A 3D circular edge element map. More...

#include <mappingEdge3D.hh>

Inheritance diagram for concepts::CircleMappingEdge3d:

Public Member Functions
	CircleMappingEdge3d (const CircleMappingEdge3d &other)
	Copy Constructor. More...

	CircleMappingEdge3d (const Real3d &vtx0, const Real3d &vtx1, const Real radius, const Real3d &center, const Real tol=1e6 *std::numeric_limits< double >::epsilon())
	Constructor. More...

CircleMappingEdge3d *	clone () const override
	Virtual constructor. More...

Real3d	derivative (const Real t, const uint n=1) const override
	Evaluates the n-th derivative of the edge mapping at the coordinate t. More...

Real3d	getCenter () const

Real	getRadius () const

CircleMappingEdge3d *	inverse () const override
	Create a heap-allocated copy of this edge with reversed parametrization. More...

Real3d	operator() (const Real t) const override
	Evaluates the edge mapping at the coordinate t. More...

const Real3d &	vtx (uint i) const
	Returns i-th physical vertex of the edge. More...

	~CircleMappingEdge3d () override
	Destructor. More...

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

Protected Attributes
std::array< Real3d, 2 >	vtx_
	Physical vertices $\{ F_K(0), F_K(1) \}$ . More...

Private Attributes
Real3d	center_
	Center of the circle. More...

Real	radius_
	Radius of the circle. More...

Detailed Description

A 3D circular edge element map.

Element parametrization:

$F_K (t) = c + r \frac{ F^{\text{lin}}_K (t) - c }{ \| F^{\text{lin}}_K (t) - c \|_2 },$

where $F^{\text{lin}}_K$ is the $\mathbb{Q}_1$ linear edge element interpolating between and , $c \in \mathbb{R}^3$ is the center of this edge and $r \in \mathbb{R}$ the radius. This corresponds to the shortest edge connecting to on the sphere .

Todo:: Use SphereData type instead of bare radius and center

Author: Lukas Drescher, 2014

Definition at line 115 of file mappingEdge3D.hh.

Constructor & Destructor Documentation

◆ CircleMappingEdge3d() [1/2]

concepts::CircleMappingEdge3d::CircleMappingEdge3d	(	const Real3d &	vtx0,
		const Real3d &	vtx1,
		const Real	radius,
		const Real3d &	center,
		const Real	tol = `1e6 *std::numeric_limits< double >::epsilon()`
	)

Constructor.

Parameters

vtx0	physical coordinate of first vertex of the edge
vtx1	physical coordinate of second vertex of the edge
r	radius of the sphere on which the edge lies
center	center of the sphere on which the edge lies

◆ CircleMappingEdge3d() [2/2]

concepts::CircleMappingEdge3d::CircleMappingEdge3d ( const CircleMappingEdge3d & other )

Copy Constructor.

◆ ~CircleMappingEdge3d()

concepts::CircleMappingEdge3d::~CircleMappingEdge3d ( )

override

Destructor.

Member Function Documentation

◆ clone()

CircleMappingEdge3d* concepts::CircleMappingEdge3d::clone ( ) const

overridevirtual

Virtual constructor.

Create a heap-allocated copy of this edge.

Returns: Pointer to heap-allocated edge copy. To be deleted by the user.

Implements concepts::MappingEdge3d.

◆ derivative()

Real3d concepts::CircleMappingEdge3d::derivative	(	const Real	t,
		const uint	n = `1`
	)		const

overridevirtual

Evaluates the n-th derivative of the edge mapping at the coordinate t.

Parameters

n	order of the derivative (<= 1 for most concrete types)

Returns: $F^{(n)}_K(t)$

Implements concepts::MappingEdge3d.

◆ getCenter()

Real3d concepts::CircleMappingEdge3d::getCenter ( ) const

inline

Definition at line 136 of file mappingEdge3D.hh.

◆ getRadius()

Real concepts::CircleMappingEdge3d::getRadius ( ) const

inline

Definition at line 135 of file mappingEdge3D.hh.

◆ info()

std::ostream& concepts::CircleMappingEdge3d::info ( std::ostream & os ) const

overrideprotectedvirtual

Returns information in an output stream.

Reimplemented from concepts::MappingEdge3d.

◆ inverse()

CircleMappingEdge3d* concepts::CircleMappingEdge3d::inverse ( ) const

overridevirtual

Create a heap-allocated copy of this edge with reversed parametrization.

Returns: Pointer to heap-allocated edge copy. Has to be deleted by the user.

Implements concepts::MappingEdge3d.

◆ operator()()

Real3d concepts::CircleMappingEdge3d::operator() ( const Real t ) const

overridevirtual

Evaluates the edge mapping at the coordinate t.

Returns

Implements concepts::MappingEdge3d.

◆ vtx()

const Real3d& concepts::MappingEdge3d::vtx ( uint i ) const

inlineinherited

Returns i-th physical vertex of the edge.

Returns

Definition at line 64 of file mappingEdge3D.hh.

Member Data Documentation

◆ center_

Real3d concepts::CircleMappingEdge3d::center_

private

Center of the circle.

Definition at line 143 of file mappingEdge3D.hh.

◆ radius_

Real concepts::CircleMappingEdge3d::radius_

private

Radius of the circle.

Definition at line 141 of file mappingEdge3D.hh.

◆ vtx_

std::array<Real3d,2> concepts::MappingEdge3d::vtx_

protectedinherited

Physical vertices $\{ F_K(0), F_K(1) \}$ .

Definition at line 68 of file mappingEdge3D.hh.

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

geometry/mappingEdge3D.hh

concepts::CircleMappingEdge3d Class Reference

Public Member Functions

Protected Member Functions

Protected Attributes

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ CircleMappingEdge3d() [1/2]

◆ CircleMappingEdge3d() [2/2]

◆ ~CircleMappingEdge3d()

Member Function Documentation

◆ clone()

◆ derivative()

◆ getCenter()

◆ getRadius()

◆ info()

◆ inverse()

◆ operator()()

◆ vtx()

Member Data Documentation

◆ center_

◆ radius_

◆ vtx_