2D element map for an circular arc. More...

#include <elementMaps.hh>

Inheritance diagram for concepts::CircleMappingEdge2d:

Collaboration diagram for concepts::CircleMappingEdge2d:

Public Member Functions
	CircleMappingEdge2d (const Real r, const Real2d vtx0, const Real2d vtx1)
	Constructor.
	CircleMappingEdge2d (const Real2d center, const Real r, const Real angle0, const Real angle1)
	Constructor.
	CircleMappingEdge2d (const CircleMappingEdge2d &edgemap)
	Copy Constructor.
	CircleMappingEdge2d (const Real2d vtx0, const Real2d vtxm, const Real2d vtx1)
	Constructor.
virtual CircleMappingEdge2d *	clone () const
	Virtual copy constructor.
virtual Real	curvature (const Real t, const uint n=0) const
	Returns the n-th derivative of the curvature.
virtual Real2d	derivative (const Real t, const uint n=1) const
	Returns the n-th derivative.
virtual MappingEdge2d *	inverse () const
	Returns the mapping of the edge in inverse direction.
Real2d	n0 (const Real t) const
	Returns the normalised right normal vector.
virtual Real2d	normal (const Real t) const
	Returns the right normal vector, length is that of the derivative.
virtual Real2d	operator() (const Real t) const
	Application operator.
MappingEdge2d *	part (const Real t0, const Real t1) const
	Returns a new object of an element map for a rectangular part of the reference cell defined by the two points.
const Real2d &	vtx (uint i) const
	Spit out one vertex of the edge.
Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.
Protected Attributes
Real2d	vtx_ [2]
	Coordinates of the vertices at either end of the edge.
Private Member Functions
Real	phi_ (const Real t) const
Private Attributes
Real	angle0_
	Angles between one vertex and the circle center.
Real	angle1_
Real2d	m_
	Mid point of the circle.
Real	r_
	Radius of the circle, zero if straight line (no sign)

Detailed Description

2D element map for an circular arc.

The edge is given by two vertices and a radius that determines the curvature of the edge.

This class may be used in connection with BlendingQuad2d.

See also:: BlendingQuad2d

Author:: , Kersten Schmidt, 2004

Definition at line 257 of file elementMaps.hh.

Constructor & Destructor Documentation

concepts::CircleMappingEdge2d::CircleMappingEdge2d	(	const Real	r,
		const Real2d	vtx0,
		const Real2d	vtx1
	)

Constructor.

Use the sign of the radius to bend the edge. r > 0 Arc is on the right side of line from 1st to 2nd vertex r < 0 Arc is on the left side of line from 1st to 2nd vertex

Minimal radius is half of the distance between the vertices.

There are always two possibilites for the angle of the arc ( $\phi$ and $2\pi - \phi$ . The smaller angle is taken. So the maximal angle is $\pi$ .

Parameters:

r	radius
vtx0,vtx1	coordinates of the vertices

concepts::CircleMappingEdge2d::CircleMappingEdge2d	(	const Real2d	center,
		const Real	r,
		const Real	angle0,
		const Real	angle1
	)

Constructor.

Parameters:

center	center of the circle
r	radius
angle0	beginning angle
angle1	ending angle

concepts::CircleMappingEdge2d::CircleMappingEdge2d	(	const Real2d	vtx0,
		const Real2d	vtxm,
		const Real2d	vtx1
	)

Constructor.

Use three points from the edge to find the radius and center. The basic formulae come from the following website, and then the full formulae derived by Mengyu Wang, 2011 http://mathforum.org/dr.math/faq/formulas/faq.analygeom_2.html#twocircles

Parameters:

vtx0	beginning point
vtxm	middle point
vtx1	ending point

concepts::CircleMappingEdge2d::CircleMappingEdge2d ( const CircleMappingEdge2d & edgemap )

Copy Constructor.

Member Function Documentation

virtual CircleMappingEdge2d* concepts::CircleMappingEdge2d::clone ( ) const [virtual]

Virtual copy constructor.

Implements concepts::MappingEdge2d.

virtual Real concepts::CircleMappingEdge2d::curvature	(	const Real	t,
		const uint	n = `0`
	)		const `[virtual]`

Returns the n-th derivative of the curvature.

It's implemented in general for n = 0,1 and works with curved edges. Can be overwritten in derived classes for performance reasons.

Reimplemented from concepts::MappingEdge2d.

virtual Real2d concepts::CircleMappingEdge2d::derivative	(	const Real	t,
		const uint	n = `1`
	)		const `[virtual]`

Returns the n-th derivative.

Implements concepts::MappingEdge2d.

virtual std::ostream& concepts::CircleMappingEdge2d::info ( std::ostream & os ) const [protected, virtual]

Returns information in an output stream.

Reimplemented from concepts::MappingEdge2d.

virtual MappingEdge2d* concepts::CircleMappingEdge2d::inverse ( ) const [virtual]

Returns the mapping of the edge in inverse direction.

Reimplemented from concepts::MappingEdge2d.

Real2d concepts::MappingEdge2d::n0 ( const Real t ) const [inline, inherited]

Returns the normalised right normal vector.

Reimplemented in concepts::MappingParallelEdge2d.

Definition at line 105 of file elementMaps.hh.

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virtual Real2d concepts::MappingEdge2d::normal ( const Real t ) const [virtual, inherited]

Returns the right normal vector, length is that of the derivative.

virtual Real2d concepts::CircleMappingEdge2d::operator() ( const Real t ) const [virtual]

Application operator.

Maps the point from the parameter domain onto the physical space.

Implements concepts::MappingEdge2d.

MappingEdge2d* concepts::CircleMappingEdge2d::part	(	const Real	t0,
		const Real	t1
	)		const `[virtual]`

Returns a new object of an element map for a rectangular part of the reference cell defined by the two points.

Reimplemented from concepts::MappingEdge2d.

Real concepts::CircleMappingEdge2d::phi_ ( const Real t ) const [inline, private]

Definition at line 316 of file elementMaps.hh.

const Real2d& concepts::MappingEdge2d::vtx ( uint i ) const [inline, inherited]

Spit out one vertex of the edge.

Definition at line 122 of file elementMaps.hh.

Member Data Documentation

Real concepts::CircleMappingEdge2d::angle0_ [private]

Angles between one vertex and the circle center.

Definition at line 314 of file elementMaps.hh.

Real concepts::CircleMappingEdge2d::angle1_ [private]

Definition at line 314 of file elementMaps.hh.

Real2d concepts::CircleMappingEdge2d::m_ [private]

Mid point of the circle.

Definition at line 312 of file elementMaps.hh.

Real concepts::CircleMappingEdge2d::r_ [private]

Radius of the circle, zero if straight line (no sign)

Definition at line 310 of file elementMaps.hh.

Real2d concepts::MappingEdge2d::vtx_[2] [protected, inherited]

Coordinates of the vertices at either end of the edge.

Definition at line 126 of file elementMaps.hh.

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

geometry/elementMaps.hh

Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation