This namespace contains helper functions for the projection of two triangular surface on each other. More...

Classes
class	EdgeIntersectionHelper
	Helper class that provides static methods for the computation of the intersection of surface element edges projected onto each other. More...

class	EdgeIntersectionHelper< 1, 2, T >

class	EdgeIntersectionHelper< 2, 3, T >

class	ProjectionHelper
	Helper class that provides static methods to compute the projection and inverse projection of a point along some given directions. More...

class	ProjectionHelper< 1, 2, T >

class	ProjectionHelper< 2, 3, T >

Functions
template<class T , int dim>
static Dune::FieldVector< T, dim >	crossProduct (const Dune::FieldVector< T, dim > &a, const Dune::FieldVector< T, dim > &b)
	Compute the cross product of two vectors. More...

template<int dim, int dimworld, class T >
static bool	projection (const Dune::FieldVector< T, dimworld > &corner, const Dune::FieldVector< T, dimworld > &direction, const std::vector< Dune::FieldVector< T, dimworld > > &targetCorners, Dune::FieldVector< T, dim > &image, const T overlap=1e-1)
	Compute the projection of a point along a given direction into the convex hull of some target points. More...

template<int dim, int dimworld, class T >
static bool	inverseProjection (const std::vector< Dune::FieldVector< T, dimworld > > &corners, const std::vector< Dune::FieldVector< T, dimworld > > &directions, const Dune::FieldVector< T, dimworld > &target, Dune::FieldVector< T, dim > &preImage, const T overlap=1e-1)
	Compute the inverse projection of a point onto some surface element where the projection is done across directions which are associated to corners of an surface element. More...

template<int dim, int dimworld, class T = double>
static void	addEdgeIntersections (const std::vector< Dune::FieldVector< T, dimworld > > &corners1, const std::vector< Dune::FieldVector< T, dimworld > > &corners2, const std::vector< Dune::FieldVector< T, dimworld > > &directions1, const Dune::GeometryType &gt1, const Dune::GeometryType &gt2, std::vector< Dune::array< Dune::FieldVector< T, dim >, 2 > > &polygonCorners, const std::vector< int > &hitCorners, std::bitset<(1<< dim)> &neighborIntersects1, std::bitset<(1<< dim)> &neighborIntersects2, const T overlap=1e-1)
	Compute the projection along given directions of surface element edges onto target edges. More...

Detailed Description

This namespace contains helper functions for the projection of two triangular surface on each other.

Function Documentation

template<int dim, int dimworld, class T = double>

static void Projection::addEdgeIntersections	(	const std::vector< Dune::FieldVector< T, dimworld > > &	corners1,
		const std::vector< Dune::FieldVector< T, dimworld > > &	corners2,
		const std::vector< Dune::FieldVector< T, dimworld > > &	directions1,
		const Dune::GeometryType &	gt1,
		const Dune::GeometryType &	gt2,
		std::vector< Dune::array< Dune::FieldVector< T, dim >, 2 > > &	polygonCorners,
		const std::vector< int > &	hitCorners,
		std::bitset<(1<< dim)> &	neighborIntersects1,
		std::bitset<(1<< dim)> &	neighborIntersects2,
		const T	overlap = `1e-1`
	)

static

Compute the projection along given directions of surface element edges onto target edges.

Parameters

corners1	The coordinates of the surface element corners whose edges are projected.
corners2	The coordinates of the surface element corners on which is projected.
directions1	The directions along which the projection is done.
gt1	The geometry type of the projected surface element.
gt2	The geometry type of the target surface element.
polygonCorners	If intersection points are found their local coordinates are added to this vector.
hitCorners	Vector containing information on which surface element corners are projected on each other.
neighborIntersects1	If two edges intersect then the corresponding surface element neighbors also intersect. This information for the projected surface element is stored in the bitfield.
neighborIntersects2	If two edges intersect then the corresponding surface element neighbors also intersect. This information for the surface element on which is projected is stored in the bitfield.
overlap	The amount of overlap that is allowed, i.e. projection among the opposite direction is valid if the scaling is smaller than overlap.

References Projection::EdgeIntersectionHelper< dim, dimworld, T >::addEdgeIntersections().

template<class T , int dim>

static Dune::FieldVector<T,dim> Projection::crossProduct	(	const Dune::FieldVector< T, dim > &	a,
		const Dune::FieldVector< T, dim > &	b
	)

static

Compute the cross product of two vectors.

Referenced by Projection::ProjectionHelper< 2, 3, T >::inverseProjection().

template<int dim, int dimworld, class T >

static bool Projection::inverseProjection	(	const std::vector< Dune::FieldVector< T, dimworld > > &	corners,
		const std::vector< Dune::FieldVector< T, dimworld > > &	directions,
		const Dune::FieldVector< T, dimworld > &	target,
		Dune::FieldVector< T, dim > &	preImage,
		const T	overlap = `1e-1`
	)

static

Compute the inverse projection of a point onto some surface element where the projection is done across directions which are associated to corners of an surface element.

Parameters

corners	The coordinates of the corners.
directions	The directions along which the projection is done.
target	The point whose inverse projection is computed.
preImage	The pre-image of the target point in local coordinates of the surface element.
overlap	The amount of overlap that is allowed, i.e. projection among the opposite direction is valid if the scaling is smaller than overlap.

Returns: Returns true if the computed pre-image is within the convex hull of the corner points.

References Projection::ProjectionHelper< dim, dimworld, T >::inverseProjection().

template<int dim, int dimworld, class T >

static bool Projection::projection	(	const Dune::FieldVector< T, dimworld > &	corner,
		const Dune::FieldVector< T, dimworld > &	direction,
		const std::vector< Dune::FieldVector< T, dimworld > > &	targetCorners,
		Dune::FieldVector< T, dim > &	image,
		const T	overlap = `1e-1`
	)

static

Compute the projection of a point along a given direction into the convex hull of some target points.

Parameters

corner	The coordinates of the point that is projected.
direction	The direction along which an intersection with the target surface element is searched.
targetCorners	The corner coordinates of the target surface element.
image	The projected corner in local coordinates of the target surface element.
overlap	The amount of overlap that is allowed, i.e. projection among the opposite direction is valid if the scaling is smaller than overlap.

Returns: Returns true if the computed image is within the convex hull of the target corner points.

References Projection::ProjectionHelper< dim, dimworld, T >::projection().

Classes

Functions

Detailed Description

Function Documentation