Functions
template<typename Coordinate , typename Field >
Coordinate	corner (unsigned c)

std::pair< unsigned, unsigned >	edgeToCorners (unsigned edge)

template<typename Coordinate , typename Corners >
Corners::value_type	interpolate (const Coordinate &x, const Corners &corners)

template<typename Coordinate , typename Normals >
Normals::value_type	interpolate_unit_normals (const Coordinate &x, const Normals &normals)

template<typename Coordinate , typename Field >
bool	inside (const Coordinate &x, const Field &epsilon)

Function Documentation

template<typename Coordinate , typename Field >

Coordinate Dune::GridGlue::ProjectionImplementation::corner ( unsigned c )

inline

Return corner coordinates of a simplex.

Given the number c of a corner, this function returns the coordinate of the cth corner of the standard simplex with the same dimension as Coordinate.

Parameters

c	corner number

Returns: coordinate of cth corner of the standard simplex

Referenced by Dune::GridGlue::ConformingMerge< dim, dimworld, T >::ConformingMerge(), Dune::GridGlue::StandardMerge< T, dim1, dim2, dimworld >::enableBruteForce(), and Dune::GridGlue::StandardMerge< T, grid1Dim, grid2Dim, dimworld >::nSimplices().

std::pair<unsigned, unsigned> Dune::GridGlue::ProjectionImplementation::edgeToCorners ( unsigned edge )

inline

Translate edge to corner numbers.

Given the number edge of an edge of a triangle, this function returns the number of the corners belonging to it.

Parameters

edge	edge number of a triangle

Returns: numbers of corners of the edge

Referenced by Dune::GridGlue::Projection< Coordinate >::epsilon().

template<typename Coordinate , typename Field >

bool Dune::GridGlue::ProjectionImplementation::inside	(	const Coordinate &	x,
		const Field &	epsilon
	)

inline

Check if the point x is inside the standard simplex.

This functions checks if the point x is in the inside (or on the boundary) of the standard simplex, that is xᵢ ≥ 0 and ∑ xᵢ ≤ 1.

Parameters

x	coordinates of point to check
epsilon	tolerance used for floating-point comparisions

Returns: true if x is inside, false otherwise

References Dune::GridGlue::Projection< Coordinate >::Projection().

Referenced by Dune::GridGlue::Projection< Coordinate >::epsilon().

template<typename Coordinate , typename Corners >

Corners::value_type Dune::GridGlue::ProjectionImplementation::interpolate	(	const Coordinate &	x,
		const Corners &	corners
	)

inline

Convert barycentric coordinates to euclidian coordinates.

This function converts barycentric coordinates x with respect to the triangle with corners corners to euclidian coordinates. For the result y the following equation holds: yᵢ = (cornersᵢ₊₁ - corners₀) xᵢ

Note that this can also be for linear interpolation of normals given on the corners, but this does not preserve the norm (e.g. for unit normals).

Parameters

x	barycentric coordinates
corners	coordinates or normals at the corners

Returns: euclidian coordinates or interpolated normal

Referenced by Dune::GridGlue::Projection< Coordinate >::epsilon(), interpolate_unit_normals(), Dune::GridGlue::ProjectionWriterImplementation::write_edge_intersection_points(), and Dune::GridGlue::ProjectionWriterImplementation::write_points().

template<typename Coordinate , typename Normals >

Normals::value_type Dune::GridGlue::ProjectionImplementation::interpolate_unit_normals	(	const Coordinate &	x,
		const Normals &	normals
	)

inline

Interpolate between unit normals on corners of a simplex.

This functions interpolates between unit normals given on corners of a simplex using linear interpolation.

Parameters

x	barycentric coordinates
normals	unit normals at corners

Returns: unit normal at x interpolate(const Coordinate&, const Corners&)

References interpolate().

Referenced by Dune::GridGlue::Projection< Coordinate >::epsilon(), Dune::GridGlue::ProjectionWriterImplementation::write_edge_intersection_normals(), and Dune::GridGlue::ProjectionWriterImplementation::write_normals().

Functions

Function Documentation