Class representing a 2d triangular linear interpolation based on area coordinates. More...

#include <fei2dtrlin.h>

Inheritance diagram for oofem::FEI2dTrLin:

Collaboration diagram for oofem::FEI2dTrLin:

Public Member Functions
	FEI2dTrLin (int ind1, int ind2)

virtual integrationDomain	giveIntegrationDomain () const
	Returns the integration domain of the interpolator. More...

virtual integrationDomain	giveBoundaryIntegrationDomain (int ib) const
	Returns boundary integration domain. More...

virtual integrationDomain	giveBoundarySurfaceIntegrationDomain (int isurf) const
	Returns boundary integration domain. More...

virtual integrationDomain	giveBoundaryEdgeIntegrationDomain (int iedge) const
	Returns boundary integration domain. More...

virtual Element_Geometry_Type	giveGeometryType () const
	Returns the geometry type fo the interpolator. More...

virtual void	evalN (FloatArray &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the array of interpolation functions (shape functions) at given point. More...

virtual double	evaldNdx (FloatMatrix &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the matrix of derivatives of interpolation functions (shape functions) at given point. More...

virtual void	local2global (FloatArray &answer, const FloatArray &gcoords, const FEICellGeometry &cellgeo)
	Evaluates global coordinates from given local ones. More...

virtual int	global2local (FloatArray &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Default implementation using Newton's method to find the local coordinates. More...

virtual double	giveTransformationJacobian (const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the determinant of the transformation. More...

virtual double	giveArea (const FEICellGeometry &cellgeo) const
	Computes the exact area. More...

virtual int	giveNumberOfNodes () const
	Returns the number of geometric nodes of the receiver. More...

virtual bool	inside (const FloatArray &lcoords) const

virtual void	computeLocalEdgeMapping (IntArray &edgeNodes, int iedge)

virtual int	giveNumberOfEdges () const
	Returns number of edges. More...

virtual void	edgeEvalN (FloatArray &answer, int iedge, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the array of edge interpolation functions (shape functions) at given point. More...

virtual double	edgeEvalNormal (FloatArray &normal, int iedge, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the normal on the given edge. More...

virtual void	edgeEvaldNds (FloatArray &answer, int iedge, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the matrix of derivatives of edge interpolation functions (shape functions) at given point. More...

virtual void	edgeLocal2global (FloatArray &answer, int iedge, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates edge global coordinates from given local ones. More...

virtual double	evalNXIntegral (int iEdge, const FEICellGeometry &cellgeo)
	Computes the integral $\int_S n \cdot x \mathrm{d}s$ . More...

virtual IntegrationRule *	giveIntegrationRule (int order)
	Sets up a suitable integration rule for numerical integrating over volume. More...

Public Member Functions inherited from oofem::FEInterpolation2d
	FEInterpolation2d (int o, int ind1, int ind2)

virtual int	giveNsd ()
	Returns number of spatial dimensions. More...

virtual double	giveCharacteristicLength (const FEICellGeometry &cellgeo) const
	Returns a characteristic length of the geometry, typically a diagonal or edge length. More...

virtual void	giveJacobianMatrixAt (FloatMatrix &jacobianMatrix, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Gives the jacobian matrix at the local coordinates. More...

virtual void	boundaryEdgeGiveNodes (IntArray &answer, int boundary)
	Gives the boundary nodes for requested boundary number. More...

virtual void	boundaryEdgeEvalN (FloatArray &answer, int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the basis functions on the requested boundary. More...

virtual double	boundaryEdgeGiveTransformationJacobian (int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the determinant of the transformation Jacobian on the requested boundary. More...

virtual void	boundaryEdgeLocal2Global (FloatArray &answer, int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Maps the local boundary coordinates to global. More...

virtual void	boundaryGiveNodes (IntArray &answer, int boundary)
	Gives the boundary nodes for requested boundary number. More...

virtual void	boundaryEvalN (FloatArray &answer, int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the basis functions on the requested boundary. More...

virtual double	boundaryEvalNormal (FloatArray &answer, int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the normal on the requested boundary. More...

virtual double	boundaryGiveTransformationJacobian (int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the determinant of the transformation Jacobian on the requested boundary. More...

virtual void	boundaryLocal2Global (FloatArray &answer, int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Maps the local boundary coordinates to global. More...

virtual void	boundarySurfaceEvalN (FloatArray &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the array of edge interpolation functions (shape functions) at given point. More...

virtual void	boundarySurfaceEvaldNdx (FloatMatrix &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the matrix of derivatives of edge interpolation functions (shape functions) at given point. More...

virtual double	boundarySurfaceEvalNormal (FloatArray &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the normal out of the surface at given point. More...

virtual void	boundarySurfaceLocal2global (FloatArray &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates edge global coordinates from given local ones. More...

virtual double	boundarySurfaceGiveTransformationJacobian (int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the edge jacobian of transformation between local and global coordinates. More...

virtual void	boundarySurfaceGiveNodes (IntArray &answer, int boundary)
	Gives the boundary nodes for requested boundary number. More...

void	computeEdgeMapping (IntArray &edgeNodes, IntArray &elemNodes, int iedge)

virtual double	edgeGiveTransformationJacobian (int iedge, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the edge Jacobian of transformation between local and global coordinates. More...

Public Member Functions inherited from oofem::FEInterpolation
	FEInterpolation (int o)

virtual	~FEInterpolation ()

virtual IRResultType	initializeFrom (InputRecord *ir)
	Initializes receiver according to object description stored in input record. More...

std::string	errorInfo (const char *func) const

int	giveInterpolationOrder ()
	Returns the interpolation order. More...

virtual void	evald2Ndx2 (FloatMatrix &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the matrix of second derivatives of interpolation functions (shape functions) at given point. More...

virtual void	evaldNdxi (FloatMatrix &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the matrix of derivatives of interpolation functions (shape functions) at given point. More...

virtual void	giveLocalNodeCoords (FloatMatrix &answer)
	Returns a matrix containing the local coordinates for each node corresponding to the interpolation. More...

virtual IntegrationRule *	giveBoundaryEdgeIntegrationRule (int order, int boundary)
	Sets up a suitable integration rule for integrating over the requested boundary. More...

virtual IntegrationRule *	giveBoundarySurfaceIntegrationRule (int order, int boundary)
	Sets up a suitable integration rule for integrating over the requested boundary. More...

virtual IntegrationRule *	giveBoundaryIntegrationRule (int order, int boundary)
	Sets up a suitable integration rule for integrating over the requested boundary. More...

virtual int	giveKnotSpanBasisFuncMask (const IntArray &knotSpan, IntArray &mask)
	Returns indices (zero based) of nonzero basis functions for given knot span. More...

virtual int	giveNumberOfKnotSpanBasisFunctions (const IntArray &knotSpan)
	Returns the number of nonzero basis functions at individual knot span,. More...

virtual bool	hasSubPatchFormulation ()
	Returns true, if receiver is formulated on sub-patch basis. More...

virtual const double const	giveKnotVector ()
	Returns the subdivision of patch parametric space. More...

virtual int	giveNumberOfKnotSpans (int dim)
	Returns the number of knot spans of the receiver. More...

virtual const FloatArray *	giveKnotValues (int dim)
	Returns the knot values of the receiver. More...

virtual const IntArray *	giveKnotMultiplicity (int dim)
	Returns the knot multiplicity of the receiver. More...

Protected Member Functions
double	edgeComputeLength (IntArray &edgeNodes, const FEICellGeometry &cellgeo)

Additional Inherited Members
Protected Attributes inherited from oofem::FEInterpolation2d
int	xind

int	yind

Protected Attributes inherited from oofem::FEInterpolation
int	order

Detailed Description

Class representing a 2d triangular linear interpolation based on area coordinates.

Definition at line 44 of file fei2dtrlin.h.

Constructor & Destructor Documentation

oofem::FEI2dTrLin::FEI2dTrLin	(	int	ind1,
		int	ind2
	)

inline

Definition at line 47 of file fei2dtrlin.h.

Member Function Documentation

void oofem::FEI2dTrLin::computeLocalEdgeMapping	(	IntArray &	edgeNodes,
		int	iedge
	)

virtual

Implements oofem::FEInterpolation2d.

Definition at line 230 of file fei2dtrlin.C.

References oofem::IntArray::at(), OOFEM_ERROR, and oofem::IntArray::resize().

Referenced by oofem::Tr1Darcy::computeEdgeBCSubVectorAt(), oofem::DKTPlate3d::computeLoadLEToLRotationMatrix(), oofem::CCTPlate::computeLoadLEToLRotationMatrix(), oofem::DKTPlate::computeLoadLEToLRotationMatrix(), edgeEvaldNds(), edgeEvalNormal(), oofem::FEI2dTrLinAxi::edgeGiveTransformationJacobian(), edgeLocal2global(), and evalNXIntegral().

double oofem::FEI2dTrLin::edgeComputeLength	(	IntArray &	edgeNodes,
		const FEICellGeometry &	cellgeo
	)

protected

Definition at line 253 of file fei2dtrlin.C.

References oofem::IntArray::at(), oofem::FloatArray::at(), oofem::FEICellGeometry::giveVertexCoordinates(), oofem::FEInterpolation2d::xind, and oofem::FEInterpolation2d::yind.

Referenced by edgeEvaldNds().

void oofem::FEI2dTrLin::edgeEvaldNds	(	FloatArray &	answer,
		int	iedge,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo
	)

virtual

Evaluates the matrix of derivatives of edge interpolation functions (shape functions) at given point.

These derivatives are in global coordinate system (where the nodal coordinates are defined).

Parameters

answer	Contains resulting array of derivatives, the member at i position contains value of $\frac{\mathrm{d}N_i}{\mathrm{d}s}$ .
iedge	Determines the edge number.
lcoords	Array containing (local) coordinates.
cellgeo	Underlying cell geometry.

Implements oofem::FEInterpolation2d.

Definition at line 191 of file fei2dtrlin.C.

References computeLocalEdgeMapping(), and edgeComputeLength().

void oofem::FEI2dTrLin::edgeEvalN	(	FloatArray &	answer,
		int	iedge,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo
	)

virtual

Evaluates the array of edge interpolation functions (shape functions) at given point.

Parameters

answer	Contains resulting array of evaluated interpolation functions.
iedge	Edge number.
lcoords	Array containing (local) coordinates.
cellgeo	Underlying cell geometry.

Implements oofem::FEInterpolation2d.

Definition at line 184 of file fei2dtrlin.C.

References oofem::FloatArray::at().

Referenced by oofem::Tr1BubbleStokes::computeBoundarySurfaceLoadVector(), oofem::Tr1Darcy::computeEdgeBCSubVectorAt(), oofem::TR1_2D_PFEM::computeEdgeBCSubVectorAt(), oofem::DKTPlate::computeEdgeNMatrix(), oofem::TrPlanestressRotAllman::computeEgdeNMatrixAt(), oofem::FEI2dTrLinAxi::edgeGiveTransformationJacobian(), and edgeLocal2global().

double oofem::FEI2dTrLin::edgeEvalNormal	(	FloatArray &	answer,
		int	iedge,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo
	)

virtual

Evaluates the normal on the given edge.

Parameters

answer	Contains the evaluated normal.
iedge	Determines the edge number.
lcoords	Array containing (local) coordinates.
cellgeo	Underlying cell geometry.

Implements oofem::FEInterpolation2d.

Definition at line 201 of file fei2dtrlin.C.

References oofem::IntArray::at(), computeLocalEdgeMapping(), oofem::FEICellGeometry::giveVertexCoordinates(), oofem::FloatArray::normalize(), oofem::FEInterpolation2d::xind, and oofem::FEInterpolation2d::yind.

void oofem::FEI2dTrLin::edgeLocal2global	(	FloatArray &	answer,
		int	iedge,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo
	)

virtual

Evaluates edge global coordinates from given local ones.

These derivatives are in global coordinate system (where the nodal coordinates are defined).

Parameters

answer	Contains resulting global coordinates.
iedge	Determines edge number.
lcoords	Array containing (local) coordinates.
cellgeo	Underlying cell geometry.

Implements oofem::FEInterpolation2d.

Definition at line 213 of file fei2dtrlin.C.

References oofem::IntArray::at(), oofem::FloatArray::at(), computeLocalEdgeMapping(), edgeEvalN(), oofem::FEICellGeometry::giveVertexCoordinates(), oofem::FloatArray::resize(), oofem::FEInterpolation2d::xind, and oofem::FEInterpolation2d::yind.

Referenced by oofem::Tr1Darcy::computeEdgeBCSubVectorAt(), oofem::TR1_2D_PFEM::computeEdgeBCSubVectorAt(), and oofem::TrAxisym1_ht::computeEdgeVolumeAround().

double oofem::FEI2dTrLin::evaldNdx	(	FloatMatrix &	answer,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo
	)

virtual

Evaluates the matrix of derivatives of interpolation functions (shape functions) at given point.

These derivatives are in global coordinate system (where the nodal coordinates are defined)

Parameters

answer	Contains resulting matrix of derivatives, the member at i,j position contains value of dNi/dxj.
lcoords	Array containing (local) coordinates.
cellgeo	Underlying cell geometry.

Returns: Determinant of the Jacobian.

Implements oofem::FEInterpolation.

Definition at line 53 of file fei2dtrlin.C.

References oofem::FloatArray::at(), oofem::FloatMatrix::at(), oofem::FEICellGeometry::giveVertexCoordinates(), oofem::FloatMatrix::resize(), oofem::FEInterpolation2d::xind, and oofem::FEInterpolation2d::yind.

Referenced by oofem::QTrPlaneStrainGrad::computeBkappaMatrixAt(), oofem::QTrPlaneStressGrad::computeBkappaMatrixAt(), oofem::Tr_Warp::computeBmatrixAt(), oofem::Tria1PlateSubSoil::computeBmatrixAt(), oofem::TR21_2D_SUPG::computeGradPMatrix(), oofem::Tr1Darcy::computeInternalForcesVector(), oofem::Tr1BubbleStokes::computeInternalForcesVector(), oofem::DKTPlate::computeShearForces(), oofem::Tr1Darcy::computeStiffnessMatrix(), and oofem::Tr1BubbleStokes::computeStiffnessMatrix().

void oofem::FEI2dTrLin::evalN	(	FloatArray &	answer,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo
	)

virtual

Evaluates the array of interpolation functions (shape functions) at given point.

Parameters

answer	Contains resulting array of evaluated interpolation functions.
lcoords	Array containing (local) coordinates.
cellgeo	Underlying cell geometry.

Implements oofem::FEInterpolation.

Definition at line 43 of file fei2dtrlin.C.

References oofem::FloatArray::at().

Referenced by oofem::InterfaceElement3dTrLin::computeBmatrixAt(), oofem::Tria1PlateSubSoil::computeBmatrixAt(), oofem::TR1_2D_PFEM::computeBodyLoadVectorAt(), oofem::Tr21Stokes::computeField(), oofem::Tr1BubbleStokes::computeField(), oofem::InterfaceElement3dTrLin::computeGlobalCoordinates(), oofem::Tr1Darcy::computeInternalForcesVector(), oofem::Tr21Stokes::computeInternalForcesVector(), oofem::Tr1BubbleStokes::computeInternalForcesVector(), oofem::Tr1BubbleStokes::computeLoadVector(), oofem::QTrPlaneStrainGrad::computeNkappaMatrixAt(), oofem::QTrPlaneStressGrad::computeNkappaMatrixAt(), oofem::TrPlanestressRotAllman::computeNmatrixAt(), oofem::TR21_2D_SUPG::computeNpMatrix(), oofem::TR1_2D_SUPG_AXI::computeNVector(), oofem::TR1_2D_SUPG2_AXI::computeNVector(), oofem::TR1_2D_SUPG2::computeNVector(), oofem::Tr21Stokes::computeStiffnessMatrix(), oofem::Tr1BubbleStokes::computeStiffnessMatrix(), and oofem::FEI2dTrLinAxi::giveTransformationJacobian().

double oofem::FEI2dTrLin::evalNXIntegral	(	int	boundary,
		const FEICellGeometry &	cellgeo
	)

virtual

Computes the integral $\int_S n \cdot x \mathrm{d}s$ .

Parameters

boundary	Boundary number.
cellgeo	Underlying cell geometry.

Returns: Evaluated integral.

Reimplemented from oofem::FEInterpolation.

Definition at line 286 of file fei2dtrlin.C.

References oofem::IntArray::at(), oofem::FloatArray::at(), computeLocalEdgeMapping(), oofem::FEICellGeometry::giveVertexCoordinates(), oofem::FEInterpolation2d::xind, and oofem::FEInterpolation2d::yind.

double oofem::FEI2dTrLin::giveArea ( const FEICellGeometry & cellgeo ) const

virtual

Computes the exact area.

Parameters

cellgeo Cell geometry for the element.

Returns: Area of geometry.

Reimplemented from oofem::FEInterpolation2d.

Definition at line 267 of file fei2dtrlin.C.

References oofem::FloatArray::at(), and oofem::FEICellGeometry::giveVertexCoordinates().

Referenced by oofem::Axisymm3d::giveArea(), oofem::TrPlanestressRotAllman::giveArea(), and oofem::TrPlaneStress2d::giveArea().

virtual integrationDomain oofem::FEI2dTrLin::giveBoundaryEdgeIntegrationDomain ( int boundary ) const

inlinevirtual

Returns boundary integration domain.

Implements oofem::FEInterpolation.

Definition at line 52 of file fei2dtrlin.h.

References oofem::_Line.

virtual integrationDomain oofem::FEI2dTrLin::giveBoundaryIntegrationDomain ( int boundary ) const

inlinevirtual

Returns boundary integration domain.

Implements oofem::FEInterpolation.

Definition at line 50 of file fei2dtrlin.h.

References oofem::_Line.

virtual integrationDomain oofem::FEI2dTrLin::giveBoundarySurfaceIntegrationDomain ( int boundary ) const

inlinevirtual

Returns boundary integration domain.

Implements oofem::FEInterpolation.

Definition at line 51 of file fei2dtrlin.h.

References oofem::_Triangle.

virtual Element_Geometry_Type oofem::FEI2dTrLin::giveGeometryType ( ) const

inlinevirtual

Returns the geometry type fo the interpolator.

Implements oofem::FEInterpolation.

Definition at line 55 of file fei2dtrlin.h.

virtual integrationDomain oofem::FEI2dTrLin::giveIntegrationDomain ( ) const

inlinevirtual

Returns the integration domain of the interpolator.

Implements oofem::FEInterpolation.

Definition at line 49 of file fei2dtrlin.h.

References oofem::_Triangle.

IntegrationRule * oofem::FEI2dTrLin::giveIntegrationRule ( int order )

virtual

Sets up a suitable integration rule for numerical integrating over volume.

The required polynomial order for the determinant of the jacobian is added automatically.

Parameters

order Polynomial order of integrand (should NOT including determinant of jacobian).

Reimplemented from oofem::FEInterpolation.

Definition at line 306 of file fei2dtrlin.C.

References oofem::_Triangle, oofem::IntegrationRule::getRequiredNumberOfIntegrationPoints(), and oofem::IntegrationRule::SetUpPointsOnTriangle().

virtual int oofem::FEI2dTrLin::giveNumberOfEdges ( ) const

inlinevirtual

Returns number of edges.

Reimplemented from oofem::FEInterpolation.

Definition at line 70 of file fei2dtrlin.h.

virtual int oofem::FEI2dTrLin::giveNumberOfNodes ( ) const

inlinevirtual

Returns the number of geometric nodes of the receiver.

Reimplemented from oofem::FEInterpolation.

Definition at line 64 of file fei2dtrlin.h.

double oofem::FEI2dTrLin::giveTransformationJacobian	(	const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo
	)

virtual

Evaluates the determinant of the transformation.

Parameters

lcoords	Array containing (local) coordinates.
cellgeo	Underlying cell geometry.

Returns: Determinant of the transformation.

Reimplemented from oofem::FEInterpolation.

Reimplemented in oofem::FEI2dTrLinAxi.

Definition at line 147 of file fei2dtrlin.C.

References oofem::FloatArray::at(), oofem::FEICellGeometry::giveVertexCoordinates(), oofem::FEInterpolation2d::xind, and oofem::FEInterpolation2d::yind.

int oofem::FEI2dTrLin::global2local	(	FloatArray &	answer,
		const FloatArray &	gcoords,
		const FEICellGeometry &	cellgeo
	)

virtual

Default implementation using Newton's method to find the local coordinates.

Can be overloaded if desired.

Reimplemented from oofem::FEInterpolation2d.

Definition at line 103 of file fei2dtrlin.C.

References oofem::FloatArray::at(), oofem::FEICellGeometry::giveVertexCoordinates(), inside(), POINT_TOL, oofem::FloatArray::resize(), oofem::FEInterpolation2d::xind, and oofem::FEInterpolation2d::yind.

Referenced by oofem::CCTPlate3d::computeLocalCoordinates(), oofem::CCTPlate::computeLocalCoordinates(), oofem::DKTPlate3d::computeLocalCoordinates(), oofem::DKTPlate::computeLocalCoordinates(), oofem::TR1_2D_SUPG2_AXI::updateIntegrationRules(), and oofem::TR1_2D_SUPG2::updateIntegrationRules().

bool oofem::FEI2dTrLin::inside ( const FloatArray & lcoords ) const

virtual

Reimplemented from oofem::FEInterpolation2d.

Definition at line 162 of file fei2dtrlin.C.

References oofem::FloatArray::at().

Referenced by global2local().

void oofem::FEI2dTrLin::local2global	(	FloatArray &	answer,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo
	)

virtual

Evaluates global coordinates from given local ones.

Parameters

answer	Contains resulting global coordinates.
lcoords	Array containing (local) coordinates.
cellgeo	Underlying cell geometry.

Implements oofem::FEInterpolation.

Definition at line 81 of file fei2dtrlin.C.

References oofem::FloatArray::at(), oofem::FEICellGeometry::giveVertexCoordinates(), oofem::FloatArray::resize(), oofem::FEInterpolation2d::xind, oofem::FEInterpolation2d::yind, and oofem::FloatArray::zero().

Referenced by oofem::PatchIntegrationRule::SetUpPointsOnTriangle(), and oofem::PatchIntegrationRule::SetUpPointsOnWedge().

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

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation