A 2D cell: triangle. More...

#include <cell2D.hh>

Inheritance diagram for concepts::Triangle2d:

Collaboration diagram for concepts::Triangle2d:

Classes
struct	Index
	Subclass of Triangle2d representing its index. More...
Public Member Functions
Real	area () const
	Returns the area of the element.
Real3d	center () const
	Returns the center of the cell.
Real2d	chi (Real xi, Real eta) const
	Evaluates the element map.
virtual const Triangle2d *	child (uint i) const
	Returns a child.
virtual Triangle2d *	child (uint i)
	Returns a child.
Triangle2d *	clone (Triangle &cntr, MappingTriangle2d *map) const
	Returns a copy of itself.
Triangle &	connector () const
	Returns the triangle connector (topology)
virtual Real3d	elemMap (const Real3d &coord_local) const
	Element map from point local coordinates in 3D.
Real3d	elemMap (const Real2d &coord_local) const
	Element map from point local coordinates in 2D.
virtual Real3d	elemMap (const Real coord_local) const
	Element map from point local coordinates in 1D.
bool	hasChildren () const
	Returns true if there is a least one child.
MapReal2d	jacobian (Real x, Real y) const
	Returns the Jacobian in a 2D linear map.
Real	jacobianDeterminant (const Real x, const Real y) const
	Returns determinant of the Jacobian.
MapReal2d	jacobianInverse (const Real x, const Real y) const
	Returns the inverse of the Jacobian in a 2D linear map.
ushort	level () const
	Returns the level of the cell.
const MappingTriangle2d *	map () const
	Returns the element map.
	Triangle2d (Triangle &cntr, const MappingTriangle2d &map)
	Constructor.
Real3d	vertex (uint i) const
	Returns the coordinates of the ith vertex.
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`.
Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.
Private Member Functions
	Triangle2d (Triangle &cntr, MappingTriangle2d *map, const Index &idx)
	Private constructor.
Private Attributes
Triangle2d *	chld_
	Pointer to the first child.
Triangle &	cntr_
	Reference to the triangle connector (topology)
Index	idx_
	Index of this element.
Triangle2d *	lnk_
	Pointer to a sibling.
MappingTriangle2d *	map_
	Pointer to the element map.
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 28 of file cell2D.hh.

Constructor & Destructor Documentation

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

virtual concepts::Triangle2d::~Triangle2d ( ) [virtual]

concepts::Triangle2d::Triangle2d	(	Triangle &	cntr,
		MappingTriangle2d *	map,
		const Index &	idx
	)		`[private]`

Private constructor.

Member Function Documentation

Real concepts::Triangle2d::area ( ) const

Returns the area of the element.

Real3d concepts::Triangle2d::center ( ) const [inline, virtual]

Returns the center of the cell.

Implements concepts::Cell2.

Definition at line 128 of file cell2D.hh.

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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	$\in [0,1]$

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.

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.

Triangle2d* concepts::Triangle2d::clone	(	Triangle &	cntr,
		MappingTriangle2d *	map
	)		const `[inline]`

Returns a copy of itself.

Definition at line 133 of file cell2D.hh.

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Triangle& concepts::Triangle2d::connector ( ) const [inline, virtual]

Returns the triangle connector (topology)

Implements concepts::Cell2.

Definition at line 76 of file cell2D.hh.

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

Maps coordinates from $\{(\xi,\eta) : 0 \leq \eta \leq \xi \leq 1\}$ to $[0,1]^2$ to use them in chi.

virtual Real3d concepts::Cell2::elemMap ( const Real3d & coord_local ) const [inline, virtual, inherited]

Element map from point local coordinates in 3D.

Reference element is 2D, third component is omitted.

Reimplemented from concepts::Cell.

Definition at line 100 of file cell.hh.

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virtual Real3d concepts::Cell::elemMap ( const Real coord_local ) const [virtual, inherited]

Element map from point local coordinates in 1D.

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

Real3d concepts::Triangle2d::elemMap ( const Real2d & coord_local ) const [inline, virtual]

Element map from point local coordinates in 2D.

Implements concepts::Cell2.

Definition at line 97 of file cell2D.hh.

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bool concepts::Cell::hasChildren ( ) const [inline, inherited]

Returns true if there is a least one child.

Reimplemented in concepts::Quad2d, and concepts::InfiniteRect2d.

Definition at line 48 of file cell.hh.

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virtual std::ostream& concepts::Triangle2d::info ( std::ostream & os ) const [protected, virtual]

Returns information in an output stream.

Implements concepts::Cell.

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 $[0,1]^2$ to $T$ .

Parameters:

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

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

Returns determinant of the Jacobian.

See also:: jacobian

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

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 83 of file cell2D.hh.

const MappingTriangle2d* concepts::Triangle2d::map ( ) const [inline]

Returns the element map.

Definition at line 130 of file cell2D.hh.

Real3d concepts::Triangle2d::vertex ( uint i ) const [virtual]

Returns the coordinates of the ith vertex.

Implements concepts::Cell2.