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

#include <singularSet.hh>

Collaboration diagram for hp3D::SingularEdge:

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`.
Real	distanceV0 (const concepts::Real3d point, const Hexahedron *elm) const
	Returns the the square of the distance of `point` to `vtx0_`.
Real	distanceV1 (const concepts::Real3d point, const Hexahedron *elm) const
	Returns the the square of the distance of `point` to `vtx1_`.
const concepts::Connector1 *	edge () const
	Returns a pointer to the edge object (topological, connector)
	SingularEdge (const concepts::Connector1 *edge, const concepts::Real3d vtx0, const concepts::Real3d vtx1)
	Constructor.
Private Attributes
concepts::Real3d	diffVector_
	Difference vector between the 2 vertices: $x_c - x_{c'}$ .
concepts::Real3d	diffVectorNormed_
	Scaled difference vector: $(x_c - x_{c'})/\|x_c - x_{c'}\|^2$ .
concepts::Real	diffVectorTimesVtx0Normed_
	Scalar product of the scaled difference vector and the vector to the first vertex: $(x_c - x_{c'}) \cdot x_c /\|x_c - x_{c'}\|^2$ .
const concepts::Connector1 *	edge_
	Pointer to the edge object (topological, connector)
const concepts::Real3d	vtx0_
	Coordinates of the vertices of the edge ( and $x_{c'}$ )
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 28 of file singularSet.hh.

Constructor & Destructor Documentation

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 38 of file singularSet.hh.

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Member Function Documentation

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

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

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

where $a$ = diffVectorNormed_ and $b$ = diffVectorTimesVtx0Normed_ respectively.

If $0 < t < 1$ , the closest point on the edge is not one of the corners and the distance $x - k(t)$ is computed. Otherwise, the distance to the closer corner is computed.