A 2D cell: triangle. More...

#include <cell2D.hh>

Inheritance diagram for concepts::Triangle2d:

Classes
struct	Index
	Subclass of Triangle2d representing its index. More...

Public Types
typedef uint	index_type

Public Member Functions
Real	area () const
	Returns the area of the element. More...

Real3d	center () const
	Returns the center of the cell. More...

Real2d	chi (Real xi, Real eta) const
	Evaluates the element map. More...

virtual Triangle2d *	child (uint i)
	Returns a child. More...

virtual const Triangle2d *	child (uint i) const
	Returns a child. More...

Triangle2d *	clone (Triangle &cntr, MappingTriangle2d *map) const
	Returns a copy of itself. More...

Triangle &	connector () const
	Returns the triangle connector (topology) More...

virtual Real3d	elemMap (const Real coord_local) const
	Element map from point local coordinates in 1D. More...

Real3d	elemMap (const Real2d &coord_local) const
	Element map from point local coordinates in 2D. More...

virtual Real3d	elemMap (const Real3d &coord_local) const
	Element map from point local coordinates in 3D. More...

bool	hasChildren () const
	Returns true if there is a least one child. More...

MapReal2d	jacobian (Real x, Real y) const
	Returns the Jacobian in a 2D linear map. More...

Real	jacobianDeterminant (const Real x, const Real y) const
	Returns determinant of the Jacobian. More...

MapReal2d	jacobianInverse (const Real x, const Real y) const
	Returns the inverse of the Jacobian in a 2D linear map. More...

ushort	level () const
	Returns the level of the cell. More...

const MappingTriangle2d *	map () const
	Returns the element map. More...

	Triangle2d (Triangle &cntr, const MappingTriangle2d &map)
	Constructor. More...

Real3d	vertex (uint i) const
	Returns the coordinates of the ith vertex. More...

virtual	~Triangle2d ()

Static Public Member Functions
static Real2d	duffyInv (const Real2d &x)
	Maps coordinates from $\{(\xi,\eta) : 0 \leq \eta \leq \xi \leq 1\}$ to to use them in `chi`. More...

Static Public Attributes
static uint	MAX_LEVEL

Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream. More...

Private Member Functions
	Triangle2d (Triangle &cntr, MappingTriangle2d *map, const Index &idx)
	Private constructor. More...

Private Attributes
Triangle2d *	chld_
	Pointer to the first child. More...

Triangle &	cntr_
	Reference to the triangle connector (topology) More...

Index	idx_
	Index of this element. More...

Triangle2d *	lnk_
	Pointer to a sibling. More...

MappingTriangle2d *	map_
	Pointer to the element map. More...

Friends
std::ostream &	operator<< (std::ostream &os, const Triangle2d::Index &i)

Detailed Description

A 2D cell: triangle.

If a triangle is subdivided, four new children are created.

See also: Cell for more information on cells in a mesh.

Examples: meshes.cc.

Definition at line 31 of file cell2D.hh.

Member Typedef Documentation

◆ index_type

typedef uint concepts::Triangle2d::index_type

Definition at line 39 of file cell2D.hh.

Constructor & Destructor Documentation

◆ Triangle2d() [1/2]

concepts::Triangle2d::Triangle2d	(	Triangle &	cntr,
		const MappingTriangle2d &	map
	)

Constructor.

Takes the connector cntr and the element map map and creates a cell.

Parameters

cntr	Topological information of the triangle
map	Element map of the triangle

◆ ~Triangle2d()

virtual concepts::Triangle2d::~Triangle2d ( )

virtual

◆ Triangle2d() [2/2]

concepts::Triangle2d::Triangle2d	(	Triangle &	cntr,
		MappingTriangle2d *	map,
		const Index &	idx
	)

private

Private constructor.

Member Function Documentation

◆ area()

Real concepts::Triangle2d::area ( ) const

Returns the area of the element.

◆ center()

Real3d concepts::Triangle2d::center ( ) const

inlinevirtual

Returns the center of the cell.

Implements concepts::Cell2.

Definition at line 143 of file cell2D.hh.

◆ chi()

Real2d concepts::Triangle2d::chi	(	Real	xi,
		Real	eta
	)		const

Evaluates the element map.

Maps a corner from the unit square [0,1]² onto the element. The three vertices are (0, 0), (1, 0) and (1, 1). If you already have coordinates in the triangle, use duffyInv.

Returns: Point in 2D in physical coordinates.

Parameters

xi	$\in [0,1]$
eta	$\in [0,1]$

◆ child() [1/2]

virtual Triangle2d* concepts::Triangle2d::child ( uint i )

virtual

Returns a child.

If no children exist, four new children are created. The triangle is cut into four new triangles by joining the midpoints of its edges.

Parameters

i	Index of the child to be returned.

Implements concepts::Cell2.

◆ child() [2/2]

virtual const Triangle2d* concepts::Triangle2d::child ( uint i ) const

virtual

Returns a child.

If no children exist, none are created and 0 is returned.

Parameters

i	Index of the child to be returned.

Implements concepts::Cell2.

◆ clone()

Triangle2d* concepts::Triangle2d::clone	(	Triangle &	cntr,
		MappingTriangle2d *	map
	)		const

inline

Returns a copy of itself.

Definition at line 148 of file cell2D.hh.

◆ connector()

Triangle& concepts::Triangle2d::connector ( ) const

inlinevirtual

Returns the triangle connector (topology)

Implements concepts::Cell2.

Definition at line 91 of file cell2D.hh.

◆ duffyInv()

static Real2d concepts::Triangle2d::duffyInv ( const Real2d & x )

static

Maps coordinates from $\{(\xi,\eta) : 0 \leq \eta \leq \xi \leq 1\}$ to to use them in chi.

◆ elemMap() [1/3]

virtual Real3d concepts::Cell::elemMap ( const Real coord_local ) const

virtualinherited

Element map from point local coordinates in 1D.

Reimplemented in concepts::Edge2d, concepts::Edge1d, concepts::Sphere3d, and concepts::SphericalSurface3d.

◆ elemMap() [2/3]

Real3d concepts::Triangle2d::elemMap ( const Real2d & coord_local ) const

inlinevirtual

Element map from point local coordinates in 2D.

Implements concepts::Cell2.

Definition at line 112 of file cell2D.hh.

◆ elemMap() [3/3]

virtual Real3d concepts::Cell2::elemMap ( const Real3d & coord_local ) const

inlinevirtualinherited

Element map from point local coordinates in 3D.

Reference element is 2D, third component is omitted.

Reimplemented from concepts::Cell.

Definition at line 104 of file cell.hh.

◆ hasChildren()

bool concepts::Cell::hasChildren ( ) const

inlineinherited

Returns true if there is a least one child.

Definition at line 50 of file cell.hh.

◆ info()

virtual std::ostream& concepts::Triangle2d::info ( std::ostream & os ) const

protectedvirtual

Returns information in an output stream.

Implements concepts::Cell.

◆ jacobian()

MapReal2d concepts::Triangle2d::jacobian	(	Real	x,
		Real	y
	)		const

Returns the Jacobian in a 2D linear map.

The input is a point from [0,1]², the output is the Jacobian of the map at the given point. The Jacobian includes the map from $T = \{(\xi,\eta) : 0 \leq \eta \leq \xi \leq 1\}$ into the physical coordinates but not the map from to .

Parameters

x	$\in [0,1]$
y	$\in [0,1]$

◆ jacobianDeterminant()

Real concepts::Triangle2d::jacobianDeterminant	(	const Real	x,
		const Real	y
	)		const

Returns determinant of the Jacobian.

See also: jacobian

◆ jacobianInverse()

MapReal2d concepts::Triangle2d::jacobianInverse	(	const Real	x,
		const Real	y
	)		const

Returns the inverse of the Jacobian in a 2D linear map.

See also: jacobian

◆ level()

ushort concepts::Triangle2d::level ( ) const

inline

Returns the level of the cell.

The level describes the refinements in both directions with respect to the parent cell in the initial mesh. This level information is taken into account when evaluating the element map or the Jacobian.

Definition at line 98 of file cell2D.hh.

◆ map()

const MappingTriangle2d* concepts::Triangle2d::map ( ) const

inline

Returns the element map.

Definition at line 145 of file cell2D.hh.

◆ vertex()

Real3d concepts::Triangle2d::vertex ( uint i ) const

virtual

Returns the coordinates of the ith vertex.

Implements concepts::Cell2.

Friends And Related Function Documentation

◆ operator<<

std::ostream& operator<<	(	std::ostream &	os,
		const Triangle2d::Index &	i
	)

friend

Member Data Documentation

◆ chld_

Triangle2d* concepts::Triangle2d::chld_

private

Pointer to the first child.

The children are stored in a linked list.

Definition at line 171 of file cell2D.hh.

◆ cntr_

Triangle& concepts::Triangle2d::cntr_

private

Reference to the triangle connector (topology)

Definition at line 163 of file cell2D.hh.

◆ idx_

Index concepts::Triangle2d::idx_

private

Index of this element.

Definition at line 160 of file cell2D.hh.

◆ lnk_

Triangle2d* concepts::Triangle2d::lnk_

private

Pointer to a sibling.

Definition at line 166 of file cell2D.hh.

◆ map_

MappingTriangle2d* concepts::Triangle2d::map_

private

Pointer to the element map.

Definition at line 174 of file cell2D.hh.

◆ MAX_LEVEL

uint concepts::Triangle2d::MAX_LEVEL

static

Definition at line 43 of file cell2D.hh.

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

geometry/cell2D.hh

concepts::Triangle2d Class ReferenceGeometry

Classes

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Private Member Functions

Private Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ index_type

Constructor & Destructor Documentation

◆ Triangle2d() [1/2]

◆ ~Triangle2d()

◆ Triangle2d() [2/2]

Member Function Documentation

◆ area()

◆ center()

◆ chi()

◆ child() [1/2]

◆ child() [2/2]

◆ clone()

◆ connector()

◆ duffyInv()

◆ elemMap() [1/3]

◆ elemMap() [2/3]

◆ elemMap() [3/3]

◆ hasChildren()

◆ info()

◆ jacobian()

◆ jacobianDeterminant()

◆ jacobianInverse()

◆ level()

◆ map()

◆ vertex()

Friends And Related Function Documentation

◆ operator<<

Member Data Documentation

◆ chld_

◆ cntr_

◆ idx_

◆ lnk_

◆ map_

◆ MAX_LEVEL

concepts::Triangle2d Class Reference
Geometry