#include <tria2platesubsoil.h>

Inheritance diagram for oofem::Tria2PlateSubSoil:

Collaboration diagram for oofem::Tria2PlateSubSoil:

Public Member Functions
	Tria2PlateSubSoil (int n, Domain *d)
virtual	~Tria2PlateSubSoil ()
FEInterpolation *	giveInterpolation () const override
FEInterpolation *	giveInterpolation (DofIDItem id) const override
const char *	giveInputRecordName () const override
const char *	giveClassName () const override
Element_Geometry_Type	giveGeometryType () const override
int	computeNumberOfDofs () override
Public Member Functions inherited from oofem::Tria1PlateSubSoil
	Tria1PlateSubSoil (int n, Domain *d)
virtual	~Tria1PlateSubSoil ()
MaterialMode	giveMaterialMode () override
int	testElementExtension (ElementExtension ext) override
void	giveDofManDofIDMask (int inode, IntArray &) const override
void	computeMidPlaneNormal (FloatArray &answer, const GaussPoint *gp) override
double	giveCharacteristicLength (const FloatArray &normalToCrackPlane) override
double	computeVolumeAround (GaussPoint *gp) override
void	computeLumpedMassMatrix (FloatMatrix &answer, TimeStep *tStep) override
void	computeMassMatrix (FloatMatrix &answer, TimeStep *tStep) override
int	giveIPValue (FloatArray &answer, GaussPoint gp, InternalStateType type, TimeStep tStep) override
Interface *	giveInterface (InterfaceType it) override
Public Member Functions inherited from oofem::StructuralElement
	StructuralElement (int n, Domain *d)
virtual	~StructuralElement ()
	Destructor.
void	giveCharacteristicMatrix (FloatMatrix &answer, CharType, TimeStep *tStep) override
void	giveCharacteristicVector (FloatArray &answer, CharType type, ValueModeType mode, TimeStep *tStep) override
virtual void	computeConsistentMassMatrix (FloatMatrix &answer, TimeStep tStep, double &mass, const double ipDensity=NULL)
virtual void	giveMassMtrxIntegrationgMask (IntArray &answer)
virtual void	computeStiffnessMatrix (FloatMatrix &answer, MatResponseMode rMode, TimeStep *tStep)
void	computeStiffnessMatrix_withIRulesAsSubcells (FloatMatrix &answer, MatResponseMode rMode, TimeStep *tStep)
virtual void	computeInitialStressMatrix (FloatMatrix &answer, TimeStep *tStep)
virtual void	computeLumpedInitialStressMatrix (FloatMatrix &answer, TimeStep *tStep)
void	computeField (ValueModeType mode, TimeStep *tStep, const FloatArray &lcoords, FloatArray &answer) override
virtual void	giveInternalForcesVector (FloatArray &answer, TimeStep *tStep, int useUpdatedGpRecord=0)
virtual void	giveInternalForcesVector_withIRulesAsSubcells (FloatArray &answer, TimeStep *tStep, int useUpdatedGpRecord=0)
virtual void	computeStrainVector (FloatArray &answer, GaussPoint gp, TimeStep tStep)
virtual void	computeResultingIPTemperatureAt (FloatArray &answer, TimeStep tStep, GaussPoint gp, ValueModeType mode)
virtual void	computeResultingIPEigenstrainAt (FloatArray &answer, TimeStep tStep, GaussPoint gp, ValueModeType mode)
void	updateBeforeNonlocalAverage (TimeStep *tStep) override
virtual void	giveNonlocalLocationArray (IntArray &locationArray, const UnknownNumberingScheme &us)
virtual void	addNonlocalStiffnessContributions (SparseMtrx &dest, const UnknownNumberingScheme &s, TimeStep *tStep)
int	adaptiveUpdate (TimeStep *tStep) override
void	updateInternalState (TimeStep *tStep) override
void	updateYourself (TimeStep *tStep) override
int	checkConsistency () override
void	giveInputRecord (DynamicInputRecord &input) override
int	giveInternalStateAtNode (FloatArray &answer, InternalStateType type, InternalStateMode mode, int node, TimeStep *tStep) override
void	showSparseMtrxStructure (CharType mtrx, oofegGraphicContext &gc, TimeStep *tStep) override
	Shows sparse structure.
void	showExtendedSparseMtrxStructure (CharType mtrx, oofegGraphicContext &gc, TimeStep *tStep) override
	Shows extended sparse structure (for example, due to nonlocal interactions for tangent stiffness).
void	computeLoadVector (FloatArray &answer, BodyLoad load, CharType type, ValueModeType mode, TimeStep tStep) override
void	computeBoundarySurfaceLoadVector (FloatArray &answer, BoundaryLoad load, int boundary, CharType type, ValueModeType mode, TimeStep tStep, bool global=true) override
void	computeBoundaryEdgeLoadVector (FloatArray &answer, BoundaryLoad load, int boundary, CharType type, ValueModeType mode, TimeStep tStep, bool global=true) override
virtual void	computeEdgeNMatrix (FloatMatrix &answer, int boundaryID, const FloatArray &lcoords)
	computes edge interpolation matrix
StructuralCrossSection *	giveStructuralCrossSection ()
	Helper function which returns the structural cross-section for the element.
virtual void	createMaterialStatus ()
Public Member Functions inherited from oofem::Element
	Element (int n, Domain *aDomain)
	Element (const Element &src)=delete
Element &	operator= (const Element &src)=delete
virtual	~Element ()
	Virtual destructor.
void	giveLocationArray (IntArray &locationArray, const UnknownNumberingScheme &s, IntArray *dofIds=NULL) const
void	giveLocationArray (IntArray &locationArray, const IntArray &dofIDMask, const UnknownNumberingScheme &s, IntArray *dofIds=NULL) const
virtual void	giveBoundaryLocationArray (IntArray &locationArray, const IntArray &bNodes, const UnknownNumberingScheme &s, IntArray *dofIds=NULL)
virtual void	giveBoundaryLocationArray (IntArray &locationArray, const IntArray &bNodes, const IntArray &dofIDMask, const UnknownNumberingScheme &s, IntArray *dofIds=NULL)
virtual int	giveNumberOfDofs ()
virtual int	giveNumberOfInternalDofManagers () const
virtual DofManager *	giveInternalDofManager (int i) const
virtual void	setInternalDofManager (int num, std::unique_ptr< DofManager > dm)
virtual double	giveCharacteristicValue (CharType type, TimeStep *tStep)
virtual void	computeTangentFromSurfaceLoad (FloatMatrix &answer, BoundaryLoad load, int boundary, MatResponseMode rmode, TimeStep tStep)
virtual void	computeTangentFromEdgeLoad (FloatMatrix &answer, BoundaryLoad load, int boundary, MatResponseMode rmode, TimeStep tStep)
const IntArray &	giveBodyLoadList () const
const IntArray &	giveBoundaryLoadList () const
void	computeVectorOf (ValueModeType u, TimeStep *tStep, FloatArray &answer)
void	computeVectorOf (const IntArray &dofIDMask, ValueModeType u, TimeStep *tStep, FloatArray &answer, bool padding=false)
void	computeBoundaryVectorOf (const IntArray &bNodes, const IntArray &dofIDMask, ValueModeType u, TimeStep *tStep, FloatArray &answer, bool padding=false)
void	computeVectorOf (PrimaryField &field, const IntArray &dofIDMask, ValueModeType u, TimeStep *tStep, FloatArray &answer, bool padding=false)
void	computeVectorOfPrescribed (ValueModeType u, TimeStep *tStep, FloatArray &answer)
void	computeVectorOfPrescribed (const IntArray &dofIDMask, ValueModeType type, TimeStep *tStep, FloatArray &answer)
virtual int	computeNumberOfGlobalDofs ()
int	computeNumberOfPrimaryMasterDofs ()
virtual bool	computeGtoLRotationMatrix (FloatMatrix &answer)
virtual bool	giveRotationMatrix (FloatMatrix &answer)
virtual bool	computeDofTransformationMatrix (FloatMatrix &answer, const IntArray &nodes, bool includeInternal)
virtual void	giveInternalDofManDofIDMask (int inode, IntArray &answer) const
virtual void	giveElementDofIDMask (IntArray &answer) const
virtual double	computeVolumeAreaOrLength ()
	Computes the volume, area or length of the element depending on its spatial dimension.
double	computeMeanSize ()
virtual double	computeVolume ()
virtual double	computeArea ()
virtual double	computeLength ()
virtual IntArray	giveBoundaryEdgeNodes (int boundary, bool includeHierarchical=false) const
virtual IntArray	giveBoundarySurfaceNodes (int boundary, bool includeHierarchical=false) const
virtual IntArray	giveBoundaryNodes (int boundary) const
virtual std::unique_ptr< IntegrationRule >	giveBoundaryEdgeIntegrationRule (int order, int boundary)
virtual std::unique_ptr< IntegrationRule >	giveBoundarySurfaceIntegrationRule (int order, int boundary)
int	giveDofManagerNumber (int i) const
const IntArray &	giveDofManArray () const
void	addDofManager (DofManager *dMan)
DofManager *	giveDofManager (int i) const
Node *	giveNode (int i) const
virtual ElementSide *	giveSide (int i) const
virtual const FEInterpolation *	getGeometryInterpolation () const
virtual Material *	giveMaterial ()
int	giveMaterialNumber () const
CrossSection *	giveCrossSection ()
int	getActivityTimeFunctionNumber ()
void	setActivityTimeFunctionNumber (int funcIndx)
void	setMaterial (int matIndx)
virtual void	setCrossSection (int csIndx)
virtual int	giveNumberOfDofManagers () const
void	setNumberOfDofManagers (int i)
	Sets number of element dof managers.
virtual int	giveNumberOfNodes () const
void	setDofManagers (const IntArray &dmans)
void	setDofManager (int id, int dm)
void	setBodyLoads (const IntArray &bodyLoads)
void	setIntegrationRules (std ::vector< std ::unique_ptr< IntegrationRule > > irlist)
virtual integrationDomain	giveIntegrationDomain () const
virtual int	giveIntegrationRuleLocalCodeNumbers (IntArray &answer, IntegrationRule &ie)
int	giveRegionNumber ()
virtual void	initializeYourself (TimeStep *timeStepWhenICApply)
virtual bool	isActivated (TimeStep *tStep)
virtual bool	isCast (TimeStep *tStep)
virtual void	initForNewStep ()
virtual Element_Geometry_Type	giveEdgeGeometryType (int id) const
	Returns the receiver edge geometry type.
virtual Element_Geometry_Type	giveSurfaceGeometryType (int id) const
	Returns the receiver surface geometry type.
virtual int	giveSpatialDimension ()
virtual int	giveNumberOfBoundarySides ()
	Returns number of boundaries (entities of element_dimension-1: points, edges, surfaces).
virtual int	giveNumberOfEdges () const
virtual int	giveNumberOfSurfaces () const
virtual int	giveDefaultIntegrationRule () const
virtual IntegrationRule *	giveDefaultIntegrationRulePtr ()
int	giveNumberOfIntegrationRules ()
virtual IntegrationRule *	giveIntegrationRule (int i)
std::vector< std ::unique_ptr< IntegrationRule > > &	giveIntegrationRulesArray ()
int	giveGlobalIPValue (FloatArray &answer, GaussPoint gp, InternalStateType type, TimeStep tStep)
virtual double	giveLengthInDir (const FloatArray &normalToCrackPlane)
double	giveCharacteristicLengthForPlaneElements (const FloatArray &normalToCrackPlane)
double	giveCharacteristicLengthForAxisymmElements (const FloatArray &normalToCrackPlane)
virtual double	giveCharacteristicSize (GaussPoint *gp, FloatArray &normalToCrackPlane, ElementCharSizeMethod method)
virtual double	giveParentElSize () const
virtual int	computeGlobalCoordinates (FloatArray &answer, const FloatArray &lcoords)
virtual bool	computeLocalCoordinates (FloatArray &answer, const FloatArray &gcoords)
virtual int	giveLocalCoordinateSystem (FloatMatrix &answer)
virtual void	giveLocalCoordinateSystemVector (InternalStateType isttype, FloatArray &answer)
virtual int	adaptiveMap (Domain oldd, TimeStep tStep)
virtual int	mapStateVariables (Domain &iOldDom, const TimeStep &iTStep)
virtual int	adaptiveFinish (TimeStep *tStep)
void	updateLocalNumbering (EntityRenumberingFunctor &f) override
template<class T>
void	ipEvaluator (T src, void(T ::f)(GaussPoint *gp))
	Integration point evaluator, loops over receiver IP's and calls given function (passed as f parameter) on them. The IP is parameter to function f.
template<class T, class S>
void	ipEvaluator (T src, void(T ::f)(GaussPoint *, S &), S &_val)
	Integration point evaluator, loops over receiver IP's and calls given function (passed as f parameter) on them. The IP is parameter to function f as well as additional array.
virtual void	drawYourself (oofegGraphicContext &gc, TimeStep *tStep)
virtual void	drawAnnotation (oofegGraphicContext &gc, TimeStep *tStep)
virtual void	drawRawGeometry (oofegGraphicContext &gc, TimeStep *tStep)
virtual void	drawDeformedGeometry (oofegGraphicContext &gc, TimeStep *tStep, UnknownType)
virtual void	drawScalar (oofegGraphicContext &gc, TimeStep *tStep)
virtual void	drawSpecial (oofegGraphicContext &gc, TimeStep *tStep)
virtual void	giveLocalIntVarMaxMin (oofegGraphicContext &gc, TimeStep *tStep, double &emin, double &emax)
virtual int	giveInternalStateAtSide (FloatArray &answer, InternalStateType type, InternalStateMode mode, int side, TimeStep *tStep)
int	giveLabel () const
int	giveGlobalNumber () const
void	setGlobalNumber (int num)
elementParallelMode	giveParallelMode () const
void	setParallelMode (elementParallelMode _mode)
	Sets parallel mode of element.
virtual elementParallelMode	giveKnotSpanParallelMode (int) const
int	packUnknowns (DataStream &buff, TimeStep *tStep)
int	unpackAndUpdateUnknowns (DataStream &buff, TimeStep *tStep)
int	estimatePackSize (DataStream &buff)
const IntArray *	givePartitionList () const
void	setPartitionList (IntArray &pl)
virtual double	predictRelativeComputationalCost ()
virtual double	giveRelativeSelfComputationalCost ()
virtual double	predictRelativeRedistributionCost ()
IntArray *	giveBodyLoadArray ()
	Returns array containing load numbers of loads acting on element.
IntArray *	giveBoundaryLoadArray ()
	Returns array containing load numbers of boundary loads acting on element.
void	initializeFrom (InputRecord &ir, int priority) override
void	initializeFinish () override
void	postInitialize () override
	Performs post initialization steps.
void	saveContext (DataStream &stream, ContextMode mode) override
void	restoreContext (DataStream &stream, ContextMode mode) override
void	printOutputAt (FILE file, TimeStep tStep) override
virtual const IntArray	giveLocation ()
virtual void	recalculateCoordinates (int nodeNumber, FloatArray &coords)
void	setSharedEdgeID (int iedge, int globalID)
void	setSharedSurfaceID (int isurf, int globalID)
const IntArray *	giveSharedEdgeIDs () const
const IntArray *	giveSharedSurfaceIDs () const
Public Member Functions inherited from oofem::FEMComponent
	FEMComponent (int n, Domain *d)
virtual	~FEMComponent ()=default
	Virtual destructor.
Domain *	giveDomain () const
virtual void	setDomain (Domain *d)
int	giveNumber () const
void	setNumber (int num)
virtual void	initializeFrom (InputRecord &ir)
virtual void	printYourself ()
	Prints receiver state on stdout. Useful for debugging.
std::string	errorInfo (const char *func) const
	Returns string for prepending output (used by error reporting macros).
Public Member Functions inherited from oofem::ZZNodalRecoveryModelInterface
	ZZNodalRecoveryModelInterface (Element *element)
	Constructor.
virtual bool	ZZNodalRecoveryMI_computeNValProduct (FloatMatrix &answer, InternalStateType type, TimeStep *tStep)
virtual void	ZZNodalRecoveryMI_computeNNMatrix (FloatArray &answer, InternalStateType type)
Public Member Functions inherited from oofem::Interface
	Interface ()
	Constructor.
virtual	~Interface ()
Public Member Functions inherited from oofem::SPRNodalRecoveryModelInterface
	SPRNodalRecoveryModelInterface ()
	Constructor.

Protected Member Functions
void	computeGaussPoints () override
void	computeBmatrixAt (GaussPoint *gp, FloatMatrix &answer, int=1, int=ALL_STRAINS) override
void	SPRNodalRecoveryMI_giveSPRAssemblyPoints (IntArray &pap) override
void	SPRNodalRecoveryMI_giveDofMansDeterminedByPatch (IntArray &answer, int pap) override
SPRPatchType	SPRNodalRecoveryMI_givePatchType () override
Surface load support
void	computeNmatrixAt (const FloatArray &iLocCoord, FloatMatrix &answer) override
void	computeSurfaceNMatrix (FloatMatrix &answer, int boundaryID, const FloatArray &lcoords) override
Protected Member Functions inherited from oofem::Tria1PlateSubSoil
void	computeBodyLoadVectorAt (FloatArray &answer, Load load, TimeStep tStep, ValueModeType mode) override
void	computeStressVector (FloatArray &answer, const FloatArray &strain, GaussPoint gp, TimeStep tStep) override
void	computeConstitutiveMatrixAt (FloatMatrix &answer, MatResponseMode rMode, GaussPoint gp, TimeStep tStep) override
int	SPRNodalRecoveryMI_giveNumberOfIP () override
virtual void	computePointLoadVectorAt (FloatArray &answer, Load load, TimeStep tStep, ValueModeType mode, bool global=true)
virtual void	giveEdgeDofMapping (IntArray &answer, int iEdge) const
virtual void	giveSurfaceDofMapping (IntArray &answer, int iSurf) const
virtual double	computeEdgeVolumeAround (GaussPoint *gp, int iEdge)
virtual double	computeSurfaceVolumeAround (GaussPoint *gp, int iSurf)
virtual int	computeLoadGToLRotationMtrx (FloatMatrix &answer)
virtual int	computeLoadLEToLRotationMatrix (FloatMatrix &answer, int iEdge, GaussPoint *gp)
virtual int	computeLoadLSToLRotationMatrix (FloatMatrix &answer, int iSurf, GaussPoint *gp)
virtual int	giveNumberOfIPForMassMtrxIntegration ()
void	condense (FloatMatrix stiff, FloatMatrix mass, FloatArray load, IntArray what)
virtual void	setupIRForMassMtrxIntegration (IntegrationRule &iRule)

Static Protected Attributes
static FEI2dTrQuad	interp_quad
Static Protected Attributes inherited from oofem::Tria1PlateSubSoil
static FEI2dTrLin	interp_lin

Additional Inherited Members
Static Public Attributes inherited from oofem::Element
static ParamKey	IPK_Element_mat
static ParamKey	IPK_Element_crosssect
static ParamKey	IPK_Element_nodes
static ParamKey	IPK_Element_bodyload
static ParamKey	IPK_Element_boundaryload
static ParamKey	IPK_Element_lcs
static ParamKey	IPK_Element_partitions
static ParamKey	IPK_Element_remote
static ParamKey	IPK_Element_activityTimeFunction
static ParamKey	IPK_Element_nip
Protected Attributes inherited from oofem::StructuralElement
std::unique_ptr< FloatArray >	initialDisplacements
	Initial displacement vector, describes the initial nodal displacements when element has been casted.
Protected Attributes inherited from oofem::Element
int	numberOfDofMans
	Number of dofmanagers.
IntArray	dofManArray
	Array containing dofmanager numbers.
int	material
	Number of associated material.
int	crossSection
	Number of associated cross section.
IntArray	bodyLoadArray
IntArray	boundaryLoadArray
std::vector< std ::unique_ptr< IntegrationRule > >	integrationRulesArray
FloatMatrix	elemLocalCS
	Transformation material matrix, used in orthotropic and anisotropic materials, global->local transformation.
int	activityTimeFunction
	Element activity time function. If defined, nonzero value indicates active receiver, zero value inactive element.
int	globalNumber
int	numberOfGaussPoints
elementParallelMode	parallel_mode
	Determines the parallel mode of the element.
IntArray	partitions
IntArray	globalEdgeIDs
IntArray	globalSurfaceIDs
Protected Attributes inherited from oofem::FEMComponent
int	number
	Component number.
Domain *	domain
	Link to domain object, useful for communicating with other FEM components.

Detailed Description

This class implements an triangular six-node plate subsoil element with quadratic interpolation in xy plane. Each node has 1 degree of freedom (out-of-plane displacement).

Loading types supported;

Reference: Bittnar, Sejnoha: Numerical Methods in Structural Mechanics, Thomas Telford, Jan 1, 1996, ISBN-13: 978-0784401705

Author: Borek Patzak

Definition at line 55 of file tria2platesubsoil.h.

Constructor & Destructor Documentation

◆ Tria2PlateSubSoil()

oofem::Tria2PlateSubSoil::Tria2PlateSubSoil	(	int	n,
		Domain *	d )

Definition at line 47 of file tria2platesubsoil.C.

References oofem::Element::numberOfDofMans, oofem::Element::numberOfGaussPoints, and oofem::Tria1PlateSubSoil::Tria1PlateSubSoil().

◆ ~Tria2PlateSubSoil()

virtual oofem::Tria2PlateSubSoil::~Tria2PlateSubSoil ( )

inlinevirtual

Definition at line 62 of file tria2platesubsoil.h.

Member Function Documentation

◆ computeBmatrixAt()

void oofem::Tria2PlateSubSoil::computeBmatrixAt	(	GaussPoint *	gp,
		FloatMatrix &	answer,
		int	lowerIndx = 1,
		int	upperIndx = ALL_STRAINS )

overrideprotectedvirtual

Computes the geometrical matrix of receiver in given integration point. The product of this matrix (assembled at given integration point) and element displacement vector is element strain vector. If lowerIndx and upperIndx parameters are specified, answer is formed only for strains within this interval. This will affects the size of answer.

Parameters

gp	Integration point for which answer is computed.
answer	Geometric matrix of receiver.
lowerIndx	If specified, answer is formed only for strain with index equal and greater than lowerIndx. This parameter has default value 1 (answer is formed from first strain).
upperIndx	If specified, answer is formed only for strain with index less and equal than upperIndx. This parameter has default value ALL_STRAINS (answer is formed for all strains).

Todo: Check sign here

Todo: Check sign here

Reimplemented from oofem::Tria1PlateSubSoil.

Definition at line 80 of file tria2platesubsoil.C.

References oofem::GaussPoint::giveNaturalCoordinates(), interp_quad, oofem::FloatMatrix::resize(), and oofem::FloatMatrix::zero().

◆ computeGaussPoints()

void oofem::Tria2PlateSubSoil::computeGaussPoints ( )

overrideprotectedvirtual

Initializes the array of integration rules member variable. Element can have multiple integration rules for different tasks. For example structural element family class uses this feature to implement transparent support for reduced and selective integration of some strain components. Must be defined by terminator classes.

See also: IntegrationRule

Reimplemented from oofem::Tria1PlateSubSoil.

Definition at line 67 of file tria2platesubsoil.C.

References oofem::Element::giveCrossSection(), oofem::Element::integrationRulesArray, and oofem::Element::numberOfGaussPoints.

◆ computeNmatrixAt()

void oofem::Tria2PlateSubSoil::computeNmatrixAt	(	const FloatArray &	iLocCoord,
		FloatMatrix &	answer )

overrideprotectedvirtual

Computes interpolation matrix for element unknowns. The order and meaning of unknowns is element dependent.

Parameters

iLocCoord	Local coordinates.
answer	Interpolation matrix evaluated at gp.

Reimplemented from oofem::Tria1PlateSubSoil.

Definition at line 141 of file tria2platesubsoil.C.

References oofem::FloatMatrix::beNMatrixOf(), giveInterpolation(), and N.

Referenced by computeSurfaceNMatrix().

◆ computeNumberOfDofs()

int oofem::Tria2PlateSubSoil::computeNumberOfDofs ( )

inlineoverridevirtual

Computes or simply returns total number of element's local DOFs. Must be defined by particular element.

Returns: Number of local DOFs of element.

Reimplemented from oofem::Tria1PlateSubSoil.

Definition at line 72 of file tria2platesubsoil.h.

◆ computeSurfaceNMatrix()

void oofem::Tria2PlateSubSoil::computeSurfaceNMatrix	(	FloatMatrix &	answer,
		int	boundaryID,
		const FloatArray &	lcoords )

overrideprotectedvirtual

Computes surface interpolation matrix. Interpolation matrix provide way, how to compute local surface unknowns (nonzero element unknowns on surface) at any integration point of surface, based on local unknowns in surface nodes. Local coordinate system of surface edge and element surface numbering is element dependent. The integration point is specified using two-dimensional iso coordinates, or using area coordinates for triangular surface.

Parameters