Dune::GridGlue::Projection< Coordinate > Class Template Reference

Projection of a line (triangle) on another line (triangle). More...

#include <dune/grid-glue/common/projection.hh>

Classes
struct	EdgeIntersection
	Intersection between two edges of a triangle. More...

Public Types
typedef Coordinate::field_type	Field
	Scalar type.
typedef std::array< Coordinate, dim >	Images
	List of corner images. More...
typedef Images	Preimages

Public Member Functions
	Projection (const Field overlap=Field(0), const Field max_normal_product=Field(-0.1))
void	epsilon (const Field epsilon)
	Set epsilon used for floating-point comparisons. More...
template<typename Corners , typename Normals >
void	project (const std::tuple< Corners &, Corners & > &corners, const std::tuple< Normals &, Normals & > &normals)
	Do the actual projection. More...
const std::tuple< Images, Preimages > &	images () const
	Images and preimages of corners. More...
const std::tuple< std::bitset< dim >, std::bitset< dim > > &	success () const
	Indicate whether projection (inverse projection) is valid for each corner or not. More...
unsigned	numberOfEdgeIntersections () const
	Number of edge intersections. More...
const std::array< EdgeIntersection, maxEdgeIntersections > &	edgeIntersections () const
	Edge-edge intersections. More...

Static Public Attributes
static constexpr unsigned	dim = Coordinate::dimension
	dimension of coordinates
static constexpr unsigned	maxEdgeIntersections = dim == 3 ? 9 : 0
	maximum number of edge-edge intersections More...

Detailed Description

template<typename Coordinate>
class Dune::GridGlue::Projection< Coordinate >

Projection of a line (triangle) on another line (triangle).

This class implements methods to project a line (2d) or triangle (3d) on another line (triangle) along normal field given by values at the corners.

Member Typedef Documentation

Images

template<typename Coordinate >

typedef std::array<Coordinate, dim> Dune::GridGlue::Projection< Coordinate >::Images

List of corner images.

This type is used to return the list of images Φ(xᵢ) of the corners xᵢ in barycentric coordinates with respect to the image simplex. The last entry is used to return the (signed) distance along the normal.

Preimages

template<typename Coordinate >

typedef Images Dune::GridGlue::Projection< Coordinate >::Preimages

List of corner preimages.

This is used as Images, but for the preimages Φ⁻¹(yᵢ) of the corners yᵢ of the image simplex.

Constructor & Destructor Documentation

Projection()

template<typename Coordinate >

Dune::GridGlue::Projection< Coordinate >::Projection	(	const Field	overlap = Field(0),
		const Field	max_normal_product = Field(-0.1)
	)

Parameters

overlap	allowed overlap
max_normal_product	maximum value for scalar product ν(x)·ν(Φ(x))

Member Function Documentation

edgeIntersections()

template<typename Coordinate >

const std::array< EdgeIntersection, maxEdgeIntersections > & Dune::GridGlue::Projection< Coordinate >::edgeIntersections ( ) const

inline

Edge-edge intersections.

Note

project() must be called before this method can be used.

Warning

Only the first numberOfEdgeIntersections() entries are valid edge intersections.

epsilon()

template<typename Coordinate >

void Dune::GridGlue::Projection< Coordinate >::epsilon

(

const Field

epsilon

)

Set epsilon used for floating-point comparisons.

Parameters

epsilon

new epsilon used for floating-point comaprisons

images()

template<typename Coordinate >

const std::tuple< Images, Preimages > & Dune::GridGlue::Projection< Coordinate >::images ( ) const

inline

Images and preimages of corners.

Returns a pair of arrays. The first array contains the images Φ(xᵢ) of the corners xᵢ. The second array contains the preimages Φ⁻¹(yⱼ) of the corners yⱼ.

The first d-1 values are the barycentric coordinates with respect to the corners of the (pre)image, the last value is the signed distance between the projected point and its (pre)image along the normal at the projected preimage corner or the inverse projected image corner.

Note

project() must be called before this method can be used.

Returns

pair of arrays giving ((Φ(xᵢ))ᵢ, (Φ⁻¹(yⱼ))ⱼ) in barycentric coordinates

success()

numberOfEdgeIntersections()

template<typename Coordinate >

unsigned Dune::GridGlue::Projection< Coordinate >::numberOfEdgeIntersections ( ) const

inline

Number of edge intersections.

Note

project() must be called before this method can be used.

edgeIntersections()

project()

template<typename Coordinate >

template<typename Corners , typename Normals >

void Dune::GridGlue::Projection< Coordinate >::project	(	const std::tuple< Corners &, Corners & > &	corners,
		const std::tuple< Normals &, Normals & > &	normals
	)

Do the actual projection.

Parameters

corners	euclidean coordinates of corners of preimage and image
normals	normals at corners of preimage and image

Template Parameters

Corners	list of corner coordinates, should be std::vector<Coordinate> or std::array<Coordinate, n>
Normals	list of corner normals, should be std::vector<Coordinate> or std::array<Coordinate, n>

success()

template<typename Coordinate >

const std::tuple< std::bitset< dim >, std::bitset< dim > > & Dune::GridGlue::Projection< Coordinate >::success ( ) const

inline

Indicate whether projection (inverse projection) is valid for each corner or not.

Returns a pair of bitsets. The first bitset indicates if the projection Φ(xᵢ) is valid for each corner xᵢ, that is that Φ(xᵢ) could be computed and lies in the image simplex. The second bitset indicates the same for the inverse projection Φ⁻¹(yⱼ) for the corners yⱼ.

Note

project() must be called before this method can be used.

Returns

pair of bitsets indicating success of (inverse) projection at corners xᵢ (yⱼ)

Member Data Documentation

maxEdgeIntersections

template<typename Coordinate >

constexpr unsigned Dune::GridGlue::Projection< Coordinate >::maxEdgeIntersections = dim == 3 ? 9 : 0

staticconstexpr

maximum number of edge-edge intersections

See also \seealso edgeIntersections()

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

• dune/grid-glue/common/projection.hh
• dune/grid-glue/common/projection_impl.hh