returns points that are more uniformly distributed on the sphere, and it is invariant with respect to rotations of the coordinate system, therefore avoiding the problems that PolarManifold has at the poles. Notice, in particular, that computing tangent vectors at the poles with a PolarManifold is not well defined, while it is perfectly fine with this class.
For mathematical reasons, it is impossible to construct a unique map of a sphere using only geodesic curves, and therefore, using this class with MappingManifold is discouraged. If you use this Manifold to describe the geometry of a sphere, you should use MappingQ as the underlying mapping, and not MappingManifold.
This Manifold can be used only on geometries where a ball with finite radius is removed from the center. Indeed, the center is a singular point for this manifold, and if you try to connect two points across the center, they would travel on spherical coordinates, avoiding the center.
The ideal geometry for this Manifold is a hyper shell. If you plan to use this Manifold on a hyper ball, you have to make sure you do not attach this Manifold to the cell containing the center. It is advisable to combine this class with TransfiniteInterpolationManifold to ensure a smooth transition from a curved shape to the straight coordinate system in the center of the ball. (See also the extensive discussion in step-65.)
Definition at line 262 of file manifold_lib.h.
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inherited |
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 305 of file manifold.h.
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privateinherited |
The data type used in counter_map.
Definition at line 229 of file subscriptor.h.
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privateinherited |
The iterator type used in counter_map.
Definition at line 234 of file subscriptor.h.
| SphericalManifold< dim, spacedim >::SphericalManifold | ( | const Point< spacedim > | center = Point<spacedim>() | ) |
Constructor.
| [in] | center | The center of the coordinate system. Defaults to the origin. |
Definition at line 359 of file manifold_lib.cc.
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overridevirtual |
Make a clone of this Manifold object.
Implements Manifold< dim, dim >.
Definition at line 370 of file manifold_lib.cc.
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overridevirtual |
Given any two points in space, first project them on the surface of a sphere with unit radius, then connect them with a geodesic and find the intermediate point, and finally rescale the final radius so that the resulting one is the convex combination of the starting radii.
Reimplemented from Manifold< dim, dim >.
Definition at line 379 of file manifold_lib.cc.
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overridevirtual |
Compute the derivative of the get_intermediate_point() function with parameter w equal to zero.
Reimplemented from Manifold< dim, dim >.
Definition at line 445 of file manifold_lib.cc.
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overridevirtual |
Return the normal vector to a face embedded in this manifold, at the point p. It is not required that the normals actually point outward from the domain even if the face iterator given points to a face on the boundary of the domain. If p is not in fact on the surface, but only close-by, 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.)
This function only makes sense if dim==spacedim because otherwise there is no unique normal vector but in fact a (spacedim-dim+1)-dimensional tangent space of vectors that are all both normal to the face and normal to the dim-dimensional surface that lives in spacedim-dimensional space. For example, think of a two-dimensional mesh that covers a two-dimensional surface in three-dimensional space. In that case, each face (edge) is one-dimensional, and there are two linearly independent vectors that are both normal to the edge: one is normal to the edge and tangent to the surface (intuitively, that would be the one that points from the current cell to the neighboring one, if the surface was locally flat), and the other one is rooted in the edge but points perpendicular to the surface (which is also perpendicular to the edge that lives within the surface). Thus, because there are no obviously correct semantics for this function if spacedim is greater than dim, the function will simply throw an error in that situation.
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 FlatManifold 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 from Manifold< dim, dim >.
Definition at line 496 of file manifold_lib.cc.
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overridevirtual |
Compute the normal vectors to the boundary at each vertex.
Definition at line 548 of file manifold_lib.cc.
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overridevirtual |
Compute a new set of points that interpolate between the given points surrounding_points. weights is a table with as many columns as surrounding_points.size(). The number of rows in weights must match the length of new_points.
This function is optimized to perform on a collection of new points, by collecting operations that are not dependent on the weights outside of the loop over all new points.
The implementation does not allow for surrounding_points and new_points to point to the same array, so make sure to pass different objects into the function.
Reimplemented from Manifold< dim, dim >.
Definition at line 575 of file manifold_lib.cc.
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overridevirtual |
Return a point on the spherical manifold which is intermediate with respect to the surrounding points.
Reimplemented from Manifold< dim, dim >.
Definition at line 592 of file manifold_lib.cc.
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inline |
Return the center of the spherical coordinate system.
Definition at line 1266 of file manifold_lib.h.
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private |
Return a point on the spherical manifold which is intermediate with respect to the surrounding points. This function uses a linear average of the directions to find an estimated point. It returns a pair of radius and direction from the center point to the candidate point.
Definition at line 973 of file manifold_lib.cc.
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private |
This function provides an internal implementation of the get_new_points() interface.
It computes a new set of points that interpolate between the given points surrounding_points. weights is an array view with as many entries as surrounding_points.size() times new_points.size().
This function is optimized to perform on a collection of new points, by collecting operations that are not dependent on the weights outside of the loop over all new points.
The implementation does not allow for surrounding_points and new_points to point to the same array, so make sure to pass different objects into the function.
Definition at line 757 of file manifold_lib.cc.
| void SphericalManifold< 1, 1 >::get_normals_at_vertices | ( | const Triangulation< 1 >::face_iterator & | , |
| Manifold< 1, 1 >::FaceVertexNormals & | ) const |
Definition at line 526 of file manifold_lib.cc.
| void SphericalManifold< 1, 2 >::get_normals_at_vertices | ( | const Triangulation< 1, 2 >::face_iterator & | , |
| Manifold< 1, 2 >::FaceVertexNormals & | ) const |
Definition at line 537 of file manifold_lib.cc.
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virtualinherited |
Given a point which lies close to the given manifold, it modifies it and projects it to manifold itself.
This class is used by the default implementation of the function get_new_point() and should be implemented by derived classes. The default implementation simply throws an exception if called.
If your manifold is simple, you could implement this function only, and the default behavior should work out of the box.
Reimplemented in FlatManifold< dim, spacedim >.
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virtualinherited |
Backward compatibility interface. 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).
The default implementation of this function passes its argument to the Manifolds::get_default_points_and_weights() function, and then calls the Manifold<dim,spacedim>::get_new_point() function. User derived classes can overload Manifold<dim,spacedim>::get_new_point() or Manifold<dim,spacedim>::project_to_manifold(), which is called by the default implementation of Manifold<dim,spacedim>::get_new_point().
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virtualinherited |
Backward compatibility interface. 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 quad are refined, so you may want to use the information provided by quad->line(i)->child(j), i=0...3, j=0,1.
The default implementation of this function passes its argument to the Manifolds::get_default_points_and_weights() function, and then calls the Manifold<dim,spacedim>::get_new_point() function. User derived classes can overload Manifold<dim,spacedim>::get_new_point() or Manifold<dim,spacedim>::project_to_manifold(), which is called by the default implementation of Manifold<dim,spacedim>::get_new_point().
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virtualinherited |
Backward compatibility interface. Return the point which shall become the common point of the eight children of a hex in three or 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 all the bounding objects of the given hex are refined, so you may want to use the information provided by hex->quad(i)->line(j)->child(k), i=0...5, j=0...3, k=0,1.
The default implementation of this function passes its argument to the Manifolds::get_default_points_and_weights() function, and then calls the Manifold<dim,spacedim>::get_new_point() function. User derived classes can overload Manifold<dim,spacedim>::get_new_point() or Manifold<dim,spacedim>::project_to_manifold(), which is called by the default implementation of Manifold<dim,spacedim>::get_new_point().
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inherited |
Backward compatibility interface. Depending on dim=2 or dim=3 this function calls the get_new_point_on_line or the get_new_point_on_quad function. It throws an exception for dim=1. This wrapper allows dimension independent programming.
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inherited |
Backward compatibility interface. Depending on dim=1, dim=2 or dim=3 this function calls the get_new_point_on_line, get_new_point_on_quad or the get_new_point_on_hex function. This wrapper allows dimension independent programming.
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virtualinherited |
Compute the normal vectors to the boundary at each vertex of the given face embedded in the Manifold. 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 calls normal_vector() on each vertex.
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.
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inherited |
Subscribes a user of the object by storing the pointer validity. The subscriber may be identified by text supplied as identifier.
Definition at line 135 of file subscriptor.cc.
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inherited |
Unsubscribes a user from the object.
identifier and the validity pointer must be the same as the one supplied to subscribe(). Definition at line 155 of file subscriptor.cc.
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inlineinherited |
Return the present number of subscriptions to this object. This allows to use this class for reference counted lifetime determination where the last one to unsubscribe also deletes the object.
Definition at line 300 of file subscriptor.h.
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inlineinherited |
List the subscribers to the input stream.
Definition at line 317 of file subscriptor.h.
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inherited |
List the subscribers to deallog.
Definition at line 203 of file subscriptor.cc.
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inlineinherited |
Read or write the data of this object to or from a stream for the purpose of serialization using the BOOST serialization library.
This function does not actually serialize any of the member variables of this class. The reason is that what this class stores is only who subscribes to this object, but who does so at the time of storing the contents of this object does not necessarily have anything to do with who subscribes to the object when it is restored. Consequently, we do not want to overwrite the subscribers at the time of restoring, and then there is no reason to write the subscribers out in the first place.
Definition at line 309 of file subscriptor.h.
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privatenoexceptinherited |
Check that there are no objects subscribing to this object. If this check passes then it is safe to destroy the current object. It this check fails then this function will either abort or print an error message to deallog (by using the AssertNothrow mechanism), but will not throw an exception.
Definition at line 52 of file subscriptor.cc.
| const Point<spacedim> SphericalManifold< dim, spacedim >::center |
The center of the spherical coordinate system.
Definition at line 356 of file manifold_lib.h.
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private |
The center of the spherical coordinate system.
Definition at line 364 of file manifold_lib.h.
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private |
A manifold description to be used for get_new_point in 2d.
Definition at line 402 of file manifold_lib.h.
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mutableprivateinherited |
Store the number of objects which subscribed to this object. Initially, this number is zero, and upon destruction it shall be zero again (i.e. all objects which subscribed should have unsubscribed again).
The creator (and owner) of an object is counted in the map below if HE manages to supply identification.
We use the mutable keyword in order to allow subscription to constant objects also.
This counter may be read from and written to concurrently in multithreaded code: hence we use the std::atomic class template.
Definition at line 218 of file subscriptor.h.
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mutableprivateinherited |
In this map, we count subscriptions for each different identification string supplied to subscribe().
Definition at line 224 of file subscriptor.h.
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mutableprivateinherited |
In this vector, we store pointers to the validity bool in the SmartPointer objects that subscribe to this class.
Definition at line 240 of file subscriptor.h.
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mutableprivateinherited |
Pointer to the typeinfo object of this object, from which we can later deduce the class name. Since this information on the derived class is neither available in the destructor, nor in the constructor, we obtain it in between and store it here.
Definition at line 248 of file subscriptor.h.
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staticprivateinherited |
A mutex used to ensure data consistency when accessing the mutable members of this class. This lock is used in the subscribe() and unsubscribe() functions, as well as in list_subscribers().
Definition at line 271 of file subscriptor.h.
1.11.0