Class for storing a singular edge with coordinates of its corners. More...

#include <singularSet.hh>

Public Member Functions
Real	distance (const concepts::Real3d point, const Hexahedron *elm) const
	Returns the square of the distance from the edge to a `point` inside `elm`. More...

Real	distanceV0 (const concepts::Real3d point, const Hexahedron *elm) const
	Returns the the square of the distance of `point` to `vtx0_`. More...

Real	distanceV1 (const concepts::Real3d point, const Hexahedron *elm) const
	Returns the the square of the distance of `point` to `vtx1_`. More...

const concepts::Connector1 *	edge () const
	Returns a pointer to the edge object (topological, connector) More...

	SingularEdge (const concepts::Connector1 *edge, const concepts::Real3d vtx0, const concepts::Real3d vtx1)
	Constructor. More...

Private Attributes
concepts::Real3d	diffVector_
	Difference vector between the 2 vertices: $x_c - x_{c'}$ . More...

concepts::Real3d	diffVectorNormed_
	Scaled difference vector: $(x_c - x_{c'})/\|x_c - x_{c'}\|^2$ . More...

concepts::Real	diffVectorTimesVtx0Normed_
	Scalar product of the scaled difference vector and the vector to the first vertex: $(x_c - x_{c'}) \cdot x_c /\|x_c - x_{c'}\|^2$ More...

const concepts::Connector1 *	edge_
	Pointer to the edge object (topological, connector) More...

const concepts::Real3d	vtx0_
	Coordinates of the vertices of the edge ( and $x_{c'}$ ) More...

const concepts::Real3d	vtx1_

Friends
std::ostream &	operator<< (std::ostream &os, const SingularEdge &s)

Detailed Description

Class for storing a singular edge with coordinates of its corners.

The class also provides methods to compute a distance from a given point (in local coordinates in an element) to the edge. The returned results are the Euclidiean distance squared.

Author: Kersten Schmidt, 2002

Definition at line 30 of file singularSet.hh.

Constructor & Destructor Documentation

◆ SingularEdge()

hp3D::SingularEdge::SingularEdge	(	const concepts::Connector1 *	edge,
		const concepts::Real3d	vtx0,
		const concepts::Real3d	vtx1
	)

inline

Constructor.

Precomputes diffVector_, diffVectorNormed_ and diffVectorTimesVtx0Normed_ to allow fast computations in the distance function.

Parameters

edge	Edge object
vtx0,vtx1	Coordinates of the corners of the edge

Definition at line 40 of file singularSet.hh.

Member Function Documentation

◆ distance()

Real hp3D::SingularEdge::distance	(	const concepts::Real3d	point,
		const Hexahedron *	elm
	)		const

Returns the square of the distance from the edge to a point inside elm.

Parameters

point	Point in reference coordinates $\xi \in [0,1]^3$
elm	Hexahedron in which the point is located

Let be a straight line along the edge, in parameters:

$k(t) := x_c + (x_{c'}- x_c) \cdot t = x_c + x_D \cdot t$

where and $x_{c'}$ are the corners of the edge.

To determine the root point of ( is $\xi$ in physical coordinates) on , compute

$t = x \cdot\frac{x_D}{|x_D|^2} - \frac{x_c\cdot x_D}{|x_D|^2} = x \cdot a - b$

where = diffVectorNormed_ and = diffVectorTimesVtx0Normed_ respectively.

If , the closest point on the edge is not one of the corners and the distance is computed. Otherwise, the distance to the closer corner is computed.

◆ distanceV0()

Real hp3D::SingularEdge::distanceV0	(	const concepts::Real3d	point,
		const Hexahedron *	elm
	)		const

Returns the the square of the distance of point to vtx0_.

◆ distanceV1()

Real hp3D::SingularEdge::distanceV1	(	const concepts::Real3d	point,
		const Hexahedron *	elm
	)		const

Returns the the square of the distance of point to vtx1_.

◆ edge()

const concepts::Connector1* hp3D::SingularEdge::edge ( ) const

inline

Returns a pointer to the edge object (topological, connector)

Definition at line 48 of file singularSet.hh.

Friends And Related Function Documentation

◆ operator<<

std::ostream& operator<<	(	std::ostream &	os,
		const SingularEdge &	s
	)

friend

Member Data Documentation

◆ diffVector_

concepts::Real3d hp3D::SingularEdge::diffVector_

private

Difference vector between the 2 vertices: $x_c - x_{c'}$ .

Definition at line 86 of file singularSet.hh.

◆ diffVectorNormed_

concepts::Real3d hp3D::SingularEdge::diffVectorNormed_

private

Scaled difference vector: $(x_c - x_{c'})/|x_c - x_{c'}|^2$ .

Definition at line 88 of file singularSet.hh.

◆ diffVectorTimesVtx0Normed_

concepts::Real hp3D::SingularEdge::diffVectorTimesVtx0Normed_

private

Scalar product of the scaled difference vector and the vector to the first vertex: $(x_c - x_{c'}) \cdot x_c /|x_c - x_{c'}|^2$

Definition at line 92 of file singularSet.hh.

◆ edge_

const concepts::Connector1* hp3D::SingularEdge::edge_

private

Pointer to the edge object (topological, connector)

Definition at line 82 of file singularSet.hh.

◆ vtx0_

const concepts::Real3d hp3D::SingularEdge::vtx0_

private

Coordinates of the vertices of the edge ( and $x_{c'}$ )

Definition at line 84 of file singularSet.hh.

◆ vtx1_

const concepts::Real3d hp3D::SingularEdge::vtx1_

private

Definition at line 84 of file singularSet.hh.

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

hp3D/singularSet.hh

hp3D::SingularEdge Class ReferenceMaxwell's Equations » Three Dimensions » Weighted Regularization

Public Member Functions

Private Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ SingularEdge()

Member Function Documentation

◆ distance()

◆ distanceV0()

◆ distanceV1()

◆ edge()

Friends And Related Function Documentation

◆ operator<<

Member Data Documentation

◆ diffVector_

◆ diffVectorNormed_

◆ diffVectorTimesVtx0Normed_

◆ edge_

◆ vtx0_

◆ vtx1_

hp3D::SingularEdge Class Reference
Maxwell's Equations » Three Dimensions » Weighted Regularization