Dune::GridGlue::ProjectionImplementation Namespace Reference

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

corner()

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

edgeToCorners()

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

inside()

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 comparisons

Returns

true if x is inside, false otherwise

interpolate()

template<typename Coordinate , typename Corners >

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

inline

Convert barycentric coordinates to euclidean coordinates.

This function converts barycentric coordinates x with respect to the triangle with corners corners to euclidean 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

euclidean coordinates or interpolated normal

interpolate_unit_normals()

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 \seealso interpolate(const Coordinate&, const Corners&)