#include <deal.II/grid/manifold.h>

Inheritance diagram for FlatManifold< dim, spacedim >:

Public Member Functions
	FlatManifold (const Tensor< 1, spacedim > &periodicity=Tensor< 1, spacedim >(), const double tolerance=1e-10)

virtual std::unique_ptr< Manifold< dim, spacedim > >	clone () const override

virtual Point< spacedim >	get_new_point (const ArrayView< const Point< spacedim >> &surrounding_points, const ArrayView< const double > &weights) 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 >	project_to_manifold (const ArrayView< const Point< spacedim >> &points, const Point< spacedim > &candidate) 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

const Tensor< 1, spacedim > &	get_periodicity () 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

void	get_normals_at_vertices (const Triangulation< 1, 3 >::face_iterator &, Manifold< 1, 3 >::FaceVertexNormals &) const

void	get_normals_at_vertices (const Triangulation< 2 >::face_iterator &face, Manifold< 2, 2 >::FaceVertexNormals &face_vertex_normals) const

void	get_normals_at_vertices (const Triangulation< 2, 3 >::face_iterator &, Manifold< 2, 3 >::FaceVertexNormals &) const

void	get_normals_at_vertices (const Triangulation< 3 >::face_iterator &face, Manifold< 3, 3 >::FaceVertexNormals &face_vertex_normals) const

Tensor< 1, 1 >	normal_vector (const Triangulation< 1, 1 >::face_iterator &, const Point< 1 > &) const

Tensor< 1, 2 >	normal_vector (const Triangulation< 1, 2 >::face_iterator &, const Point< 2 > &) const

Tensor< 1, 3 >	normal_vector (const Triangulation< 1, 3 >::face_iterator &, const Point< 3 > &) const

Tensor< 1, 2 >	normal_vector (const Triangulation< 2, 2 >::face_iterator &face, const Point< 2 > &p) const

Public Member Functions inherited from Manifold< dim, dim >
virtual	~Manifold () override=default

virtual std::unique_ptr< Manifold< dim, spacedim > >	clone () const=0

Point< 1 >	get_new_point_on_quad (const Triangulation< 1, 1 >::quad_iterator &) const

Point< 2 >	get_new_point_on_quad (const Triangulation< 1, 2 >::quad_iterator &) const

Point< 3 >	get_new_point_on_quad (const Triangulation< 1, 3 >::quad_iterator &) const

Point< 3 >	get_new_point_on_hex (const Triangulation< 3, 3 >::hex_iterator &hex) const

Point< 1 >	get_new_point_on_face (const Triangulation< 1, 1 >::face_iterator &) const

Point< 2 >	get_new_point_on_face (const Triangulation< 1, 2 >::face_iterator &) const

Point< 3 >	get_new_point_on_face (const Triangulation< 1, 3 >::face_iterator &) const

Tensor< 1, 2 >	normal_vector (const Triangulation< 2, 2 >::face_iterator &face, const Point< 2 > &p) const

Tensor< 1, 3 >	normal_vector (const Triangulation< 3, 3 >::face_iterator &face, const Point< 3 > &p) const

void	get_normals_at_vertices (const Triangulation< 2, 2 >::face_iterator &face, FaceVertexNormals &n) const

void	get_normals_at_vertices (const Triangulation< 3, 3 >::face_iterator &face, FaceVertexNormals &n) const

virtual Point< spacedim >	get_intermediate_point (const Point< spacedim > &p1, const Point< spacedim > &p2, const double w) 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

virtual void	get_normals_at_vertices (const typename Triangulation< dim, spacedim >::face_iterator &face, FaceVertexNormals &face_vertex_normals) const

Public Member Functions inherited from Subscriptor
	Subscriptor ()

	Subscriptor (const Subscriptor &)

	Subscriptor (Subscriptor &&) noexcept

virtual	~Subscriptor ()

Subscriptor &	operator= (const Subscriptor &)

Subscriptor &	operator= (Subscriptor &&) noexcept

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

template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

Static Private Member Functions
static ::ExceptionBase &	ExcPeriodicBox (int arg1, Point< spacedim > arg2, double arg3)

Private Attributes
const Tensor< 1, spacedim >	periodicity

const double	tolerance

Additional Inherited Members
Public Types inherited from Manifold< dim, dim >
using	FaceVertexNormals = std::array< Tensor< 1, spacedim >, GeometryInfo< dim >::vertices_per_face >

Static Public Member Functions inherited from Subscriptor
static ::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)

static ::ExceptionBase &	ExcNoSubscriber (std::string arg1, std::string arg2)

Detailed Description

template<int dim, int spacedim = dim>
class FlatManifold< dim, spacedim >

Specialization of Manifold<dim,spacedim>, which represent a possibly periodic Euclidean space of dimension dim embedded in the Euclidean space of spacedim dimensions. The main characteristic of this Manifold is the fact that the function FlatManifold<dim,spacedim>::project_to_manifold() is the identity function.

Author: Luca Heltai, 2014

Definition at line 682 of file manifold.h.

Constructor & Destructor Documentation

◆ FlatManifold()

template<int dim, int spacedim>

FlatManifold< dim, spacedim >::FlatManifold	(	const Tensor< 1, spacedim > &	periodicity = `Tensor<1, spacedim>()`,
		const double	tolerance = `1e-10`
	)

Default constructor. The optional argument can be used to specify the periodicity of the spacedim-dimensional manifold (one period per direction). A periodicity value of zero means that along that direction there is no periodicity. By default no periodicity is assumed.

Periodicity affects the way a middle point is computed. It is assumed that if two points are more than half period distant, then the distance should be computed by crossing the periodicity boundary, i.e., the average is computed by adding a full period to the sum of the two. For example, if along direction 0 we have 2*pi periodicity, then the average of (2*pi-eps) and (eps) is not pi, but 2*pi (or zero), since, on a periodic manifold, these two points are at distance 2*eps and not (2*pi- eps). Special cases are taken into account, to ensure that the behavior is always as expected. The third argument is used as a relative tolerance when computing distances.

Periodicity will be intended in the following way: the domain is considered to be the box contained in [Point<spacedim>(), periodicity) where the right extreme is excluded. If any of the components of this box has zero length, then no periodicity is assumed in that direction. Whenever a function that tries to compute averages is called, an exception will be thrown if one of the points which you are using for the average lies outside the periodicity box. The return points are guaranteed to lie in the periodicity box plus or minus tolerance*periodicity.norm().

Definition at line 517 of file manifold.cc.

Member Function Documentation

◆ clone()

template<int dim, int spacedim>

std::unique_ptr< Manifold< dim, spacedim > > FlatManifold< dim, spacedim >::clone

overridevirtual

Return a copy of this manifold.

Reimplemented in OpenCASCADE::NormalToMeshProjectionManifold< dim, spacedim >, OpenCASCADE::NormalToMeshProjectionBoundary< dim, spacedim >, OpenCASCADE::DirectionalProjectionManifold< dim, spacedim >, OpenCASCADE::DirectionalProjectionBoundary< dim, spacedim >, OpenCASCADE::NormalProjectionManifold< dim, spacedim >, and OpenCASCADE::NormalProjectionBoundary< dim, spacedim >.

Definition at line 528 of file manifold.cc.

◆ get_new_point()

template<int dim, int spacedim>

Point< spacedim > FlatManifold< dim, spacedim >::get_new_point	(	const ArrayView< const Point< spacedim >> &	surrounding_points,
		const ArrayView< const double > &	weights
	)		const

overridevirtual

Let the new point be the average sum of surrounding vertices.

This particular implementation constructs the weighted average of the surrounding points, and then calls internally the function project_to_manifold(). The reason why we do it this way, is to allow lazy programmers to implement only the project_to_manifold() function for their own Manifold classes which are small (or trivial) perturbations of a flat manifold. This is the case whenever the coarse mesh is a decent approximation of the manifold geometry. In this case, the middle point of a cell is close to true middle point of the manifold, and a projection may suffice.

For most simple geometries, it is possible to get reasonable results by deriving your own Manifold class from FlatManifold, and write a new interface only for the project_to_manifold function. You will have good approximations also with large deformations, as long as in the coarsest mesh size you are trying to refine, the middle point is not too far from the manifold mid point, i.e., as long as the coarse mesh size is small enough.

Reimplemented from Manifold< dim, dim >.

Definition at line 538 of file manifold.cc.

◆ get_new_points()

template<int dim, int spacedim>

void FlatManifold< dim, spacedim >::get_new_points	(	const ArrayView< const Point< spacedim >> &	surrounding_points,
		const Table< 2, double > &	weights,
		ArrayView< Point< spacedim >>	new_points
	)		const

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.

For this particular implementation, the interpolation of the surrounding_points according to the weights is simply performed in Cartesian space.

Reimplemented from Manifold< dim, dim >.

Definition at line 599 of file manifold.cc.

◆ project_to_manifold()

template<int dim, int spacedim>

Point< spacedim > FlatManifold< dim, spacedim >::project_to_manifold	(	const ArrayView< const Point< spacedim >> &	points,
		const Point< spacedim > &	candidate
	)		const

overridevirtual

Project to FlatManifold. This is the identity function for flat, Euclidean spaces. Note however that this function can be overloaded by derived classes, which will then benefit from the logic behind the get_new_point() function which are often very similar (if not identical) to the one implemented in this class.

Reimplemented from Manifold< dim, dim >.

Reimplemented in OpenCASCADE::NormalToMeshProjectionManifold< dim, spacedim >, OpenCASCADE::DirectionalProjectionManifold< dim, spacedim >, and OpenCASCADE::NormalProjectionManifold< dim, spacedim >.

Definition at line 681 of file manifold.cc.

◆ get_tangent_vector()

template<int dim, int spacedim>

Tensor< 1, spacedim > FlatManifold< dim, spacedim >::get_tangent_vector	(	const Point< spacedim > &	x1,
		const Point< spacedim > &	x2
	)		const

overridevirtual

Return a vector that, at \(\mathbf x_1\), is tangential to the geodesic that connects two points \(\mathbf x_1,\mathbf x_2\). For the current class, we assume that the manifold is flat, so the geodesic is the straight line between the two points, and we return \(\mathbf x_2-\mathbf x_1\). The normalization of the vector is chosen so that it fits the convention described in Manifold::get_tangent_vector().

Note: If you use this class as a stepping stone to build a manifold that only "slightly" deviates from a flat manifold, by overloading the project_to_manifold() function.

Parameters

x1	The first point that describes the geodesic, and the one at which the "direction" is to be evaluated.
x2	The second point that describes the geodesic.

Returns: A "direction" vector tangential to the geodesic. Here, this is \(\mathbf x_2-\mathbf x_1\), possibly modified by the periodicity of the domain as set in the constructor, to use the "shortest" connection between the points through the periodic boundary as necessary.

Reimplemented from Manifold< dim, dim >.

Definition at line 701 of file manifold.cc.

◆ normal_vector() [1/5]

template<int dim, int spacedim>

Tensor< 1, spacedim > FlatManifold< dim, spacedim >::normal_vector	(	const typename Triangulation< dim, spacedim >::face_iterator &	face,
		const Point< spacedim > &	p
	)		const

overridevirtual

Return the normal vector to the given face at point p taking into account that quadrilateral faces of hexahedral cells in 3d may not be planar. In those cases, the face is assumed to have a geometry described by a bilinear function, and the normal vector is computed by embedding this bilinear form into a Cartesian space with a flat metric.

Reimplemented from Manifold< dim, dim >.

Definition at line 859 of file manifold.cc.

◆ get_normals_at_vertices() [1/7]

template<int dim, int spacedim = dim>

virtual void FlatManifold< dim, spacedim >::get_normals_at_vertices	(	const typename Triangulation< dim, spacedim >::face_iterator &	face,
		typename Manifold< dim, spacedim >::FaceVertexNormals &	face_vertex_normals
	)		const

overridevirtual

Compute the normal vectors to the boundary at each vertex of the given face taking into account that quadrilateral faces of hexahedral cells in 3d may not be planar. In those cases, the face is assumed to have a geometry described by a bilinear function, and the normal vector is computed by embedding this bilinear form into a Cartesian space with a flat metric.

◆ get_periodicity()

template<int dim, int spacedim>

const Tensor< 1, spacedim > & FlatManifold< dim, spacedim >::get_periodicity

Return the periodicity of this Manifold.

Definition at line 692 of file manifold.cc.

◆ get_normals_at_vertices() [2/7]

void FlatManifold< 1 >::get_normals_at_vertices	(	const Triangulation< 1 >::face_iterator &	,
		Manifold< 1, 1 >::FaceVertexNormals &
	)		const

Definition at line 726 of file manifold.cc.

◆ get_normals_at_vertices() [3/7]

void FlatManifold< 1, 2 >::get_normals_at_vertices	(	const Triangulation< 1, 2 >::face_iterator &	,
		Manifold< 1, 2 >::FaceVertexNormals &
	)		const

Definition at line 737 of file manifold.cc.

◆ get_normals_at_vertices() [4/7]

void FlatManifold< 1, 3 >::get_normals_at_vertices	(	const Triangulation< 1, 3 >::face_iterator &	,
		Manifold< 1, 3 >::FaceVertexNormals &
	)		const

Definition at line 748 of file manifold.cc.

◆ get_normals_at_vertices() [5/7]

void FlatManifold< 2 >::get_normals_at_vertices	(	const Triangulation< 2 >::face_iterator &	face,
		Manifold< 2, 2 >::FaceVertexNormals &	face_vertex_normals
	)		const

Definition at line 759 of file manifold.cc.

◆ get_normals_at_vertices() [6/7]

void FlatManifold< 2, 3 >::get_normals_at_vertices	(	const Triangulation< 2, 3 >::face_iterator &	,
		Manifold< 2, 3 >::FaceVertexNormals &
	)		const

Definition at line 774 of file manifold.cc.

◆ get_normals_at_vertices() [7/7]

void FlatManifold< 3 >::get_normals_at_vertices	(	const Triangulation< 3 >::face_iterator &	face,
		Manifold< 3, 3 >::FaceVertexNormals &	face_vertex_normals
	)		const

Definition at line 785 of file manifold.cc.

◆ normal_vector() [2/5]

Tensor< 1, 1 > FlatManifold< 1, 1 >::normal_vector	(	const Triangulation< 1, 1 >::face_iterator &	,
		const Point< 1 > &
	)		const

Definition at line 813 of file manifold.cc.

◆ normal_vector() [3/5]

Tensor< 1, 2 > FlatManifold< 1, 2 >::normal_vector	(	const Triangulation< 1, 2 >::face_iterator &	,
		const Point< 2 > &
	)		const

Definition at line 824 of file manifold.cc.

◆ normal_vector() [4/5]

Tensor< 1, 3 > FlatManifold< 1, 3 >::normal_vector	(	const Triangulation< 1, 3 >::face_iterator &	,
		const Point< 3 > &
	)		const

Definition at line 835 of file manifold.cc.

◆ normal_vector() [5/5]

Tensor< 1, 2 > FlatManifold< 2, 2 >::normal_vector	(	const Triangulation< 2, 2 >::face_iterator &	face,
		const Point< 2 > &	p
	)		const

Definition at line 846 of file manifold.cc.

Member Data Documentation

◆ periodicity

template<int dim, int spacedim = dim>

const Tensor<1, spacedim> FlatManifold< dim, spacedim >::periodicity

private

The periodicity of this Manifold. Periodicity affects the way a middle point is computed. It is assumed that if two points are more than half period distant, then the distance should be computed by crossing the periodicity boundary, i.e., the average is computed by adding a full period to the sum of the two. For example, if along direction 0 we have 2*pi periodicity, then the average of (2*pi-eps) and (eps) is not pi, but 2*pi (or zero), since, on a periodic manifold, these two points are at distance 2*eps and not (2*pi-eps).

A periodicity 0 along one direction means no periodicity. This is the default value for all directions.

Definition at line 844 of file manifold.h.

◆ tolerance

template<int dim, int spacedim = dim>

const double FlatManifold< dim, spacedim >::tolerance

private

Relative tolerance. This tolerance is used to compute distances in double precision.

Definition at line 858 of file manifold.h.

The documentation for this class was generated from the following files:

include/deal.II/grid/manifold.h
source/grid/manifold.cc

Public Member Functions

Static Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<int dim, int spacedim = dim> class FlatManifold< dim, spacedim >

Constructor & Destructor Documentation

◆ FlatManifold()

Member Function Documentation

◆ clone()

◆ get_new_point()

◆ get_new_points()

◆ project_to_manifold()

◆ get_tangent_vector()

◆ normal_vector() [1/5]

◆ get_normals_at_vertices() [1/7]

◆ get_periodicity()

◆ get_normals_at_vertices() [2/7]

◆ get_normals_at_vertices() [3/7]

◆ get_normals_at_vertices() [4/7]

◆ get_normals_at_vertices() [5/7]

◆ get_normals_at_vertices() [6/7]

◆ get_normals_at_vertices() [7/7]

◆ normal_vector() [2/5]

◆ normal_vector() [3/5]

◆ normal_vector() [4/5]

◆ normal_vector() [5/5]

Member Data Documentation

◆ periodicity

◆ tolerance

template<int dim, int spacedim = dim>
class FlatManifold< dim, spacedim >