Base class for shape geometry information. More...

#include <Geometry.h>

Inheritance diagram for Nektar::SpatialDomains::Geometry:

Public Member Functions
	Geometry ()
	Default constructor.

	Geometry (int coordim)
	Constructor when supplied a coordinate dimension.

virtual	~Geometry ()=default

int	GetCoordim () const
	Return the coordinate dimension of this object (i.e. the dimension of the space in which this object is embedded).

void	SetCoordim (int coordim)
	Sets the coordinate dimension of this object (i.e. the dimension of the space in which this object is embedded).

GeomFactorsUniquePtr	GenGeomFactors (LibUtilities::PointsKeyVector &keyTgt)
	Used by Expansion to generate associated GeomFactors.

LibUtilities::ShapeType	GetShapeType (void)
	Get the geometric shape type of this object.

int	GetGlobalID (void) const
	Get the ID of this object.

void	SetGlobalID (int globalid)
	Set the ID of this object.

int	GetVid (int i) const
	Returns global id of vertex `i` of this object.

int	GetEid (int i) const
	Get the ID of edge `i` of this object.

int	GetFid (int i) const
	Get the ID of face `i` of this object.

int	GetTid (int i) const
	Get the ID of trace `i` of this object.

PointGeom *	GetVertex (int i) const
	Returns vertex `i` of this object.

Geometry1D *	GetEdge (int i) const
	Returns edge `i` of this object.

Geometry2D *	GetFace (int i) const
	Returns face `i` of this object.

StdRegions::Orientation	GetEorient (const int i) const
	Returns the orientation of edge `i` with respect to the ordering of edges in the standard element.

StdRegions::Orientation	GetForient (const int i) const
	Returns the orientation of face `i` with respect to the ordering of faces in the standard element.

int	GetNumVerts () const
	Get the number of vertices of this object.

int	GetNumEdges () const
	Get the number of edges of this object.

int	GetNumFaces () const
	Get the number of faces of this object.

int	GetShapeDim () const
	Get the object's shape dimension.

StdRegions::StdExpansionSharedPtr	GetXmap () const
	Return the mapping object Geometry::m_xmap that represents the coordinate transformation from standard element to physical element.

const Array< OneD, const NekDouble > &	GetCoeffs (const int i) const
	Return the coefficients of the transformation Geometry::m_xmap in coordinate direction `i`.

void	FillGeom ()
	Populate the coordinate mapping Geometry::m_coeffs information from any children geometry elements.

std::array< NekDouble, 6 >	GetBoundingBox ()
	Generates the bounding box for the element.

void	ClearBoundingBox ()

bool	ContainsPoint (const Array< OneD, const NekDouble > &gloCoord, NekDouble tol=0.0)
	Determine whether an element contains a particular Cartesian coordinate \((x,y,z)\).

bool	ContainsPoint (const Array< OneD, const NekDouble > &gloCoord, Array< OneD, NekDouble > &locCoord, NekDouble tol)
	Determine whether an element contains a particular Cartesian coordinate \((x,y,z)\).

bool	ContainsPoint (const Array< OneD, const NekDouble > &gloCoord, Array< OneD, NekDouble > &locCoord, NekDouble tol, NekDouble &dist)
	Determine whether an element contains a particular Cartesian coordinate \(\vec{x} = (x,y,z)\).

NekDouble	GetLocCoords (const Array< OneD, const NekDouble > &coords, Array< OneD, NekDouble > &Lcoords)
	Determine the local collapsed coordinates that correspond to a given Cartesian coordinate for this geometry object.

NekDouble	GetCoord (const int i, const Array< OneD, const NekDouble > &Lcoord)
	Given local collapsed coordinate `Lcoord`, return the value of physical coordinate in direction `i`.

int	PreliminaryCheck (const Array< OneD, const NekDouble > &gloCoord)
	A fast and robust check if a given global coord is outside of a deformed element. For regular elements, this check is unnecessary.

bool	MinMaxCheck (const Array< OneD, const NekDouble > &gloCoord)
	Check if given global coord is within the BoundingBox of the element.

bool	ClampLocCoords (Array< OneD, NekDouble > &locCoord, NekDouble tol=std::numeric_limits< NekDouble >::epsilon())
	Clamp local coords to be within standard regions [-1, 1]^dim.

NekDouble	FindDistance (const Array< OneD, const NekDouble > &xs, Array< OneD, NekDouble > &xi)

int	GetVertexEdgeMap (int i, int j) const
	Returns the standard element edge IDs that are connected to a given vertex.

int	GetVertexFaceMap (int i, int j) const
	Returns the standard element face IDs that are connected to a given vertex.

int	GetEdgeFaceMap (int i, int j) const
	Returns the standard element edge IDs that are connected to a given face.

int	GetEdgeNormalToFaceVert (int i, int j) const
	Returns the standard lement edge IDs that are normal to a given face vertex.

int	GetDir (const int i, const int j=0) const
	Returns the element coordinate direction corresponding to a given face coordinate direction.

GeomType	CalcGeomType ()

void	Reset (CurveMap &curvedEdges, CurveMap &curvedFaces)
	Reset this geometry object: unset the current state, zero Geometry::m_coeffs and remove allocated GeomFactors.

void	ResetNonRecursive (CurveMap &curvedEdges, CurveMap &curvedFaces)
	Reset this geometry object non-recursively: unset the current state, zero Geometry::m_coeffs and remove allocated GeomFactors.

void	Setup ()

Protected Member Functions
virtual int	v_GetVid (int i) const
	Get the ID of vertex `i` of this object.

virtual PointGeom *	v_GetVertex (const int i) const
	Returns vertex `i` of this object.

virtual Geometry1D *	v_GetEdge (const int i) const
	Returns edge `i` of this object.

virtual Geometry2D *	v_GetFace (const int i) const
	Returns face `i` of this object.

virtual StdRegions::Orientation	v_GetEorient (const int i) const
	Returns the orientation of edge `i` with respect to the ordering of edges in the standard element.

virtual StdRegions::Orientation	v_GetForient (const int i) const
	Returns the orientation of face `i` with respect to the ordering of faces in the standard element.

virtual int	v_GetNumVerts () const
	Get the number of vertices of this object.

virtual int	v_GetNumEdges () const
	Get the number of edges of this object.

virtual int	v_GetNumFaces () const
	Get the number of faces of this object.

virtual int	v_GetShapeDim () const
	Get the object's shape dimension.

virtual GeomFactorsUniquePtr	v_GenGeomFactors (LibUtilities::PointsKeyVector &keyTgt)
	Used by Expansion to generate associated GeomFactors.

virtual StdRegions::StdExpansionSharedPtr	v_GetXmap () const
	Return the mapping object Geometry::m_xmap that represents the coordinate transformation from standard element to physical element.

virtual void	v_FillGeom ()
	Populate the coordinate mapping Geometry::m_coeffs information from any children geometry elements.

virtual bool	v_ContainsPoint (const Array< OneD, const NekDouble > &gloCoord, Array< OneD, NekDouble > &locCoord, NekDouble tol, NekDouble &dist)
	Determine whether an element contains a particular Cartesian coordinate \(\vec{x} = (x,y,z)\).

virtual int	v_AllLeftCheck (const Array< OneD, const NekDouble > &gloCoord)

virtual NekDouble	v_GetCoord (const int i, const Array< OneD, const NekDouble > &Lcoord)
	Given local collapsed coordinate `Lcoord`, return the value of physical coordinate in direction `i`.

virtual NekDouble	v_GetLocCoords (const Array< OneD, const NekDouble > &coords, Array< OneD, NekDouble > &Lcoords)
	Determine the local collapsed coordinates that correspond to a given Cartesian coordinate for this geometry object.

virtual NekDouble	v_FindDistance (const Array< OneD, const NekDouble > &xs, Array< OneD, NekDouble > &xi)

virtual int	v_GetVertexEdgeMap (int i, int j) const
	Returns the standard element edge IDs that are connected to a given vertex.

virtual int	v_GetVertexFaceMap (int i, int j) const
	Returns the standard element face IDs that are connected to a given vertex.

virtual int	v_GetEdgeFaceMap (int i, int j) const
	Returns the standard element edge IDs that are connected to a given face.

virtual int	v_GetEdgeNormalToFaceVert (const int i, const int j) const
	Returns the standard lement edge IDs that are normal to a given face vertex.

virtual int	v_GetDir (const int faceidx, const int facedir) const
	Returns the element coordinate direction corresponding to a given face coordinate direction.

virtual GeomType	v_CalcGeomType ()

virtual void	v_Reset (CurveMap &curvedEdges, CurveMap &curvedFaces)
	Reset this geometry object: unset the current state, zero Geometry::m_coeffs and remove allocated GeomFactors.

virtual void	v_Setup ()

void	SetUpCoeffs (const int nCoeffs)
	Initialise the Geometry::m_coeffs array.

virtual void	v_CalculateInverseIsoParam ()

Protected Attributes
int	m_coordim
	Coordinate dimension of this geometry object.

StdRegions::StdExpansionSharedPtr	m_xmap
	\(\chi\) mapping containing isoparametric transformation.

GeomState	m_state
	Enumeration to dictate whether coefficients are filled.

bool	m_setupState
	Wether or not the setup routines have been run.

LibUtilities::ShapeType	m_shapeType
	Type of shape.

int	m_globalID
	Global ID.

std::vector< Array< OneD, NekDouble > >	m_coeffs
	Array containing expansion coefficients of `m_xmap`.

Array< OneD, NekDouble >	m_boundingBox
	Array containing bounding box.

Array< OneD, Array< OneD, NekDouble > >	m_isoParameter

Array< OneD, Array< OneD, NekDouble > >	m_invIsoParam

int	m_straightEdge

Detailed Description

Base class for shape geometry information.

Definition at line 83 of file Geometry.h.

Constructor & Destructor Documentation

◆ Geometry() [1/2]

Nektar::SpatialDomains::Geometry::Geometry ( )

Default constructor.

Definition at line 47 of file Geometry.cpp.

    : m_coordim(0), m_state(eNotFilled), m_setupState(false),
      m_shapeType(LibUtilities::eNoShapeType), m_globalID(-1), m_straightEdge(0)
{
}

◆ Geometry() [2/2]

Nektar::SpatialDomains::Geometry::Geometry ( int coordim )

Constructor when supplied a coordinate dimension.

Definition at line 56 of file Geometry.cpp.

    : m_coordim(coordim), m_state(eNotFilled), m_setupState(false),
      m_shapeType(LibUtilities::eNoShapeType), m_globalID(-1), m_straightEdge(0)
{
}

◆ ~Geometry()

virtual Nektar::SpatialDomains::Geometry::~Geometry ( )

virtualdefault

Member Function Documentation

◆ CalcGeomType()

GeomType Nektar::SpatialDomains::Geometry::CalcGeomType ( )

inline

A geometric shape is considered regular if it has constant geometric information, and deformed if this information changes throughout the shape.

Returns: The type of geometry.

See also: GeomType

Definition at line 306 of file Geometry.h.

{
    return v_CalcGeomType();
}

References v_CalcGeomType().

◆ ClampLocCoords()

bool Nektar::SpatialDomains::Geometry::ClampLocCoords	(	Array< OneD, NekDouble > &	locCoord,
		NekDouble	tol = `std::numeric_limits<NekDouble>::epsilon()`
	)

Clamp local coords to be within standard regions [-1, 1]^dim.

Parameters

Lcoords Corresponding local coordinates

Definition at line 525 of file Geometry.cpp.

{
    // Validation checks
    ASSERTL1(locCoord.size() >= GetShapeDim(),
             "Expects local coordinates to be same or "
             "larger than shape dimension.");
 
    // If out of range clamp locCoord to be within [-1,1]^dim
    // since any larger value will be very oscillatory if
    // called by 'returnNearestElmt' option in
    // ExpList::GetExpIndex
    bool clamp = false;
    for (int i = 0; i < GetShapeDim(); ++i)
    {
        if (!std::isfinite(locCoord[i]))
        {
            locCoord[i] = 0.;
            clamp       = true;
        }
        else if (locCoord[i] < -(1. + tol))
        {
            locCoord[i] = -(1. + tol);
            clamp       = true;
        }
        else if (locCoord[i] > (1. + tol))
        {
            locCoord[i] = 1. + tol;
            clamp       = true;
        }
    }
    return clamp;
}

References ASSERTL1, and GetShapeDim().

Referenced by Nektar::SpatialDomains::Geometry2D::NewtonIterationForLocCoord(), Nektar::SpatialDomains::Geometry3D::NewtonIterationForLocCoord(), Nektar::FieldUtils::ProcessWallNormalData::NewtonIterForLocCoordOnBndElmt(), v_ContainsPoint(), Nektar::SpatialDomains::Geometry2D::v_FindDistance(), Nektar::SpatialDomains::SegGeom::v_FindDistance(), Nektar::SpatialDomains::Geometry2D::v_GetLocCoords(), and Nektar::SpatialDomains::Geometry3D::v_GetLocCoords().

◆ ClearBoundingBox()

void Nektar::SpatialDomains::Geometry::ClearBoundingBox ( )

Definition at line 462 of file Geometry.cpp.

{
    m_boundingBox = {};
}

References m_boundingBox.

◆ ContainsPoint() [1/3]

bool Nektar::SpatialDomains::Geometry::ContainsPoint	(	const Array< OneD, const NekDouble > &	gloCoord,
		Array< OneD, NekDouble > &	locCoord,
		NekDouble	tol
	)

inline

Determine whether an element contains a particular Cartesian coordinate \((x,y,z)\).

See also: Geometry::ContainsPoint

Definition at line 486 of file Geometry.h.

{
    NekDouble dist;
    return v_ContainsPoint(gloCoord, locCoord, tol, dist);
}

References v_ContainsPoint().

◆ ContainsPoint() [2/3]

bool Nektar::SpatialDomains::Geometry::ContainsPoint	(	const Array< OneD, const NekDouble > &	gloCoord,
		Array< OneD, NekDouble > &	locCoord,
		NekDouble	tol,
		NekDouble &	dist
	)

inline

Determine whether an element contains a particular Cartesian coordinate \(\vec{x} = (x,y,z)\).

For curvilinear and non-affine elements (i.e. where the Jacobian varies as a function of the standard element coordinates), this is a non-linear optimisation problem that requires the use of a Newton iteration. Note therefore that this can be an expensive operation.

The parameter tol which is by default 0, can be used to expand the coordinate range of the standard element from \([-1,1]^d\) to \([-1-\epsilon,1+\epsilon\) to handle challenging edge cases. The function also returns the local coordinates corresponding to gloCoord that can be used to speed up subsequent searches.

Parameters

gloCoord	The coordinate \( (x,y,z) \).
locCoord	On exit, this is the local coordinate \(\vec{\xi}\) such that \(\chi(\vec{\xi}) = \vec{x}\).
tol	The tolerance used to dictate the bounding box of the standard coordinates \(\vec{\xi}\).
dist	On exit, returns the minimum distance between `gloCoord` and the quadrature points inside the element.

Returns: true if the coordinate gloCoord is contained in the element; false otherwise.

See also: Geometry::GetLocCoords.

Definition at line 522 of file Geometry.h.

{
    return v_ContainsPoint(gloCoord, locCoord, tol, dist);
}

References v_ContainsPoint().

◆ ContainsPoint() [3/3]

bool Nektar::SpatialDomains::Geometry::ContainsPoint	(	const Array< OneD, const NekDouble > &	gloCoord,
		NekDouble	tol = `0.0`
	)

inline

Determine whether an element contains a particular Cartesian coordinate \((x,y,z)\).

See also: Geometry::ContainsPoint

Definition at line 472 of file Geometry.h.

{
    Array<OneD, NekDouble> locCoord(GetCoordim(), 0.0);
    NekDouble dist;
    return v_ContainsPoint(gloCoord, locCoord, tol, dist);
}

References GetCoordim(), and v_ContainsPoint().

Referenced by Geometry_ContainsPoint().

◆ FillGeom()

void Nektar::SpatialDomains::Geometry::FillGeom ( )

inline

Populate the coordinate mapping Geometry::m_coeffs information from any children geometry elements.

See also: v_FillGeom()

Definition at line 461 of file Geometry.h.

{
    v_FillGeom();
}

References v_FillGeom().

Referenced by export_Geometry(), Nektar::LocalRegions::HexExp::v_GetCoord(), Nektar::LocalRegions::PrismExp::v_GetCoord(), Nektar::LocalRegions::QuadExp::v_GetCoord(), Nektar::LocalRegions::SegExp::v_GetCoord(), Nektar::LocalRegions::TriExp::v_GetCoord(), and Nektar::LocalRegions::Expansion::v_GetCoords().

◆ FindDistance()

NekDouble Nektar::SpatialDomains::Geometry::FindDistance	(	const Array< OneD, const NekDouble > &	xs,
		Array< OneD, NekDouble > &	xi
	)

inline

Definition at line 565 of file Geometry.h.

{
    return v_FindDistance(xs, xi);
}

References v_FindDistance().

◆ GenGeomFactors()

GeomFactorsUniquePtr Nektar::SpatialDomains::Geometry::GenGeomFactors ( LibUtilities::PointsKeyVector & keyTgt )

inline

Used by Expansion to generate associated GeomFactors.

Definition at line 430 of file Geometry.h.

{
    return v_GenGeomFactors(keyTgt);
}

References v_GenGeomFactors().

Referenced by Nektar::LocalRegions::Expansion::GenGeomFactors(), Geometry_GenGeomFactors(), Geometry_IsValid(), Nektar::SpatialDomains::Geometry3D::NewtonIterationForLocCoord(), Nektar::SpatialDomains::Geometry3D::NewtonIterationForLocCoord(), and Nektar::FieldUtils::ProcessWallNormalData::NewtonIterForLocCoordOnBndElmt().

◆ GetBoundingBox()

std::array< NekDouble, 6 > Nektar::SpatialDomains::Geometry::GetBoundingBox ( )

Generates the bounding box for the element.

For regular elements, the vertices are sufficient to define the extent of the bounding box. For non-regular elements, the extremes of the quadrature point coordinates are used. A 10% margin is added around this computed region to account for convex hull elements where the true extent of the element may extend slightly beyond the quadrature points.

Definition at line 388 of file Geometry.cpp.

{
    if (m_boundingBox.size() == 6)
    {
        return {{m_boundingBox[0], m_boundingBox[1], m_boundingBox[2],
                 m_boundingBox[3], m_boundingBox[4], m_boundingBox[5]}};
    }
    // NekDouble minx, miny, minz, maxx, maxy, maxz;
    Array<OneD, NekDouble> min(3), max(3);
 
    // Always get vertexes min/max
    PointGeom *p = GetVertex(0);
    Array<OneD, NekDouble> x(3, 0.0);
    p->GetCoords(x[0], x[1], x[2]);
    for (int j = 0; j < 3; ++j)
    {
        min[j] = x[j];
        max[j] = x[j];
    }
    for (int i = 1; i < GetNumVerts(); ++i)
    {
        p = GetVertex(i);
        p->GetCoords(x[0], x[1], x[2]);
        for (int j = 0; j < 3; ++j)
        {
            min[j] = (x[j] < min[j] ? x[j] : min[j]);
            max[j] = (x[j] > max[j] ? x[j] : max[j]);
        }
    }
    // If element is deformed loop over quadrature points
    NekDouble marginFactor = NekConstants::kGeomFactorsTol;
    if (CalcGeomType() != eRegular)
    {
        marginFactor = 0.1;
        const int nq = GetXmap()->GetTotPoints();
        Array<OneD, Array<OneD, NekDouble>> xvec(3);
        for (int j = 0; j < 3; ++j)
        {
            xvec[j] = Array<OneD, NekDouble>(nq, 0.0);
        }
        for (int j = 0; j < GetCoordim(); ++j)
        {
            GetXmap()->BwdTrans(m_coeffs[j], xvec[j]);
        }
        for (int j = 0; j < 3; ++j)
        {
            for (int i = 0; i < nq; ++i)
            {
                min[j] = (xvec[j][i] < min[j] ? xvec[j][i] : min[j]);
                max[j] = (xvec[j][i] > max[j] ? xvec[j][i] : max[j]);
            }
        }
    }
    // Add margin to bounding box, in order to
    // return the nearest element
    for (int j = 0; j < 3; ++j)
    {
        NekDouble margin =
            marginFactor * (max[j] - min[j]) + NekConstants::kFindDistanceMin;
        min[j] -= margin;
        max[j] += margin;
    }
 
    // save bounding box
    m_boundingBox = Array<OneD, NekDouble>(6);
    for (int j = 0; j < 3; ++j)
    {
        m_boundingBox[j]     = min[j];
        m_boundingBox[j + 3] = max[j];
    }
    // Return bounding box
    return {{min[0], min[1], min[2], max[0], max[1], max[2]}};
}

References CalcGeomType(), Nektar::SpatialDomains::eRegular, GetCoordim(), GetNumVerts(), GetVertex(), GetXmap(), Nektar::NekConstants::kFindDistanceMin, Nektar::NekConstants::kGeomFactorsTol, m_boundingBox, m_coeffs, tinysimd::max(), and tinysimd::min().

Referenced by Nektar::SpatialDomains::MeshGraph::GeomRTree::InsertGeom(), and MinMaxCheck().

◆ GetCoeffs()

const Array< OneD, const NekDouble > & Nektar::SpatialDomains::Geometry::GetCoeffs ( const int i ) const

inline

Return the coefficients of the transformation Geometry::m_xmap in coordinate direction i.

Definition at line 449 of file Geometry.h.

{
    return m_coeffs[i];
}

References m_coeffs.

Referenced by Nektar::FieldUtils::ProcessWallNormalData::BndElmtContainsPoint(), export_Geometry(), Nektar::FieldUtils::ProcessBodyFittedVelocity::GenPntwiseBodyFittedCoordSys(), Nektar::FieldUtils::ProcessWallNormalData::GetNormals(), Nektar::FieldUtils::ProcessBodyFittedVelocity::LocCoordForNearestPntOnBndElmt(), Nektar::LocalRegions::Expansion::v_GetCoords(), and Nektar::FieldUtils::ProcessWallNormalData::v_Process().

◆ GetCoord()

NekDouble Nektar::SpatialDomains::Geometry::GetCoord	(	const int	i,
		const Array< OneD, const NekDouble > &	Lcoord
	)

inline

Given local collapsed coordinate Lcoord, return the value of physical coordinate in direction i.

Definition at line 559 of file Geometry.h.

{
    return v_GetCoord(i, Lcoord);
}

References v_GetCoord().

Referenced by Nektar::SpatialDomains::Geometry2D::v_FindDistance(), Nektar::SpatialDomains::SegGeom::v_FindDistance(), Nektar::LocalRegions::HexExp::v_GetCoord(), Nektar::LocalRegions::PrismExp::v_GetCoord(), Nektar::LocalRegions::PyrExp::v_GetCoord(), Nektar::LocalRegions::QuadExp::v_GetCoord(), Nektar::LocalRegions::SegExp::v_GetCoord(), Nektar::LocalRegions::TetExp::v_GetCoord(), and Nektar::LocalRegions::TriExp::v_GetCoord().

◆ GetCoordim()

int Nektar::SpatialDomains::Geometry::GetCoordim ( ) const

inline

Return the coordinate dimension of this object (i.e. the dimension of the space in which this object is embedded).

Definition at line 277 of file Geometry.h.

{
    return m_coordim;
}

References m_coordim.

◆ GetDir()

int Nektar::SpatialDomains::Geometry::GetDir	(	const int	i,
		const int	j = `0`
	)		const

inline

Returns the element coordinate direction corresponding to a given face coordinate direction.

Definition at line 662 of file Geometry.h.

{
    return v_GetDir(faceidx, facedir);
}

References v_GetDir().

Referenced by Nektar::LocalRegions::Expansion3D::v_GetLocTracePhysVals(), Nektar::LocalRegions::Expansion2D::v_TraceNormLen(), and Nektar::LocalRegions::Expansion3D::v_TraceNormLen().

◆ GetEdge()

Geometry1D * Nektar::SpatialDomains::Geometry::GetEdge ( int i ) const

inline

Returns edge i of this object.

Definition at line 361 of file Geometry.h.

{
    return v_GetEdge(i);
}

References v_GetEdge().

Referenced by export_Geometry(), GetEid(), Nektar::SpatialDomains::MeshGraph::GetElementsFromEdge(), Nektar::SpatialDomains::HexGeom::SetUpLocalEdges(), Nektar::SpatialDomains::PrismGeom::SetUpLocalEdges(), Nektar::SpatialDomains::PyrGeom::SetUpLocalEdges(), Nektar::SpatialDomains::TetGeom::SetUpLocalEdges(), Nektar::GlobalMapping::UpdateGeometry(), Nektar::LocalRegions::Expansion2D::v_GenTraceExp(), and Nektar::LocalRegions::Expansion3D::v_TraceNormLen().

◆ GetEdgeFaceMap()

int Nektar::SpatialDomains::Geometry::GetEdgeFaceMap	(	int	i,
		int	j
	)		const

inline

Returns the standard element edge IDs that are connected to a given face.

For example, on a prism, edge 0 is connnected to faces 0 and 1; GetEdgeFaceMap(0,j) would therefore return the values 0 and 1 respectively. We assume that j runs between 0 and 1 inclusive, since every face is connected to precisely two faces for all 3D elements.

This function is used in the construction of the low-energy preconditioner.

Parameters

i	The edge to query connectivity for.
j	The local face index between 0 and 1 connected to this element.

See also: MultiRegions::PreconditionerLowEnergy

Definition at line 631 of file Geometry.h.

{
    return v_GetEdgeFaceMap(i, j);
}

References v_GetEdgeFaceMap().

Referenced by Nektar::LocalRegions::Expansion3D::v_BuildTransformationMatrix().

◆ GetEdgeNormalToFaceVert()

int Nektar::SpatialDomains::Geometry::GetEdgeNormalToFaceVert	(	int	i,
		int	j
	)		const

inline

Returns the standard lement edge IDs that are normal to a given face vertex.

For example, on a hexahedron, on face 0 at vertices 0,1,2,3 the edges normal to that face are 4,5,6,7, ; so GetEdgeNormalToFaceVert(0,j) would therefore return the values 4, 5, 6 and 7 respectively. We assume that j runs between 0 and 3 inclusive on a quadrilateral face and between 0 and 2 inclusive on a triangular face.

This is used to help set up a length scale normal to an face

Parameters

i	The face to query for the normal edge
j	The local vertex index between 0 and nverts on this face

Definition at line 653 of file Geometry.h.

{
    return v_GetEdgeNormalToFaceVert(i, j);
}

References v_GetEdgeNormalToFaceVert().

Referenced by Nektar::LocalRegions::Expansion3D::v_TraceNormLen().

◆ GetEid()

int Nektar::SpatialDomains::Geometry::GetEid ( int i ) const

Get the ID of edge i of this object.

Definition at line 83 of file Geometry.cpp.

{
    return GetEdge(i)->GetGlobalID();
}

References GetEdge(), and GetGlobalID().

◆ GetEorient()

StdRegions::Orientation Nektar::SpatialDomains::Geometry::GetEorient ( const int i ) const

inline

Returns the orientation of edge i with respect to the ordering of edges in the standard element.

Definition at line 378 of file Geometry.h.

{
    return v_GetEorient(i);
}

References v_GetEorient().

Referenced by export_Geometry(), Nektar::MultiRegions::DisContField::FindPeriodicTraces(), Nektar::LocalRegions::Expansion3D::GetEdgeInverseBoundaryMap(), Nektar::LocalRegions::Expansion2D::GetTraceInverseBoundaryMap(), Nektar::GlobalMapping::UpdateGeometry(), Nektar::LocalRegions::QuadExp::v_GetTraceOrient(), and Nektar::LocalRegions::TriExp::v_GetTraceOrient().

◆ GetFace()

Geometry2D * Nektar::SpatialDomains::Geometry::GetFace ( int i ) const

inline

Returns face i of this object.

Definition at line 369 of file Geometry.h.

{
    return v_GetFace(i);
}

References v_GetFace().

Referenced by export_Geometry(), GetFid(), Nektar::SpatialDomains::MeshGraph::PopulateFaceToElMap(), Nektar::GlobalMapping::UpdateGeometry(), Nektar::LocalRegions::Expansion3D::v_GenTraceExp(), and Nektar::LocalRegions::Expansion3D::v_TraceNormLen().

◆ GetFid()

int Nektar::SpatialDomains::Geometry::GetFid ( int i ) const

Get the ID of face i of this object.

Definition at line 91 of file Geometry.cpp.

{
    return GetFace(i)->GetGlobalID();
}

References GetFace(), and GetGlobalID().

◆ GetForient()

StdRegions::Orientation Nektar::SpatialDomains::Geometry::GetForient ( const int i ) const

inline

Returns the orientation of face i with respect to the ordering of faces in the standard element.

Definition at line 387 of file Geometry.h.

{
    return v_GetForient(i);
}

References v_GetForient().

Referenced by export_Geometry(), and Nektar::LocalRegions::Expansion3D::v_GetTraceOrient().

◆ GetGlobalID()

int Nektar::SpatialDomains::Geometry::GetGlobalID ( void ) const

inline

Get the ID of this object.

Definition at line 314 of file Geometry.h.

{
    return m_globalID;
}

References m_globalID.

◆ GetLocCoords()

NekDouble Nektar::SpatialDomains::Geometry::GetLocCoords	(	const Array< OneD, const NekDouble > &	coords,
		Array< OneD, NekDouble > &	Lcoords
	)

inline

Determine the local collapsed coordinates that correspond to a given Cartesian coordinate for this geometry object.

For curvilinear and non-affine elements (i.e. where the Jacobian varies as a function of the standard element coordinates), this is a non-linear optimisation problem that requires the use of a Newton iteration. Note therefore that this can be an expensive operation.

Note that, clearly, the provided Cartesian coordinate lie outside the element. The function therefore returns the minimum distance from some position in the element to . Lcoords will also be constrained to fit within the range \([-1,1]^d\) where \( d \) is the dimension of the element.

Parameters

coords	Input Cartesian global coordinates
Lcoords	Corresponding local coordinates

Returns: Distance between obtained coordinates and provided ones.

Definition at line 549 of file Geometry.h.

{
    return v_GetLocCoords(coords, Lcoords);
}

References v_GetLocCoords().

◆ GetNumEdges()

int Nektar::SpatialDomains::Geometry::GetNumEdges ( ) const

inline

Get the number of edges of this object.

Definition at line 403 of file Geometry.h.

{
    return v_GetNumEdges();
}

References v_GetNumEdges().

Referenced by Nektar::SpatialDomains::MeshGraph::CheckRange(), export_Geometry(), Nektar::SpatialDomains::MeshGraph::GetElementsFromEdge(), and Nektar::SpatialDomains::MeshGraphIOXml::WriteXMLGeometry().

◆ GetNumFaces()

int Nektar::SpatialDomains::Geometry::GetNumFaces ( ) const

inline

Get the number of faces of this object.

Definition at line 411 of file Geometry.h.

{
    return v_GetNumFaces();
}

References v_GetNumFaces().

Referenced by Nektar::SpatialDomains::MeshGraph::CheckRange(), export_Geometry(), and Nektar::SpatialDomains::MeshGraphIOXml::WriteXMLGeometry().

◆ GetNumVerts()

int Nektar::SpatialDomains::Geometry::GetNumVerts ( ) const

inline

Get the number of vertices of this object.

Definition at line 395 of file Geometry.h.

{
    return v_GetNumVerts();
}

References v_GetNumVerts().

Referenced by Nektar::SolverUtils::CouplingCwipi::AddElementsToMesh(), Nektar::SpatialDomains::MeshGraph::CheckRange(), Nektar::SpatialDomains::MeshGraph::CheckRange(), export_Geometry(), Nektar::MultiRegions::DisContField::FindPeriodicTraces(), GetBoundingBox(), Nektar::MappingIdealToRef(), Nektar::FieldUtils::MappingIdealToRef(), Nektar::SolverUtils::DriverArnoldi::MaskInit(), Nektar::SpatialDomains::MeshGraph::PRefinementElmts(), Nektar::GlobalMapping::UpdateGeometry(), Nektar::LocalRegions::Expansion3D::v_GenTraceExp(), Nektar::FieldUtils::ProcessPowerSpectrum::v_Process(), Nektar::LocalRegions::Expansion2D::v_TraceNormLen(), Nektar::LocalRegions::Expansion3D::v_TraceNormLen(), Nektar::FieldUtils::ProcessForceDecompose::VolumeIntegrateForce(), and Nektar::SpatialDomains::MeshGraphIOXml::WriteXMLGeometry().

◆ GetShapeDim()

int Nektar::SpatialDomains::Geometry::GetShapeDim ( ) const

inline

Get the object's shape dimension.

For example, a segment is one dimensional and quadrilateral is two dimensional.

Definition at line 422 of file Geometry.h.

{
    return v_GetShapeDim();
}

References v_GetShapeDim().

Referenced by ClampLocCoords(), export_Geometry(), Nektar::SpatialDomains::MeshGraph::GetCompositeString(), Nektar::SpatialDomains::MeshGraphIO::GetCompositeString(), GetTid(), and v_ContainsPoint().

◆ GetShapeType()

LibUtilities::ShapeType Nektar::SpatialDomains::Geometry::GetShapeType ( void )

inline

Get the geometric shape type of this object.

Definition at line 294 of file Geometry.h.

{
    return m_shapeType;
}

References m_shapeType.

Referenced by Nektar::SpatialDomains::MeshGraph::CheckRange(), Nektar::SpatialDomains::MeshGraph::DefineBasisKeyFromExpansionType(), Nektar::SpatialDomains::MeshGraph::DefineBasisKeyFromExpansionTypeHomo(), export_Geometry(), Nektar::SpatialDomains::MeshGraph::GetCompositeString(), Nektar::SpatialDomains::MeshGraphIO::GetCompositeString(), Nektar::FieldUtils::MappingIdealToRef(), Nektar::GlobalMapping::UpdateGeometry(), Nektar::SpatialDomains::MeshGraphIOXml::v_ReadElements3D(), and Nektar::SpatialDomains::MeshGraphIOXmlCompressed::v_ReadElements3D().

◆ GetTid()

int Nektar::SpatialDomains::Geometry::GetTid ( int i ) const

inline

Get the ID of trace i of this object.

The trace element is the facet one dimension lower than the object; for example, a quadrilateral has four trace segments forming its boundary.

Definition at line 333 of file Geometry.h.

{
    const int nDim = GetShapeDim();
    return nDim == 1   ? GetVid(i)
           : nDim == 2 ? GetEid(i)
           : nDim == 3 ? GetFid(i)
                       : 0;
}

References GetEid(), GetFid(), GetShapeDim(), and GetVid().

Referenced by export_Geometry().

◆ GetVertex()

PointGeom * Nektar::SpatialDomains::Geometry::GetVertex ( int i ) const

inline

Returns vertex i of this object.

Definition at line 353 of file Geometry.h.

{
    return v_GetVertex(i);
}

References v_GetVertex().

◆ GetVertexEdgeMap()

int Nektar::SpatialDomains::Geometry::GetVertexEdgeMap	(	int	i,
		int	j
	)		const

inline

Returns the standard element edge IDs that are connected to a given vertex.

For example, on a prism, vertex 0 is connnected to edges 0, 3, and 4; GetVertexEdgeMap(0,j) would therefore return the values 0, 1 and 4 respectively. We assume that j runs between 0 and 2 inclusive, which is true for every 3D element asides from the pyramid.

This function is used in the construction of the low-energy preconditioner.

Parameters

i	The vertex to query connectivity for.
j	The local edge index between 0 and 2 connected to this element.

Todo:: Expand to work with pyramid elements.

See also: MultiRegions::PreconditionerLowEnergy

Definition at line 588 of file Geometry.h.

{
    return v_GetVertexEdgeMap(i, j);
}

References v_GetVertexEdgeMap().

Referenced by Nektar::LocalRegions::Expansion3D::v_BuildTransformationMatrix().

◆ GetVertexFaceMap()

int Nektar::SpatialDomains::Geometry::GetVertexFaceMap	(	int	i,
		int	j
	)		const

inline

Returns the standard element face IDs that are connected to a given vertex.

For example, on a hexahedron, vertex 0 is connnected to faces 0, 1, and 4; GetVertexFaceMap(0,j) would therefore return the values 0, 1 and 4 respectively. We assume that j runs between 0 and 2 inclusive, which is true for every 3D element asides from the pyramid.

This is used in the construction of the low-energy preconditioner.

Parameters

i	The vertex to query connectivity for.
j	The local face index between 0 and 2 connected to this element.

Todo:: Expand to work with pyramid elements.

See also: MultiRegions::PreconditionerLowEnergy

Definition at line 610 of file Geometry.h.

{
    return v_GetVertexFaceMap(i, j);
}

References v_GetVertexFaceMap().

Referenced by Nektar::LocalRegions::Expansion3D::v_BuildTransformationMatrix().

◆ GetVid()

int Nektar::SpatialDomains::Geometry::GetVid ( int i ) const

inline

Returns global id of vertex i of this object.

Definition at line 345 of file Geometry.h.

{
    return v_GetVid(i);
}

References v_GetVid().

◆ GetXmap()

StdRegions::StdExpansionSharedPtr Nektar::SpatialDomains::Geometry::GetXmap ( ) const

inline

Return the mapping object Geometry::m_xmap that represents the coordinate transformation from standard element to physical element.

Definition at line 440 of file Geometry.h.

{
    return v_GetXmap();
}

References v_GetXmap().

◆ MinMaxCheck()

bool Nektar::SpatialDomains::Geometry::MinMaxCheck ( const Array< OneD, const NekDouble > & gloCoord )

Check if given global coord is within the BoundingBox of the element.

Parameters

coords Input Cartesian global coordinates

Returns: True if within distance or False otherwise.

Definition at line 502 of file Geometry.cpp.

{
    // Validation checks
    ASSERTL1(gloCoord.size() >= m_coordim,
             "Expects number of global coordinates supplied to be greater than "
             "or equal to the mesh dimension.");
 
    std::array<NekDouble, 6> minMax = GetBoundingBox();
    for (int i = 0; i < m_coordim; ++i)
    {
        if ((gloCoord[i] < minMax[i]) || (gloCoord[i] > minMax[i + 3]))
        {
            return false;
        }
    }
    return true;
}

References ASSERTL1, GetBoundingBox(), and m_coordim.

Referenced by PreliminaryCheck().

◆ PreliminaryCheck()

int Nektar::SpatialDomains::Geometry::PreliminaryCheck ( const Array< OneD, const NekDouble > & gloCoord )

A fast and robust check if a given global coord is outside of a deformed element. For regular elements, this check is unnecessary.

Parameters

coords Input Cartesian global coordinates

Returns: 1 is inside of the element. 0 maybe inside -1 outside of the element

Definition at line 477 of file Geometry.cpp.

{
    // bounding box check
    if (!MinMaxCheck(gloCoord))
    {
        return -1;
    }
 
    // regular element check
    if (CalcGeomType() == eRegular)
    {
        return 0;
    }
 
    // All left check for straight edges/plane surfaces
    return v_AllLeftCheck(gloCoord);
}

References CalcGeomType(), Nektar::SpatialDomains::eRegular, MinMaxCheck(), and v_AllLeftCheck().

Referenced by v_ContainsPoint().

◆ Reset()

void Nektar::SpatialDomains::Geometry::Reset	(	CurveMap &	curvedEdges,
		CurveMap &	curvedFaces
	)

inline

Reset this geometry object: unset the current state, zero Geometry::m_coeffs and remove allocated GeomFactors.

Definition at line 671 of file Geometry.h.

{
    v_Reset(curvedEdges, curvedFaces);
}

References v_Reset().

◆ ResetNonRecursive()

void Nektar::SpatialDomains::Geometry::ResetNonRecursive	(	CurveMap &	curvedEdges,
		CurveMap &	curvedFaces
	)

inline

Reset this geometry object non-recursively: unset the current state, zero Geometry::m_coeffs and remove allocated GeomFactors.

Definition at line 680 of file Geometry.h.

{
    Geometry::v_Reset(curvedEdges, curvedFaces);
}

References v_Reset().

◆ SetCoordim()

void Nektar::SpatialDomains::Geometry::SetCoordim ( int coordim )

inline

Sets the coordinate dimension of this object (i.e. the dimension of the space in which this object is embedded).

Definition at line 286 of file Geometry.h.

{
    m_coordim = dim;
}

References m_coordim.

◆ SetGlobalID()

void Nektar::SpatialDomains::Geometry::SetGlobalID ( int globalid )

inline

Set the ID of this object.

Definition at line 322 of file Geometry.h.

{
    m_globalID = globalid;
}

References m_globalID.

Referenced by export_Geometry().

◆ Setup()

void Nektar::SpatialDomains::Geometry::Setup ( )

inline

Definition at line 686 of file Geometry.h.

{
    v_Setup();
}

References v_Setup().

Referenced by export_Geometry(), Geometry_GenGeomFactors(), and Geometry_IsValid().

◆ SetUpCoeffs()

void Nektar::SpatialDomains::Geometry::SetUpCoeffs ( const int nCoeffs )

inlineprotected

Initialise the Geometry::m_coeffs array.

Definition at line 694 of file Geometry.h.

{
    m_coeffs = std::vector<Array<OneD, NekDouble>>(m_coordim);
 
    for (int i = 0; i < m_coordim; ++i)
    {
        m_coeffs[i] = Array<OneD, NekDouble>(nCoeffs, 0.0);
    }
}

References m_coeffs, and m_coordim.

◆ v_AllLeftCheck()

int Nektar::SpatialDomains::Geometry::v_AllLeftCheck ( const Array< OneD, const NekDouble > & gloCoord )

protectedvirtual

Reimplemented in Nektar::SpatialDomains::Geometry3D, Nektar::SpatialDomains::QuadGeom, and Nektar::SpatialDomains::TriGeom.

Definition at line 205 of file Geometry.cpp.

{
    return 0;
}

Referenced by PreliminaryCheck().

◆ v_CalcGeomType()

GeomType Nektar::SpatialDomains::Geometry::v_CalcGeomType ( )

protectedvirtual

Calculates the GeomType (deformed, regular etc).

Reimplemented in Nektar::SpatialDomains::HexGeom, Nektar::SpatialDomains::PrismGeom, Nektar::SpatialDomains::PyrGeom, Nektar::SpatialDomains::QuadGeom, Nektar::SpatialDomains::SegGeom, Nektar::SpatialDomains::TetGeom, and Nektar::SpatialDomains::TriGeom.

Definition at line 187 of file Geometry.cpp.

{
    NEKERROR(ErrorUtil::efatal,
             "This function is only valid for shape type geometries");
    return eNoGeomType;
}

References Nektar::ErrorUtil::efatal, Nektar::SpatialDomains::eNoGeomType, and NEKERROR.

Referenced by CalcGeomType().

◆ v_CalculateInverseIsoParam()

void Nektar::SpatialDomains::Geometry::v_CalculateInverseIsoParam ( )

protectedvirtual

Reimplemented in Nektar::SpatialDomains::Geometry2D, and Nektar::SpatialDomains::Geometry3D.

Definition at line 211 of file Geometry.cpp.

{
    NEKERROR(ErrorUtil::efatal,
             "This function is only valid for shape type geometries");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

◆ v_ContainsPoint()

bool Nektar::SpatialDomains::Geometry::v_ContainsPoint	(	const Array< OneD, const NekDouble > &	gloCoord,
		Array< OneD, NekDouble > &	locCoord,
		NekDouble	tol,
		NekDouble &	dist
	)

protectedvirtual

Determine whether an element contains a particular Cartesian coordinate \(\vec{x} = (x,y,z)\).

For curvilinear and non-affine elements (i.e. where the Jacobian varies as a function of the standard element coordinates), this is a non-linear optimisation problem that requires the use of a Newton iteration. Note therefore that this can be an expensive operation.

The parameter tol which is by default 0, can be used to expand the coordinate range of the standard element from \([-1,1]^d\) to \([-1-\epsilon,1+\epsilon\) to handle challenging edge cases. The function also returns the local coordinates corresponding to gloCoord that can be used to speed up subsequent searches.

Parameters

gloCoord	The coordinate \( (x,y,z) \).
locCoord	On exit, this is the local coordinate \(\vec{\xi}\) such that \(\chi(\vec{\xi}) = \vec{x}\).
tol	The tolerance used to dictate the bounding box of the standard coordinates \(\vec{\xi}\).
dist	On exit, returns the minimum distance between `gloCoord` and the quadrature points inside the element.

Returns: true if the coordinate gloCoord is contained in the element; false otherwise.

See also: Geometry::GetLocCoords. dist is assigned value for curved elements

Reimplemented in Nektar::SpatialDomains::Geometry0D.

Definition at line 231 of file Geometry.cpp.

{
    int inside = PreliminaryCheck(gloCoord);
    if (inside == -1)
    {
        dist = std::numeric_limits<double>::max();
        return false;
    }
    dist = GetLocCoords(gloCoord, locCoord);
    if (inside == 1)
    {
        dist = 0.;
        return true;
    }
    else
    {
        Array<OneD, NekDouble> eta(GetShapeDim(), 0.);
        m_xmap->LocCoordToLocCollapsed(locCoord, eta);
        if (ClampLocCoords(eta, tol))
        {
            if (CalcGeomType() == eRegular)
            {
                dist = std::numeric_limits<double>::max();
            }
            return false;
        }
        return 3 != m_coordim ||
               (LibUtilities::eTriangle != m_shapeType &&
                LibUtilities::eQuadrilateral != m_shapeType) ||
               dist <= tol;
    }
}

References CalcGeomType(), ClampLocCoords(), Nektar::LibUtilities::eQuadrilateral, Nektar::SpatialDomains::eRegular, Nektar::LibUtilities::eTriangle, GetLocCoords(), GetShapeDim(), m_coordim, m_shapeType, m_xmap, and PreliminaryCheck().

Referenced by ContainsPoint(), ContainsPoint(), and ContainsPoint().

◆ v_FillGeom()

void Nektar::SpatialDomains::Geometry::v_FillGeom ( )

protectedvirtual

Populate the coordinate mapping Geometry::m_coeffs information from any children geometry elements.

See also: v_FillGeom()

Reimplemented in Nektar::SpatialDomains::HexGeom, Nektar::SpatialDomains::PrismGeom, Nektar::SpatialDomains::PyrGeom, Nektar::SpatialDomains::QuadGeom, Nektar::SpatialDomains::SegGeom, Nektar::SpatialDomains::TetGeom, and Nektar::SpatialDomains::TriGeom.

Definition at line 357 of file Geometry.cpp.

{
    NEKERROR(ErrorUtil::efatal,
             "This function is only valid for expansion type geometries");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by FillGeom(), Nektar::SpatialDomains::Geometry1D::v_GetLocCoords(), Nektar::SpatialDomains::Geometry2D::v_GetLocCoords(), and Nektar::SpatialDomains::Geometry3D::v_GetLocCoords().

◆ v_FindDistance()

NekDouble Nektar::SpatialDomains::Geometry::v_FindDistance	(	const Array< OneD, const NekDouble > &	xs,
		Array< OneD, NekDouble > &	xi
	)

protectedvirtual

Reimplemented in Nektar::SpatialDomains::Geometry2D, and Nektar::SpatialDomains::SegGeom.

Definition at line 266 of file Geometry.cpp.

{
    NEKERROR(ErrorUtil::efatal,
             "This function has not been defined for this geometry");
    return false;
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by FindDistance().

◆ v_GenGeomFactors()

GeomFactorsUniquePtr Nektar::SpatialDomains::Geometry::v_GenGeomFactors ( LibUtilities::PointsKeyVector & keyTgt )

protectedvirtual

Used by Expansion to generate associated GeomFactors.

Reimplemented in Nektar::SpatialDomains::HexGeom, Nektar::SpatialDomains::PointGeom, Nektar::SpatialDomains::PrismGeom, Nektar::SpatialDomains::PyrGeom, Nektar::SpatialDomains::QuadGeom, Nektar::SpatialDomains::SegGeom, Nektar::SpatialDomains::TetGeom, and Nektar::SpatialDomains::TriGeom.

Definition at line 197 of file Geometry.cpp.

{
    NEKERROR(ErrorUtil::efatal,
             "This function is only valid for shape type geometries");
    return GeomFactorsUniquePtr();
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GenGeomFactors(), and Nektar::SpatialDomains::Geometry2D::NewtonIterationForLocCoord().

◆ v_GetCoord()

NekDouble Nektar::SpatialDomains::Geometry::v_GetCoord	(	const int	i,
		const Array< OneD, const NekDouble > &	Lcoord
	)

protectedvirtual

Given local collapsed coordinate Lcoord, return the value of physical coordinate in direction i.

Reimplemented in Nektar::SpatialDomains::Geometry3D, Nektar::SpatialDomains::QuadGeom, Nektar::SpatialDomains::SegGeom, and Nektar::SpatialDomains::TriGeom.

Definition at line 333 of file Geometry.cpp.

{
    NEKERROR(ErrorUtil::efatal,
             "This function is only valid for expansion type geometries");
    return 0.0;
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GetCoord().

◆ v_GetDir()

int Nektar::SpatialDomains::Geometry::v_GetDir	(	const int	i,
		const int	j
	)		const

protectedvirtual

Returns the element coordinate direction corresponding to a given face coordinate direction.

Reimplemented in Nektar::SpatialDomains::HexGeom, Nektar::SpatialDomains::PrismGeom, Nektar::SpatialDomains::PyrGeom, Nektar::SpatialDomains::QuadGeom, Nektar::SpatialDomains::TetGeom, and Nektar::SpatialDomains::TriGeom.

Definition at line 322 of file Geometry.cpp.

{
    NEKERROR(ErrorUtil::efatal,
             "This function has not been defined for this geometry");
    return 0;
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GetDir().

◆ v_GetEdge()

Geometry1D * Nektar::SpatialDomains::Geometry::v_GetEdge ( const int i ) const

protectedvirtual

Returns edge i of this object.

Reimplemented in Nektar::SpatialDomains::HexGeom, Nektar::SpatialDomains::PrismGeom, Nektar::SpatialDomains::PyrGeom, Nektar::SpatialDomains::QuadGeom, Nektar::SpatialDomains::TetGeom, and Nektar::SpatialDomains::TriGeom.

Definition at line 109 of file Geometry.cpp.

{
    NEKERROR(ErrorUtil::efatal,
             "This function is only valid for shape type geometries");
    return nullptr;
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GetEdge().

◆ v_GetEdgeFaceMap()

int Nektar::SpatialDomains::Geometry::v_GetEdgeFaceMap	(	int	i,
		int	j
	)		const

protectedvirtual

Returns the standard element edge IDs that are connected to a given face.

For example, on a prism, edge 0 is connnected to faces 0 and 1; GetEdgeFaceMap(0,j) would therefore return the values 0 and 1 respectively. We assume that j runs between 0 and 1 inclusive, since every face is connected to precisely two faces for all 3D elements.

This function is used in the construction of the low-energy preconditioner.

Parameters

i	The edge to query connectivity for.
j	The local face index between 0 and 1 connected to this element.

See also: MultiRegions::PreconditionerLowEnergy

Reimplemented in Nektar::SpatialDomains::HexGeom, Nektar::SpatialDomains::PrismGeom, and Nektar::SpatialDomains::TetGeom.

Definition at line 300 of file Geometry.cpp.

{
    NEKERROR(ErrorUtil::efatal,
             "This function has not been defined for this geometry");
    return 0;
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GetEdgeFaceMap().

◆ v_GetEdgeNormalToFaceVert()

int Nektar::SpatialDomains::Geometry::v_GetEdgeNormalToFaceVert	(	const int	i,
		const int	j
	)		const

protectedvirtual

Returns the standard lement edge IDs that are normal to a given face vertex.

For example, on a hexahedron, on face 0 at vertices 0,1,2,3 the edges normal to that face are 4,5,6,7, ; so GetEdgeNormalToFaceVert(0,j) would therefore return the values 4, 5, 6 and 7 respectively. We assume that j runs between 0 and 3 inclusive on a quadrilateral face and between 0 and 2 inclusive on a triangular face.

This is used to help set up a length scale normal to an face

Parameters

i	The face to query for the normal edge
j	The local vertex index between 0 and nverts on this face

Reimplemented in Nektar::SpatialDomains::HexGeom, Nektar::SpatialDomains::PrismGeom, Nektar::SpatialDomains::PyrGeom, and Nektar::SpatialDomains::TetGeom.

Definition at line 311 of file Geometry.cpp.

{
    NEKERROR(ErrorUtil::efatal,
             "This function has not been defined for this geometry");
    return 0;
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GetEdgeNormalToFaceVert().

◆ v_GetEorient()

StdRegions::Orientation Nektar::SpatialDomains::Geometry::v_GetEorient ( const int i ) const

protectedvirtual

Returns the orientation of edge i with respect to the ordering of edges in the standard element.

Reimplemented in Nektar::SpatialDomains::HexGeom, Nektar::SpatialDomains::PrismGeom, Nektar::SpatialDomains::PyrGeom, Nektar::SpatialDomains::QuadGeom, Nektar::SpatialDomains::TetGeom, and Nektar::SpatialDomains::TriGeom.

Definition at line 139 of file Geometry.cpp.

{
    NEKERROR(ErrorUtil::efatal,
             "This function is not valid for this geometry.");
    return StdRegions::eForwards;
}

References Nektar::ErrorUtil::efatal, Nektar::StdRegions::eForwards, and NEKERROR.

Referenced by GetEorient().

◆ v_GetFace()

Geometry2D * Nektar::SpatialDomains::Geometry::v_GetFace ( const int i ) const

protectedvirtual

Returns face i of this object.

Reimplemented in Nektar::SpatialDomains::HexGeom, Nektar::SpatialDomains::PrismGeom, Nektar::SpatialDomains::PyrGeom, and Nektar::SpatialDomains::TetGeom.

Definition at line 119 of file Geometry.cpp.

{
    NEKERROR(ErrorUtil::efatal,
             "This function is only valid for shape type geometries");
    return nullptr;
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GetFace().

◆ v_GetForient()

StdRegions::Orientation Nektar::SpatialDomains::Geometry::v_GetForient ( const int i ) const

protectedvirtual

Returns the orientation of face i with respect to the ordering of faces in the standard element.

Reimplemented in Nektar::SpatialDomains::HexGeom, Nektar::SpatialDomains::PrismGeom, Nektar::SpatialDomains::PyrGeom, and Nektar::SpatialDomains::TetGeom.

Definition at line 150 of file Geometry.cpp.

{
    NEKERROR(ErrorUtil::efatal,
             "This function is not valid for this geometry.");
    return StdRegions::eFwd;
}

References Nektar::ErrorUtil::efatal, Nektar::StdRegions::eFwd, and NEKERROR.

Referenced by GetForient().

◆ v_GetLocCoords()

NekDouble Nektar::SpatialDomains::Geometry::v_GetLocCoords	(	const Array< OneD, const NekDouble > &	coords,
		Array< OneD, NekDouble > &	Lcoords
	)

protectedvirtual

Determine the local collapsed coordinates that correspond to a given Cartesian coordinate for this geometry object.

For curvilinear and non-affine elements (i.e. where the Jacobian varies as a function of the standard element coordinates), this is a non-linear optimisation problem that requires the use of a Newton iteration. Note therefore that this can be an expensive operation.

Note that, clearly, the provided Cartesian coordinate lie outside the element. The function therefore returns the minimum distance from some position in the element to . Lcoords will also be constrained to fit within the range \([-1,1]^d\) where \( d \) is the dimension of the element.

Parameters

coords	Input Cartesian global coordinates
Lcoords	Corresponding local coordinates

Returns: Distance between obtained coordinates and provided ones.

Reimplemented in Nektar::SpatialDomains::Geometry1D, Nektar::SpatialDomains::Geometry2D, and Nektar::SpatialDomains::Geometry3D.

Definition at line 345 of file Geometry.cpp.

{
    NEKERROR(ErrorUtil::efatal,
             "This function is only valid for expansion type geometries");
    return 0.0;
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GetLocCoords().

◆ v_GetNumEdges()

int Nektar::SpatialDomains::Geometry::v_GetNumEdges ( ) const

protectedvirtual

Get the number of edges of this object.

Reimplemented in Nektar::SpatialDomains::HexGeom, Nektar::SpatialDomains::PrismGeom, Nektar::SpatialDomains::PyrGeom, Nektar::SpatialDomains::QuadGeom, Nektar::SpatialDomains::TetGeom, and Nektar::SpatialDomains::TriGeom.

Definition at line 161 of file Geometry.cpp.

{
    return 0;
}

Referenced by GetNumEdges().

◆ v_GetNumFaces()

int Nektar::SpatialDomains::Geometry::v_GetNumFaces ( ) const

protectedvirtual

Get the number of faces of this object.

Reimplemented in Nektar::SpatialDomains::HexGeom, Nektar::SpatialDomains::PrismGeom, Nektar::SpatialDomains::PyrGeom, and Nektar::SpatialDomains::TetGeom.

Definition at line 169 of file Geometry.cpp.

{
    return 0;
}

Referenced by GetNumFaces().

◆ v_GetNumVerts()

int Nektar::SpatialDomains::Geometry::v_GetNumVerts ( ) const

protectedvirtual

Get the number of vertices of this object.

Reimplemented in Nektar::SpatialDomains::HexGeom, Nektar::SpatialDomains::PrismGeom, Nektar::SpatialDomains::PyrGeom, Nektar::SpatialDomains::QuadGeom, Nektar::SpatialDomains::TetGeom, Nektar::SpatialDomains::TriGeom, and Nektar::SpatialDomains::SegGeom.

Definition at line 129 of file Geometry.cpp.

{
    NEKERROR(ErrorUtil::efatal,
             "This function is only valid for shape type geometries");
    return 0;
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GetNumVerts().

◆ v_GetShapeDim()

int Nektar::SpatialDomains::Geometry::v_GetShapeDim ( ) const

protectedvirtual

Get the object's shape dimension.

For example, a segment is one dimensional and quadrilateral is two dimensional.

Reimplemented in Nektar::SpatialDomains::Geometry0D, Nektar::SpatialDomains::Geometry1D, Nektar::SpatialDomains::Geometry2D, and Nektar::SpatialDomains::Geometry3D.

Definition at line 177 of file Geometry.cpp.

{
    NEKERROR(ErrorUtil::efatal,
             "This function is only valid for shape type geometries");
    return 0;
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GetShapeDim().

◆ v_GetVertex()

PointGeom * Nektar::SpatialDomains::Geometry::v_GetVertex ( const int i ) const

protectedvirtual

Returns vertex i of this object.

Reimplemented in Nektar::SpatialDomains::HexGeom, Nektar::SpatialDomains::PrismGeom, Nektar::SpatialDomains::PyrGeom, Nektar::SpatialDomains::QuadGeom, Nektar::SpatialDomains::TetGeom, Nektar::SpatialDomains::TriGeom, and Nektar::SpatialDomains::SegGeom.

Definition at line 99 of file Geometry.cpp.

{
    NEKERROR(ErrorUtil::efatal,
             "This function is only valid for shape type geometries");
    return nullptr;
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GetVertex().

◆ v_GetVertexEdgeMap()

int Nektar::SpatialDomains::Geometry::v_GetVertexEdgeMap	(	int	i,
		int	j
	)		const

protectedvirtual

Returns the standard element edge IDs that are connected to a given vertex.

For example, on a prism, vertex 0 is connnected to edges 0, 3, and 4; GetVertexEdgeMap(0,j) would therefore return the values 0, 1 and 4 respectively. We assume that j runs between 0 and 2 inclusive, which is true for every 3D element asides from the pyramid.

This function is used in the construction of the low-energy preconditioner.

Parameters

i	The vertex to query connectivity for.
j	The local edge index between 0 and 2 connected to this element.

Todo:: Expand to work with pyramid elements.

See also: MultiRegions::PreconditionerLowEnergy

Reimplemented in Nektar::SpatialDomains::HexGeom, Nektar::SpatialDomains::PrismGeom, and Nektar::SpatialDomains::TetGeom.

Definition at line 278 of file Geometry.cpp.

{
    NEKERROR(ErrorUtil::efatal,
             "This function has not been defined for this geometry");
    return 0;
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GetVertexEdgeMap().

◆ v_GetVertexFaceMap()

int Nektar::SpatialDomains::Geometry::v_GetVertexFaceMap	(	int	i,
		int	j
	)		const

protectedvirtual

Returns the standard element face IDs that are connected to a given vertex.

For example, on a hexahedron, vertex 0 is connnected to faces 0, 1, and 4; GetVertexFaceMap(0,j) would therefore return the values 0, 1 and 4 respectively. We assume that j runs between 0 and 2 inclusive, which is true for every 3D element asides from the pyramid.

This is used in the construction of the low-energy preconditioner.

Parameters

i	The vertex to query connectivity for.
j	The local face index between 0 and 2 connected to this element.

Todo:: Expand to work with pyramid elements.

See also: MultiRegions::PreconditionerLowEnergy

Reimplemented in Nektar::SpatialDomains::HexGeom, Nektar::SpatialDomains::PrismGeom, and Nektar::SpatialDomains::TetGeom.

Definition at line 289 of file Geometry.cpp.

{
    NEKERROR(ErrorUtil::efatal,
             "This function has not been defined for this geometry");
    return 0;
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GetVertexFaceMap().

◆ v_GetVid()

int Nektar::SpatialDomains::Geometry::v_GetVid ( int i ) const

protectedvirtual

Get the ID of vertex i of this object.

Reimplemented in Nektar::SpatialDomains::PointGeom.

Definition at line 75 of file Geometry.cpp.

{
    return GetVertex(i)->GetGlobalID();
}

References GetGlobalID(), and GetVertex().

Referenced by GetVid().

◆ v_GetXmap()

StdRegions::StdExpansionSharedPtr Nektar::SpatialDomains::Geometry::v_GetXmap ( ) const

protectedvirtual

Return the mapping object Geometry::m_xmap that represents the coordinate transformation from standard element to physical element.

Definition at line 220 of file Geometry.cpp.

{
    return m_xmap;
}

References m_xmap.

Referenced by GetXmap().

◆ v_Reset()

void Nektar::SpatialDomains::Geometry::v_Reset	(	CurveMap &	curvedEdges,
		CurveMap &	curvedFaces
	)

protectedvirtual

Reset this geometry object: unset the current state, zero Geometry::m_coeffs and remove allocated GeomFactors.

Reimplemented in Nektar::SpatialDomains::HexGeom, Nektar::SpatialDomains::PrismGeom, Nektar::SpatialDomains::PyrGeom, Nektar::SpatialDomains::QuadGeom, Nektar::SpatialDomains::SegGeom, Nektar::SpatialDomains::TetGeom, and Nektar::SpatialDomains::TriGeom.

Definition at line 366 of file Geometry.cpp.

{
    // Reset state
    m_state = eNotFilled;
}

References Nektar::SpatialDomains::eNotFilled, and m_state.

Referenced by Reset(), ResetNonRecursive(), Nektar::SpatialDomains::HexGeom::v_Reset(), Nektar::SpatialDomains::PrismGeom::v_Reset(), Nektar::SpatialDomains::PyrGeom::v_Reset(), Nektar::SpatialDomains::QuadGeom::v_Reset(), Nektar::SpatialDomains::SegGeom::v_Reset(), Nektar::SpatialDomains::TetGeom::v_Reset(), and Nektar::SpatialDomains::TriGeom::v_Reset().

◆ v_Setup()

void Nektar::SpatialDomains::Geometry::v_Setup ( )

protectedvirtual

Reimplemented in Nektar::SpatialDomains::HexGeom, Nektar::SpatialDomains::PrismGeom, Nektar::SpatialDomains::PyrGeom, Nektar::SpatialDomains::QuadGeom, Nektar::SpatialDomains::SegGeom, Nektar::SpatialDomains::TetGeom, and Nektar::SpatialDomains::TriGeom.

Definition at line 373 of file Geometry.cpp.

{
    NEKERROR(ErrorUtil::efatal,
             "This function is only valid for expansion type geometries");
}

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by Setup().

Member Data Documentation

◆ m_boundingBox

Array<OneD, NekDouble> Nektar::SpatialDomains::Geometry::m_boundingBox

protected

Array containing bounding box.

Definition at line 198 of file Geometry.h.

Referenced by ClearBoundingBox(), and GetBoundingBox().

◆ m_coeffs

std::vector<Array<OneD, NekDouble> > Nektar::SpatialDomains::Geometry::m_coeffs

protected

Array containing expansion coefficients of m_xmap.

Definition at line 196 of file Geometry.h.

◆ m_coordim

int Nektar::SpatialDomains::Geometry::m_coordim

protected

Coordinate dimension of this geometry object.

Definition at line 184 of file Geometry.h.

◆ m_globalID

int Nektar::SpatialDomains::Geometry::m_globalID

protected

Global ID.

Definition at line 194 of file Geometry.h.

◆ m_invIsoParam

Array<OneD, Array<OneD, NekDouble> > Nektar::SpatialDomains::Geometry::m_invIsoParam

protected

Definition at line 200 of file Geometry.h.

Referenced by Nektar::SpatialDomains::Geometry2D::v_CalculateInverseIsoParam(), Nektar::SpatialDomains::Geometry3D::v_CalculateInverseIsoParam(), Nektar::SpatialDomains::Geometry2D::v_GetLocCoords(), and Nektar::SpatialDomains::Geometry3D::v_GetLocCoords().

◆ m_isoParameter

Array<OneD, Array<OneD, NekDouble> > Nektar::SpatialDomains::Geometry::m_isoParameter

protected

Definition at line 199 of file Geometry.h.

◆ m_setupState

bool Nektar::SpatialDomains::Geometry::m_setupState

protected

Wether or not the setup routines have been run.

Definition at line 190 of file Geometry.h.

◆ m_shapeType

LibUtilities::ShapeType Nektar::SpatialDomains::Geometry::m_shapeType

protected

Type of shape.

Definition at line 192 of file Geometry.h.

◆ m_state

GeomState Nektar::SpatialDomains::Geometry::m_state

protected

Enumeration to dictate whether coefficients are filled.

Definition at line 188 of file Geometry.h.

◆ m_straightEdge

int Nektar::SpatialDomains::Geometry::m_straightEdge

protected

Definition at line 201 of file Geometry.h.

◆ m_xmap

StdRegions::StdExpansionSharedPtr Nektar::SpatialDomains::Geometry::m_xmap

protected

\(\chi\) mapping containing isoparametric transformation.

Definition at line 186 of file Geometry.h.

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Geometry() [1/2]

◆ Geometry() [2/2]

◆ ~Geometry()

Member Function Documentation

◆ CalcGeomType()

◆ ClampLocCoords()

◆ ClearBoundingBox()

◆ ContainsPoint() [1/3]

◆ ContainsPoint() [2/3]

◆ ContainsPoint() [3/3]

◆ FillGeom()

◆ FindDistance()

◆ GenGeomFactors()

◆ GetBoundingBox()

◆ GetCoeffs()

◆ GetCoord()

◆ GetCoordim()

◆ GetDir()

◆ GetEdge()

◆ GetEdgeFaceMap()

◆ GetEdgeNormalToFaceVert()

◆ GetEid()

◆ GetEorient()

◆ GetFace()

◆ GetFid()

◆ GetForient()

◆ GetGlobalID()

◆ GetLocCoords()

◆ GetNumEdges()

◆ GetNumFaces()

◆ GetNumVerts()

◆ GetShapeDim()

◆ GetShapeType()

◆ GetTid()

◆ GetVertex()

◆ GetVertexEdgeMap()

◆ GetVertexFaceMap()

◆ GetVid()

◆ GetXmap()

◆ MinMaxCheck()

◆ PreliminaryCheck()

◆ Reset()

◆ ResetNonRecursive()

◆ SetCoordim()

◆ SetGlobalID()

◆ Setup()

◆ SetUpCoeffs()

◆ v_AllLeftCheck()

◆ v_CalcGeomType()

◆ v_CalculateInverseIsoParam()

◆ v_ContainsPoint()

◆ v_FillGeom()

◆ v_FindDistance()

◆ v_GenGeomFactors()

◆ v_GetCoord()

◆ v_GetDir()

◆ v_GetEdge()

◆ v_GetEdgeFaceMap()

◆ v_GetEdgeNormalToFaceVert()

◆ v_GetEorient()

◆ v_GetFace()

◆ v_GetForient()

◆ v_GetLocCoords()

◆ v_GetNumEdges()

◆ v_GetNumFaces()

◆ v_GetNumVerts()

◆ v_GetShapeDim()

◆ v_GetVertex()

◆ v_GetVertexEdgeMap()

◆ v_GetVertexFaceMap()

◆ v_GetVid()

◆ v_GetXmap()

◆ v_Reset()

◆ v_Setup()

Member Data Documentation