A three node 2D triangle geometry with linear shape functions. More...

#include <triangle_2d_3.h>

Inheritance diagram for Kratos::Triangle2D3< TPointType >:

Collaboration diagram for Kratos::Triangle2D3< TPointType >:

Public Member Functions
Life Cycle
	Triangle2D3 (typename PointType::Pointer pFirstPoint, typename PointType::Pointer pSecondPoint, typename PointType::Pointer pThirdPoint)

	Triangle2D3 (const PointsArrayType &ThisPoints)

	Triangle2D3 (const IndexType GeometryId, const PointsArrayType &rThisPoints)
	Constructor with Geometry Id. More...

	Triangle2D3 (const std::string &rGeometryName, const PointsArrayType &rThisPoints)
	Constructor with Geometry Name. More...

	Triangle2D3 (Triangle2D3 const &rOther)

template<class TOtherPointType >
	Triangle2D3 (Triangle2D3< TOtherPointType > const &rOther)

	~Triangle2D3 () override

GeometryData::KratosGeometryFamily	GetGeometryFamily () const override

GeometryData::KratosGeometryType	GetGeometryType () const override

Operators
Triangle2D3 &	operator= (const Triangle2D3 &rOther)

template<class TOtherPointType >
Triangle2D3 &	operator= (Triangle2D3< TOtherPointType > const &rOther)

Operations
BaseType::Pointer	Create (PointsArrayType const &rThisPoints) const override
	Creates a new geometry pointer. More...

BaseType::Pointer	Create (const IndexType NewGeometryId, PointsArrayType const &rThisPoints) const override
	Creates a new geometry pointer. More...

BaseType::Pointer	Create (const BaseType &rGeometry) const override
	Creates a new geometry pointer. More...

BaseType::Pointer	Create (const IndexType NewGeometryId, const BaseType &rGeometry) const override
	Creates a new geometry pointer. More...

Matrix &	PointsLocalCoordinates (Matrix &rResult) const override

Vector &	LumpingFactors (Vector &rResult, const typename BaseType::LumpingMethods LumpingMethod=BaseType::LumpingMethods::ROW_SUM) const override
	Lumping factors for the calculation of the lumped mass matrix. More...

Information
double	Length () const override

double	Area () const override

bool	HasIntersection (const BaseType &rThisGeometry) const override
	Detect if this triangle is intersected with another geometry. More...

bool	HasIntersection (const Point &rLowPoint, const Point &rHighPoint) const override

double	DomainSize () const override

virtual double	Semiperimeter () const
	Class Interface. More...

double	MinEdgeLength () const override

double	MaxEdgeLength () const override

double	AverageEdgeLength () const override

double	Circumradius () const override

double	Inradius () const override

double	InradiusToCircumradiusQuality () const override
	Quality functions. More...

double	InradiusToLongestEdgeQuality () const override

double	AreaToEdgeLengthRatio () const override

double	ShortestAltitudeToEdgeLengthRatio () const override

array_1d< double, 3 >	Normal (const CoordinatesArrayType &rPointLocalCoordinates) const override
	It returns a vector that is normal to its corresponding geometry in the given local point. More...

bool	IsInside (const CoordinatesArrayType &rPoint, CoordinatesArrayType &rResult, const double Tolerance=std::numeric_limits< double >::epsilon()) const override

CoordinatesArrayType &	PointLocalCoordinates (CoordinatesArrayType &rResult, const CoordinatesArrayType &rPoint) const override

Edge
SizeType	EdgesNumber () const override
	This method gives you number of all edges of this geometry. More...

GeometriesArrayType	GenerateEdges () const override
	This method gives you all edges of this geometry. More...

SizeType	FacesNumber () const override
	Returns the number of faces of the current geometry. More...

void	NumberNodesInFaces (DenseVector< unsigned int > &NumberNodesInFaces) const override

void	NodesInFaces (DenseMatrix< unsigned int > &NodesInFaces) const override

Shape Function
double	ShapeFunctionValue (IndexType ShapeFunctionIndex, const CoordinatesArrayType &rPoint) const override

Vector &	ShapeFunctionsValues (Vector &rResult, const CoordinatesArrayType &rCoordinates) const override

void	ShapeFunctionsIntegrationPointsGradients (ShapeFunctionsGradientsType &rResult, IntegrationMethod ThisMethod) const override

void	ShapeFunctionsIntegrationPointsGradients (ShapeFunctionsGradientsType &rResult, Vector &determinants_of_jacobian, IntegrationMethod ThisMethod) const override

Vector &	DeterminantOfJacobian (Vector &rResult, IntegrationMethod ThisMethod) const override

double	DeterminantOfJacobian (IndexType IntegrationPointIndex, IntegrationMethod ThisMethod) const override

double	DeterminantOfJacobian (const CoordinatesArrayType &rPoint) const override

Input and output
std::string	Info () const override

void	PrintInfo (std::ostream &rOStream) const override

void	PrintData (std::ostream &rOStream) const override

virtual ShapeFunctionsGradientsType	ShapeFunctionsLocalGradients (IntegrationMethod ThisMethod)

virtual ShapeFunctionsGradientsType	ShapeFunctionsLocalGradients ()

Matrix &	ShapeFunctionsLocalGradients (Matrix &rResult, const CoordinatesArrayType &rPoint) const override

virtual Matrix &	ShapeFunctionsGradients (Matrix &rResult, PointType &rPoint)

ShapeFunctionsSecondDerivativesType &	ShapeFunctionsSecondDerivatives (ShapeFunctionsSecondDerivativesType &rResult, const CoordinatesArrayType &rPoint) const override

ShapeFunctionsThirdDerivativesType &	ShapeFunctionsThirdDerivatives (ShapeFunctionsThirdDerivativesType &rResult, const CoordinatesArrayType &rPoint) const override

Public Member Functions inherited from Kratos::Geometry< TPointType >
	Geometry ()
	Standard Constructor. Generates self assigned id. More...

	Geometry (IndexType GeomertyId)
	Standard Constructor with a geometry Id. More...

	Geometry (const std::string &GeometryName)
	Standard Constructor with a Name. More...

	Geometry (const PointsArrayType &ThisPoints, GeometryData const *pThisGeometryData=&GeometryDataInstance())

	Geometry (IndexType GeometryId, const PointsArrayType &ThisPoints, GeometryData const *pThisGeometryData=&GeometryDataInstance())

	Geometry (const std::string &GeometryName, const PointsArrayType &ThisPoints, GeometryData const *pThisGeometryData=&GeometryDataInstance())

	Geometry (const Geometry &rOther)
	Copy constructor. More...

template<class TOtherPointType >
	Geometry (Geometry< TOtherPointType > const &rOther)
	Copy constructor with TOtherPointType. More...

virtual	~Geometry ()
	Destructor. Do nothing!!! More...

Geometry &	operator= (const Geometry &rOther)

template<class TOtherPointType >
Geometry &	operator= (Geometry< TOtherPointType > const &rOther)

	operator PointsArrayType & ()

TPointType &	operator[] (const SizeType &i)

TPointType const &	operator[] (const SizeType &i) const

PointPointerType &	operator() (const SizeType &i)

ConstPointPointerType &	operator() (const SizeType &i) const

iterator	begin ()

const_iterator	begin () const

iterator	end ()

const_iterator	end () const

ptr_iterator	ptr_begin ()

ptr_const_iterator	ptr_begin () const

ptr_iterator	ptr_end ()

ptr_const_iterator	ptr_end () const

PointReferenceType	front ()

ConstPointReferenceType	front () const

PointReferenceType	back ()

ConstPointReferenceType	back () const

SizeType	size () const

SizeType	PointsNumber () const

virtual SizeType	PointsNumberInDirection (IndexType LocalDirectionIndex) const
	Returns number of points per direction. More...

SizeType	max_size () const

void	swap (GeometryType &rOther)

void	push_back (PointPointerType x)

void	clear ()

void	reserve (int dim)

int	capacity ()

PointPointerContainerType &	GetContainer ()
	‍** Gives a reference to underly normal container. *‍/ More...

const PointPointerContainerType &	GetContainer () const

DataValueContainer &	GetData ()

DataValueContainer const &	GetData () const

void	SetData (DataValueContainer const &rThisData)

template<class TDataType >
bool	Has (const Variable< TDataType > &rThisVariable) const

template<class TVariableType >
void	SetValue (const TVariableType &rThisVariable, typename TVariableType::Type const &rValue)

template<class TVariableType >
TVariableType::Type &	GetValue (const TVariableType &rThisVariable)

template<class TVariableType >
TVariableType::Type const &	GetValue (const TVariableType &rThisVariable) const

virtual void	Assign (const Variable< bool > &rVariable, const bool Input)
	Assign with bool. More...

virtual void	Assign (const Variable< int > &rVariable, const int Input)
	Assign with int. More...

virtual void	Assign (const Variable< double > &rVariable, const double Input)
	Assign with double. More...

virtual void	Assign (const Variable< array_1d< double, 2 >> &rVariable, const array_1d< double, 2 > &rInput)
	Assign with array_1d<double, 2> More...

virtual void	Assign (const Variable< array_1d< double, 3 >> &rVariable, const array_1d< double, 3 > &rInput)
	Assign with array_1d<double, 3> More...

virtual void	Assign (const Variable< array_1d< double, 6 >> &rVariable, const array_1d< double, 6 > &rInput)
	Assign with array_1d<double, 6> More...

virtual void	Assign (const Variable< Vector > &rVariable, const Vector &rInput)
	Assign with Vector. More...

virtual void	Assign (const Variable< Matrix > &rVariable, const Matrix &rInput)
	Assign with Matrix. More...

virtual void	Calculate (const Variable< bool > &rVariable, bool &rOutput) const
	Calculate with bool. More...

virtual void	Calculate (const Variable< int > &rVariable, int &rOutput) const
	Calculate with int. More...

virtual void	Calculate (const Variable< double > &rVariable, double &rOutput) const
	Calculate with double. More...

virtual void	Calculate (const Variable< array_1d< double, 2 >> &rVariable, array_1d< double, 2 > &rOutput) const
	Calculate with array_1d<double, 2> More...

virtual void	Calculate (const Variable< array_1d< double, 3 >> &rVariable, array_1d< double, 3 > &rOutput) const
	Calculate with array_1d<double, 3> More...

virtual void	Calculate (const Variable< array_1d< double, 6 >> &rVariable, array_1d< double, 6 > &rOutput) const
	Calculate with array_1d<double, 6> More...

virtual void	Calculate (const Variable< Vector > &rVariable, Vector &rOutput) const
	Calculate with Vector. More...

virtual void	Calculate (const Variable< Matrix > &rVariable, Matrix &rOutput) const
	Calculate with Matrix. More...

Pointer	Create (const std::string &rNewGeometryName, PointsArrayType const &rThisPoints) const
	Creates a new geometry pointer. More...

virtual Pointer	Create (const GeometryType &rGeometry) const
	Creates a new geometry pointer. More...

virtual Pointer	Create (const IndexType NewGeometryId, const GeometryType &rGeometry) const
	Creates a new geometry pointer. More...

Pointer	Create (const std::string &rNewGeometryName, const GeometryType &rGeometry) const
	Creates a new geometry pointer. More...

void	ClonePoints ()

GeometryData const &	GetGeometryData () const
	GeometryData contains all information about dimensions and has a set of precomputed values for integration points and shape functions, including derivatives. More...

virtual void	SetGeometryShapeFunctionContainer (const GeometryShapeFunctionContainer< GeometryData::IntegrationMethod > &rGeometryShapeFunctionContainer)

virtual GeometryType &	GetGeometryParent (IndexType Index) const
	Some geometries require relations to other geometries. This is the case for e.g. quadrature points. To reach the parent geometry this function can be used. More...

virtual void	SetGeometryParent (GeometryType *pGeometryParent)
	Some geometries require relations to other geometries. This is the case for e.g. quadrature points. To set or change the parent geometry this function can be used. More...

virtual GeometryType &	GetGeometryPart (const IndexType Index)
	Used for composite geometries. It returns the the geometry part, corresponding to the Index. More...

virtual const GeometryType &	GetGeometryPart (const IndexType Index) const
	Used for composite geometries. It returns the the geometry part, corresponding to the Index. More...

virtual GeometryType::Pointer	pGetGeometryPart (const IndexType Index)
	Used for composite geometries. It returns the pointer of a geometry part, corresponding to the Index. More...

virtual const GeometryType::Pointer	pGetGeometryPart (const IndexType Index) const
	Used for composite geometries. It returns the const pointer of a geometry part, corresponding to the Index. More...

virtual void	SetGeometryPart (const IndexType Index, GeometryType::Pointer pGeometry)
	Allows to exchange certain geometries. More...

virtual IndexType	AddGeometryPart (GeometryType::Pointer pGeometry)
	Allows to enhance the coupling geometry, with another geometry. More...

virtual void	RemoveGeometryPart (GeometryType::Pointer pGeometry)
	Removes a geometry part. More...

virtual void	RemoveGeometryPart (const IndexType Index)
	Removes a geometry part. More...

virtual bool	HasGeometryPart (const IndexType Index) const
	Use to check if certain Indexed object is within the geometry parts of this geometry. More...

virtual SizeType	NumberOfGeometryParts () const

SizeType	WorkingSpaceDimension () const

SizeType	LocalSpaceDimension () const

virtual SizeType	PolynomialDegree (IndexType LocalDirectionIndex) const
	Return polynomial degree of the geometry in a certain direction. More...

virtual double	Volume () const
	This method calculate and return volume of this geometry. More...

virtual bool	HasIntersection (const GeometryType &ThisGeometry) const

virtual void	BoundingBox (TPointType &rLowPoint, TPointType &rHighPoint) const
	Calculates the boundingbox of the geometry. More...

virtual Point	Center () const

virtual array_1d< double, 3 >	Normal (IndexType IntegrationPointIndex) const
	It returns the vector, which is normal to its corresponding geometry in the given integration point for the default integration method. More...

virtual array_1d< double, 3 >	Normal (IndexType IntegrationPointIndex, IntegrationMethod ThisMethod) const
	It returns the vector, which is normal to its corresponding geometry in the given integration point. More...

virtual array_1d< double, 3 >	UnitNormal (const CoordinatesArrayType &rPointLocalCoordinates) const
	It computes the unit normal of the geometry in the given local point. More...

virtual array_1d< double, 3 >	UnitNormal (IndexType IntegrationPointIndex) const
	It returns the normalized normal vector in the given integration point. More...

virtual array_1d< double, 3 >	UnitNormal (IndexType IntegrationPointIndex, IntegrationMethod ThisMethod) const
	It returns the normalized normal vector in the given integration point. More...

double	Quality (const QualityCriteria qualityCriteria) const

virtual void	ComputeDihedralAngles (Vector &rDihedralAngles) const

virtual void	ComputeSolidAngles (Vector &rSolidAngles) const

const PointsArrayType &	Points () const

PointsArrayType &	Points ()

const TPointType::Pointer	pGetPoint (const int Index) const

TPointType::Pointer	pGetPoint (const int Index)

TPointType const &	GetPoint (const int Index) const

TPointType &	GetPoint (const int Index)

virtual int	IsInsideLocalSpace (const CoordinatesArrayType &rPointLocalCoordinates, const double Tolerance=std::numeric_limits< double >::epsilon()) const
	Checks if given point in local space coordinates of this geometry is inside the geometry boundaries. More...

virtual void	SpansLocalSpace (std::vector< double > &rSpans, IndexType LocalDirectionIndex=0) const

virtual GeometriesArrayType	GenerateBoundariesEntities () const
	This method gives you all boundaries entities of this geometry. More...

virtual GeometriesArrayType	GeneratePoints () const
	This method gives you all points of this geometry. More...

	KRATOS_DEPRECATED_MESSAGE ("This is legacy version (use GenerateEdges instead)") virtual GeometriesArrayType Edges(void)
	This method gives you all edges of this geometry. More...

	KRATOS_DEPRECATED_MESSAGE ("This is legacy version (use GenerateFaces instead)") virtual GeometriesArrayType Faces(void)
	Returns all faces of the current geometry. More...

virtual GeometriesArrayType	GenerateFaces () const
	Returns all faces of the current geometry. More...

SizeType	IntegrationPointsNumber () const

SizeType	IntegrationPointsNumber (IntegrationMethod ThisMethod) const

const IntegrationPointsArrayType &	IntegrationPoints () const

const IntegrationPointsArrayType &	IntegrationPoints (IntegrationMethod ThisMethod) const

virtual void	CreateIntegrationPoints (IntegrationPointsArrayType &rIntegrationPoints, IntegrationInfo &rIntegrationInfo) const

virtual void	CreateQuadraturePointGeometries (GeometriesArrayType &rResultGeometries, IndexType NumberOfShapeFunctionDerivatives, const IntegrationPointsArrayType &rIntegrationPoints, IntegrationInfo &rIntegrationInfo)

virtual void	CreateQuadraturePointGeometries (GeometriesArrayType &rResultGeometries, IndexType NumberOfShapeFunctionDerivatives, IntegrationInfo &rIntegrationInfo)

virtual CoordinatesArrayType &	GlobalCoordinates (CoordinatesArrayType &rResult, CoordinatesArrayType const &LocalCoordinates) const

void	GlobalCoordinates (CoordinatesArrayType &rResult, IndexType IntegrationPointIndex) const

void	GlobalCoordinates (CoordinatesArrayType &rResult, IndexType IntegrationPointIndex, const IntegrationMethod ThisMethod) const
	This method provides the global coordinates to the corresponding integration point. More...

virtual CoordinatesArrayType &	GlobalCoordinates (CoordinatesArrayType &rResult, CoordinatesArrayType const &LocalCoordinates, Matrix &DeltaPosition) const

virtual void	GlobalSpaceDerivatives (std::vector< CoordinatesArrayType > &rGlobalSpaceDerivatives, const CoordinatesArrayType &rLocalCoordinates, const SizeType DerivativeOrder) const
	This method maps from dimension space to working space and computes the number of derivatives at the dimension parameter. More...

virtual void	GlobalSpaceDerivatives (std::vector< CoordinatesArrayType > &rGlobalSpaceDerivatives, IndexType IntegrationPointIndex, const SizeType DerivativeOrder) const
	This method maps from dimension space to working space and computes the number of derivatives at the dimension parameter. More...

virtual int	ProjectionPoint (const CoordinatesArrayType &rPointGlobalCoordinates, CoordinatesArrayType &rProjectedPointGlobalCoordinates, CoordinatesArrayType &rProjectedPointLocalCoordinates, const double Tolerance=std::numeric_limits< double >::epsilon()) const
	Projects a certain point on the geometry, or finds the closest point, depending on the provided initial guess. The external point does not necessary lay on the geometry. It shall deal as the interface to the mathematical projection function e.g. the Newton-Raphson. Thus, the breaking criteria does not necessarily mean that it found a point on the surface, if it is really the closest if or not. It shows only if the breaking criteria, defined by the tolerance is reached. More...

virtual int	ProjectionPointLocalToLocalSpace (const CoordinatesArrayType &rPointLocalCoordinates, CoordinatesArrayType &rProjectionPointLocalCoordinates, const double Tolerance=std::numeric_limits< double >::epsilon()) const
	Projects a point onto the geometry Projects a certain point on the geometry, or finds the closest point, depending on the provided initial guess. The external point does not necessary lay on the geometry. It shall deal as the interface to the mathematical projection function e.g. the Newton-Raphson. Thus, the breaking criteria does not necessarily mean that it found a point on the surface, if it is really the closest if or not. It shows only if the breaking criteria, defined by the tolerance is reached. This function requires an initial guess, provided by rProjectionPointLocalCoordinates. This function can be a very costly operation. More...

virtual int	ProjectionPointGlobalToLocalSpace (const CoordinatesArrayType &rPointGlobalCoordinates, CoordinatesArrayType &rProjectionPointLocalCoordinates, const double Tolerance=std::numeric_limits< double >::epsilon()) const
	Projects a point onto the geometry Projects a certain point on the geometry, or finds the closest point, depending on the provided initial guess. The external point does not necessary lay on the geometry. It shall deal as the interface to the mathematical projection function e.g. the Newton-Raphson. Thus, the breaking criteria does not necessarily mean that it found a point on the surface, if it is really the closest if or not. It shows only if the breaking criteria, defined by the tolerance is reached. This function requires an initial guess, provided by rProjectionPointLocalCoordinates. This function can be a very costly operation. More...

virtual int	ClosestPoint (const CoordinatesArrayType &rPointGlobalCoordinates, CoordinatesArrayType &rClosestPointGlobalCoordinates, CoordinatesArrayType &rClosestPointLocalCoordinates, const double Tolerance=std::numeric_limits< double >::epsilon()) const
	Returns all coordinates of the closest point on the geometry given to an arbitrary point in global coordinates. The basic concept is to first do a projection towards this geometry and second checking if the projection was successfull or if no point on the geometry was found. More...

virtual int	ClosestPoint (const CoordinatesArrayType &rPointGlobalCoordinates, CoordinatesArrayType &rClosestPointGlobalCoordinates, const double Tolerance=std::numeric_limits< double >::epsilon()) const
	Returns global coordinates of the closest point on the geometry given to an arbitrary point in global coordinates. The basic concept is to first do a projection towards this geometry and second checking if the projection was successfull or if no point on the geometry was found. More...

virtual int	ClosestPointLocalCoordinates (const CoordinatesArrayType &rPointGlobalCoordinates, CoordinatesArrayType &rClosestPointLocalCoordinates, const double Tolerance=std::numeric_limits< double >::epsilon()) const
	Returns local coordinates of the closest point on the geometry given to an arbitrary point in global coordinates. The basic concept is to first do a projection towards this geometry and second checking if the projection was successfull or if no point on the geometry was found. More...

virtual int	ClosestPointLocalToLocalSpace (const CoordinatesArrayType &rPointLocalCoordinates, CoordinatesArrayType &rClosestPointLocalCoordinates, const double Tolerance=std::numeric_limits< double >::epsilon()) const
	Calculates the closes point projection This method calculates the closest point projection of a point in local space coordinates. More...

virtual int	ClosestPointGlobalToLocalSpace (const CoordinatesArrayType &rPointGlobalCoordinates, CoordinatesArrayType &rClosestPointLocalCoordinates, const double Tolerance=std::numeric_limits< double >::epsilon()) const
	Calculates the closes point projection This method calculates the closest point projection of a point in global space coordinates. More...

virtual double	CalculateDistance (const CoordinatesArrayType &rPointGlobalCoordinates, const double Tolerance=std::numeric_limits< double >::epsilon()) const
	Computes the distance between an point in global coordinates and the closest point of this geometry. If projection fails, double::max will be returned. More...

JacobiansType &	Jacobian (JacobiansType &rResult) const

virtual JacobiansType &	Jacobian (JacobiansType &rResult, IntegrationMethod ThisMethod) const

virtual JacobiansType &	Jacobian (JacobiansType &rResult, IntegrationMethod ThisMethod, Matrix &DeltaPosition) const

Matrix &	Jacobian (Matrix &rResult, IndexType IntegrationPointIndex) const

virtual Matrix &	Jacobian (Matrix &rResult, IndexType IntegrationPointIndex, IntegrationMethod ThisMethod) const

virtual Matrix &	Jacobian (Matrix &rResult, IndexType IntegrationPointIndex, IntegrationMethod ThisMethod, const Matrix &rDeltaPosition) const

virtual Matrix &	Jacobian (Matrix &rResult, const CoordinatesArrayType &rCoordinates) const

virtual Matrix &	Jacobian (Matrix &rResult, const CoordinatesArrayType &rCoordinates, Matrix &rDeltaPosition) const

Vector &	DeterminantOfJacobian (Vector &rResult) const

double	DeterminantOfJacobian (IndexType IntegrationPointIndex) const

JacobiansType &	InverseOfJacobian (JacobiansType &rResult) const

virtual JacobiansType &	InverseOfJacobian (JacobiansType &rResult, IntegrationMethod ThisMethod) const

Matrix &	InverseOfJacobian (Matrix &rResult, IndexType IntegrationPointIndex) const

virtual Matrix &	InverseOfJacobian (Matrix &rResult, IndexType IntegrationPointIndex, IntegrationMethod ThisMethod) const

virtual Matrix &	InverseOfJacobian (Matrix &rResult, const CoordinatesArrayType &rCoordinates) const

const Matrix &	ShapeFunctionsValues () const

const Matrix &	ShapeFunctionsValues (IntegrationMethod ThisMethod) const

double	ShapeFunctionValue (IndexType IntegrationPointIndex, IndexType ShapeFunctionIndex) const

double	ShapeFunctionValue (IndexType IntegrationPointIndex, IndexType ShapeFunctionIndex, IntegrationMethod ThisMethod) const

const ShapeFunctionsGradientsType &	ShapeFunctionsLocalGradients () const

const ShapeFunctionsGradientsType &	ShapeFunctionsLocalGradients (IntegrationMethod ThisMethod) const

const Matrix &	ShapeFunctionLocalGradient (IndexType IntegrationPointIndex) const

const Matrix &	ShapeFunctionLocalGradient (IndexType IntegrationPointIndex, IntegrationMethod ThisMethod) const

const Matrix &	ShapeFunctionLocalGradient (IndexType IntegrationPointIndex, IndexType ShapeFunctionIndex, IntegrationMethod ThisMethod) const

const Matrix &	ShapeFunctionDerivatives (IndexType DerivativeOrderIndex, IndexType IntegrationPointIndex, IntegrationMethod ThisMethod) const

const Matrix &	ShapeFunctionDerivatives (IndexType DerivativeOrderIndex, IndexType IntegrationPointIndex) const

void	ShapeFunctionsIntegrationPointsGradients (ShapeFunctionsGradientsType &rResult) const

virtual void	ShapeFunctionsIntegrationPointsGradients (ShapeFunctionsGradientsType &rResult, Vector &rDeterminantsOfJacobian, IntegrationMethod ThisMethod, Matrix &ShapeFunctionsIntegrationPointsValues) const

virtual int	Check () const

virtual std::string	Name () const
	Returns name. More...

virtual void	PrintName (std::ostream &rOstream) const
	Print name. More...

	KRATOS_CLASS_POINTER_DEFINITION (Geometry)
	Pointer definition of Geometry. More...

bool	empty () const

bool	HasIntegrationMethod (IntegrationMethod ThisMethod) const

IntegrationMethod	GetDefaultIntegrationMethod () const

virtual IntegrationInfo	GetDefaultIntegrationInfo () const
	Provides the default integration per geometry. More...

virtual bool	IsSymmetric () const

IndexType const &	Id () const
	Id of this Geometry. More...

bool	IsIdGeneratedFromString ()
	Returns if id was generated from a geometry name. More...

bool	IsIdSelfAssigned ()
	Returns if id was generated by itself. More...

void	SetId (const IndexType Id)
	Sets Id of this Geometry. More...

void	SetId (const std::string &rName)
	Sets Id with the use of the name of this geometry. More...

Friends
Private Friends
template<class TOtherPointType >
class	Triangle2D3

Friends inherited from Kratos::Geometry< TPointType >

Type Definitions
typedef Geometry< TPointType >	BaseType

typedef Line2D2< TPointType >	EdgeType

typedef GeometryData::IntegrationMethod	IntegrationMethod

typedef BaseType::GeometriesArrayType	GeometriesArrayType

typedef TPointType	PointType

typedef BaseType::IndexType	IndexType

typedef BaseType::SizeType	SizeType

typedef BaseType::PointsArrayType	PointsArrayType

typedef BaseType::CoordinatesArrayType	CoordinatesArrayType

typedef BaseType::IntegrationPointType	IntegrationPointType

typedef BaseType::IntegrationPointsArrayType	IntegrationPointsArrayType

typedef BaseType::IntegrationPointsContainerType	IntegrationPointsContainerType

typedef BaseType::ShapeFunctionsValuesContainerType	ShapeFunctionsValuesContainerType

typedef BaseType::ShapeFunctionsLocalGradientsContainerType	ShapeFunctionsLocalGradientsContainerType

typedef BaseType::JacobiansType	JacobiansType

typedef BaseType::ShapeFunctionsGradientsType	ShapeFunctionsGradientsType

typedef BaseType::ShapeFunctionsSecondDerivativesType	ShapeFunctionsSecondDerivativesType

typedef BaseType::ShapeFunctionsThirdDerivativesType	ShapeFunctionsThirdDerivativesType

typedef BaseType::NormalType	NormalType

	KRATOS_CLASS_POINTER_DEFINITION (Triangle2D3)

Serialization
class	Serializer

Additional Inherited Members
Public Types inherited from Kratos::Geometry< TPointType >
enum class	QualityCriteria { INRADIUS_TO_CIRCUMRADIUS , AREA_TO_LENGTH , SHORTEST_ALTITUDE_TO_LENGTH , INRADIUS_TO_LONGEST_EDGE , SHORTEST_TO_LONGEST_EDGE , REGULARITY , VOLUME_TO_SURFACE_AREA , VOLUME_TO_EDGE_LENGTH , VOLUME_TO_AVERAGE_EDGE_LENGTH , VOLUME_TO_RMS_EDGE_LENGTH , MIN_DIHEDRAL_ANGLE , MAX_DIHEDRAL_ANGLE , MIN_SOLID_ANGLE }

enum class	LumpingMethods { ROW_SUM , DIAGONAL_SCALING , QUADRATURE_ON_NODES }
	This defines the different methods to compute the lumping methods. More...

typedef Geometry< TPointType >	GeometryType
	This Geometry type. More...

typedef PointerVector< TPointType >	PointsArrayType

typedef GeometryData::IntegrationMethod	IntegrationMethod

typedef PointerVector< GeometryType >	GeometriesArrayType

typedef TPointType	PointType

typedef std::size_t	IndexType

typedef std::size_t	SizeType

typedef PointType::CoordinatesArrayType	CoordinatesArrayType

typedef IntegrationPoint< 3 >	IntegrationPointType

typedef std::vector< IntegrationPointType >	IntegrationPointsArrayType

typedef std::array< IntegrationPointsArrayType, static_cast< int >GeometryData::IntegrationMethod::NumberOfIntegrationMethods)>	IntegrationPointsContainerType

typedef std::array< Matrix, static_cast< int >GeometryData::IntegrationMethod::NumberOfIntegrationMethods)>	ShapeFunctionsValuesContainerType

typedef GeometryData::ShapeFunctionsLocalGradientsContainerType	ShapeFunctionsLocalGradientsContainerType

typedef DenseVector< Matrix >	JacobiansType

typedef GeometryData::ShapeFunctionsGradientsType	ShapeFunctionsGradientsType

typedef GeometryData::ShapeFunctionsSecondDerivativesType	ShapeFunctionsSecondDerivativesType

typedef GeometryData::ShapeFunctionsThirdDerivativesType	ShapeFunctionsThirdDerivativesType

typedef DenseVector< double >	NormalType

typedef PointType::Pointer	PointPointerType
	data type stores in this container. More...

typedef const PointPointerType	ConstPointPointerType

typedef TPointType &	PointReferenceType

typedef const TPointType &	ConstPointReferenceType

typedef std::vector< PointPointerType >	PointPointerContainerType

typedef PointsArrayType::iterator	iterator
	PointsArrayType typedefs. More...

typedef PointsArrayType::const_iterator	const_iterator

typedef PointsArrayType::ptr_iterator	ptr_iterator

typedef PointsArrayType::ptr_const_iterator	ptr_const_iterator

typedef PointsArrayType::difference_type	difference_type

Static Public Member Functions inherited from Kratos::Geometry< TPointType >
static bool	HasSameType (const GeometryType &rLHS, const GeometryType &rRHS)
	Checks if two GeometryType have the same type. More...

static bool	HasSameType (const GeometryType rLHS, const GeometryType rRHS)
	Checks if two GeometryType have the same type (pointer version) More...

static bool	HasSameGeometryType (const GeometryType &rLHS, const GeometryType &rRHS)
	Checks if two GeometryType have the same geometry type. More...

static bool	HasSameGeometryType (const GeometryType rLHS, const GeometryType rRHS)
	Checks if two GeometryType have the same geometry type (pointer version) More...

static bool	IsSame (const GeometryType &rLHS, const GeometryType &rRHS)
	Checks if two GeometryType are the same. More...

static bool	IsSame (const GeometryType rLHS, const GeometryType rRHS)
	Checks if two GeometryType are the same (pointer version) More...

static IndexType	GenerateId (const std::string &rName)
	Gets the corresponding hash-Id to a string name. More...

Static Public Attributes inherited from Kratos::Geometry< TPointType >
static constexpr IndexType	BACKGROUND_GEOMETRY_INDEX = std::numeric_limits<IndexType>::max()

Protected Member Functions inherited from Kratos::Geometry< TPointType >
void	SetGeometryData (GeometryData const *pGeometryData)
	updates the pointer to GeometryData of the respective geometry. More...

virtual double	ShortestToLongestEdgeQuality () const

virtual double	RegularityQuality () const

virtual double	VolumeToSurfaceAreaQuality () const

virtual double	VolumeToEdgeLengthQuality () const

virtual double	VolumeToAverageEdgeLength () const

virtual double	VolumeToRMSEdgeLength () const

virtual double	MinDihedralAngle () const

virtual double	MaxDihedralAngle () const

virtual double	MinSolidAngle () const

bool	AllPointsAreValid () const
	Checks if the geometry points are valid Checks if the geometry points are valid from the pointer value Points are not valid when the pointer value is null. More...

Detailed Description

template<class TPointType>
class Kratos::Triangle2D3< TPointType >

A three node 2D triangle geometry with linear shape functions.

While the shape functions are only defined in 2D it is possible to define an arbitrary orientation in space. Thus it can be used for defining surfaces on 3D elements. The node ordering corresponds with: v ^ | 2 |\ |\ | \ |\ | `\ 0-------—1 --> u

Author: Riccardo Rossi; Janosch Stascheit; Felix Nagel

Member Typedef Documentation

◆ BaseType

template<class TPointType >

typedef Geometry<TPointType> Kratos::Triangle2D3< TPointType >::BaseType

Geometry as base class.

◆ CoordinatesArrayType

template<class TPointType >

typedef BaseType::CoordinatesArrayType Kratos::Triangle2D3< TPointType >::CoordinatesArrayType

Array of coordinates. Can be Nodes, Points or IntegrationPoints

◆ EdgeType

template<class TPointType >

typedef Line2D2<TPointType> Kratos::Triangle2D3< TPointType >::EdgeType

Type of edge geometry

◆ GeometriesArrayType

template<class TPointType >

typedef BaseType::GeometriesArrayType Kratos::Triangle2D3< TPointType >::GeometriesArrayType

A Vector of counted pointers to Geometries. Used for returning edges of the geometry.

◆ IndexType

template<class TPointType >

typedef BaseType::IndexType Kratos::Triangle2D3< TPointType >::IndexType

Type used for indexing in geometry class. std::size_t used for indexing point or integration point access methods and also all other methods which need point or integration point index.

◆ IntegrationMethod

template<class TPointType >

typedef GeometryData::IntegrationMethod Kratos::Triangle2D3< TPointType >::IntegrationMethod

Integration methods implemented in geometry.

◆ IntegrationPointsArrayType

template<class TPointType >

typedef BaseType::IntegrationPointsArrayType Kratos::Triangle2D3< TPointType >::IntegrationPointsArrayType

A Vector of IntegrationPointType which used to hold integration points related to an integration method. IntegrationPoints functions used this type to return their results.

◆ IntegrationPointsContainerType

template<class TPointType >

typedef BaseType::IntegrationPointsContainerType Kratos::Triangle2D3< TPointType >::IntegrationPointsContainerType

A Vector of IntegrationPointsArrayType which used to hold integration points related to different integration method implemented in geometry.

◆ IntegrationPointType

template<class TPointType >

typedef BaseType::IntegrationPointType Kratos::Triangle2D3< TPointType >::IntegrationPointType

This type used for representing an integration point in geometry. This integration point is a point with an additional weight component.

◆ JacobiansType

template<class TPointType >

typedef BaseType::JacobiansType Kratos::Triangle2D3< TPointType >::JacobiansType

A third order tensor to hold jacobian matrices evaluated at integration points. Jacobian and InverseOfJacobian functions return this type as their result.

◆ NormalType

template<class TPointType >

typedef BaseType::NormalType Kratos::Triangle2D3< TPointType >::NormalType

Type of the normal vector used for normal to edges in geometry.

◆ PointsArrayType

template<class TPointType >

typedef BaseType::PointsArrayType Kratos::Triangle2D3< TPointType >::PointsArrayType

Array of counted pointers to point. This type used to hold geometry's points.

◆ PointType

template<class TPointType >

typedef TPointType Kratos::Triangle2D3< TPointType >::PointType

Redefinition of template parameter TPointType.

◆ ShapeFunctionsGradientsType

template<class TPointType >

typedef BaseType::ShapeFunctionsGradientsType Kratos::Triangle2D3< TPointType >::ShapeFunctionsGradientsType

A third order tensor to hold shape functions' local gradients. ShapefunctionsLocalGradients function return this type as its result.

◆ ShapeFunctionsLocalGradientsContainerType

template<class TPointType >

typedef BaseType::ShapeFunctionsLocalGradientsContainerType Kratos::Triangle2D3< TPointType >::ShapeFunctionsLocalGradientsContainerType

A fourth order tensor used as shape functions' local gradients container in geometry.

◆ ShapeFunctionsSecondDerivativesType

template<class TPointType >

typedef BaseType::ShapeFunctionsSecondDerivativesType Kratos::Triangle2D3< TPointType >::ShapeFunctionsSecondDerivativesType

A third order tensor to hold shape functions' local second derivatives. ShapefunctionsLocalGradients function return this type as its result.

◆ ShapeFunctionsThirdDerivativesType

template<class TPointType >

typedef BaseType::ShapeFunctionsThirdDerivativesType Kratos::Triangle2D3< TPointType >::ShapeFunctionsThirdDerivativesType

A third order tensor to hold shape functions' local third derivatives. ShapefunctionsLocalGradients function return this type as its result.

◆ ShapeFunctionsValuesContainerType

template<class TPointType >

typedef BaseType::ShapeFunctionsValuesContainerType Kratos::Triangle2D3< TPointType >::ShapeFunctionsValuesContainerType

A third order tensor used as shape functions' values container.

◆ SizeType

template<class TPointType >

typedef BaseType::SizeType Kratos::Triangle2D3< TPointType >::SizeType

This type is used to return size or dimension in geometry. Dimension, WorkingDimension, PointsNumber and ... return this type as their results.

Constructor & Destructor Documentation

◆ Triangle2D3() [1/6]

template<class TPointType >

Kratos::Triangle2D3< TPointType >::Triangle2D3	(	typename PointType::Pointer	pFirstPoint,
		typename PointType::Pointer	pSecondPoint,
		typename PointType::Pointer	pThirdPoint
	)

inline

◆ Triangle2D3() [2/6]

template<class TPointType >

Kratos::Triangle2D3< TPointType >::Triangle2D3 ( const PointsArrayType & ThisPoints )

inlineexplicit

◆ Triangle2D3() [3/6]

template<class TPointType >

Kratos::Triangle2D3< TPointType >::Triangle2D3	(	const IndexType	GeometryId,
		const PointsArrayType &	rThisPoints
	)

inlineexplicit

Constructor with Geometry Id.

◆ Triangle2D3() [4/6]

template<class TPointType >

Kratos::Triangle2D3< TPointType >::Triangle2D3	(	const std::string &	rGeometryName,
		const PointsArrayType &	rThisPoints
	)

inlineexplicit

Constructor with Geometry Name.

◆ Triangle2D3() [5/6]

template<class TPointType >

Kratos::Triangle2D3< TPointType >::Triangle2D3 ( Triangle2D3< TPointType > const & rOther )

inline

Copy constructor. Construct this geometry as a copy of given geometry.

Note: This copy constructor does not copy the points and new geometry shares points with given source geometry. It is obvious that any change to this new geometry's point affect source geometry's points too.

◆ Triangle2D3() [6/6]

template<class TPointType >

template<class TOtherPointType >

Kratos::Triangle2D3< TPointType >::Triangle2D3 ( Triangle2D3< TOtherPointType > const & rOther )

inlineexplicit

Copy constructor from a geometry with other point type. Construct this geometry as a copy of given geometry which has different type of points. The given goemetry's TOtherPointType* must be implicity convertible to this geometry PointType.

Note: This copy constructor does not copy the points and new geometry shares points with given source geometry. It is obvious that any change to this new geometry's point affect source geometry's points too.

◆ ~Triangle2D3()

template<class TPointType >

Kratos::Triangle2D3< TPointType >::~Triangle2D3 ( )

inlineoverride

Destructor. Does nothing!!!

Member Function Documentation

◆ Area()

template<class TPointType >

double Kratos::Triangle2D3< TPointType >::Area ( ) const

inlineoverridevirtual

This method calculates and returns area or surface area of this geometry depending to it's dimension. For one dimensional geometry it returns zero, for two dimensional it gives area and for three dimensional geometries it gives surface area.

Returns: double value contains area or surface area.

See also: Length(); Volume(); DomainSize() :TODO: could be replaced by something more suitable (comment by janosch)

Reimplemented from Kratos::Geometry< TPointType >.

◆ AreaToEdgeLengthRatio()

template<class TPointType >

double Kratos::Triangle2D3< TPointType >::AreaToEdgeLengthRatio ( ) const

inlineoverridevirtual

Calculates the minimum to maximum edge length quality metric. Calculates the minimum to maximum edge length quality metric. This metric is bounded by the interval (0,1) being: 1 -> Optimal value 0 -> Worst value

@formulae $$ \frac{h_{min}}{h_{max}} $$

Returns: The Inradius to Circumradius Quality metric.

Reimplemented from Kratos::Geometry< TPointType >.

◆ AverageEdgeLength()

template<class TPointType >

double Kratos::Triangle2D3< TPointType >::AverageEdgeLength ( ) const

inlineoverridevirtual

This method calculates and returns the average edge length of the geometry

Returns: double value with the average edge length

See also: MinEdgeLength(); MaxEdgeLength()

Reimplemented from Kratos::Geometry< TPointType >.

◆ Circumradius()

template<class TPointType >

double Kratos::Triangle2D3< TPointType >::Circumradius ( ) const

inlineoverridevirtual

Calculates the circumradius of the geometry. Calculates the circumradius of the geometry.

Returns: Circumradius of the geometry.

See also: Inradius()

Reimplemented from Kratos::Geometry< TPointType >.

◆ Create() [1/4]

template<class TPointType >

BaseType::Pointer Kratos::Triangle2D3< TPointType >::Create ( const BaseType & rGeometry ) const

inlineoverride

Creates a new geometry pointer.

Parameters

rGeometry reference to an existing geometry

Returns: Pointer to the new geometry

◆ Create() [2/4]

template<class TPointType >

BaseType::Pointer Kratos::Triangle2D3< TPointType >::Create	(	const IndexType	NewGeometryId,
		const BaseType &	rGeometry
	)		const

inlineoverride

Creates a new geometry pointer.

Parameters

NewGeometryId	the ID of the new geometry
rGeometry	reference to an existing geometry

Returns: Pointer to the new geometry

◆ Create() [3/4]

template<class TPointType >

BaseType::Pointer Kratos::Triangle2D3< TPointType >::Create	(	const IndexType	NewGeometryId,
		PointsArrayType const &	rThisPoints
	)		const

inlineoverridevirtual

Creates a new geometry pointer.

Parameters

NewGeometryId	the ID of the new geometry
rThisPoints	the nodes of the new geometry

Returns: Pointer to the new geometry

Reimplemented from Kratos::Geometry< TPointType >.

◆ Create() [4/4]

template<class TPointType >

BaseType::Pointer Kratos::Triangle2D3< TPointType >::Create ( PointsArrayType const & rThisPoints ) const

inlineoverridevirtual

Creates a new geometry pointer.

Parameters

rThisPoints the nodes of the new geometry

Returns: Pointer to the new geometry

Reimplemented from Kratos::Geometry< TPointType >.

◆ DeterminantOfJacobian() [1/3]

template<class TPointType >

double Kratos::Triangle2D3< TPointType >::DeterminantOfJacobian ( const CoordinatesArrayType & rPoint ) const

inlineoverridevirtual

Determinant of jacobian in given point. This method calculate determinant of jacobian matrix in given point.

Parameters

rPoint point which determinant of jacobians has to be calculated in it.

Returns: Determinamt of jacobian matrix $ |J| $ in given point.

See also: DeterminantOfJacobian; InverseOfJacobian

Reimplemented from Kratos::Geometry< TPointType >.

◆ DeterminantOfJacobian() [2/3]

template<class TPointType >

double Kratos::Triangle2D3< TPointType >::DeterminantOfJacobian	(	IndexType	IntegrationPointIndex,
		IntegrationMethod	ThisMethod
	)		const

inlineoverridevirtual

Determinant of jacobian in specific integration point of given integration method. This method calculate determinant of jacobian in given integration point of given integration method.

Parameters

IntegrationPointIndex	index of integration point which jacobians has to be calculated in it.
IntegrationPointIndex	index of integration point which determinant of jacobians has to be calculated in it.

Returns: Determinamt of jacobian matrix $ |J|_i $ where $ i $ is the given integration point index of given integration method.

See also: Jacobian; InverseOfJacobian

Reimplemented from Kratos::Geometry< TPointType >.

◆ DeterminantOfJacobian() [3/3]

template<class TPointType >

Vector& Kratos::Triangle2D3< TPointType >::DeterminantOfJacobian	(	Vector &	rResult,
		IntegrationMethod	ThisMethod
	)		const

inlineoverridevirtual

Determinant of jacobians for given integration method. This method calculates determinant of jacobian in all integrations points of given integration method.

Returns: Vector of double which is vector of determinants of jacobians $ |J|_i $ where $ i=1,2,...,n $ is the integration point index of given integration method.

See also: Jacobian; InverseOfJacobian

Reimplemented from Kratos::Geometry< TPointType >.

◆ DomainSize()

template<class TPointType >

double Kratos::Triangle2D3< TPointType >::DomainSize ( ) const

inlineoverridevirtual

This method calculates and returns length, area or volume of this geometry depending to it's dimension. For one dimensional geometry it returns its length, for two dimensional it gives area and for three dimensional geometries it gives its volume.

Returns: double value contains length, area or volume.

See also: Length(); Area(); Volume() :TODO: could be replaced by something more suitable (comment by janosch)

Reimplemented from Kratos::Geometry< TPointType >.

◆ EdgesNumber()

template<class TPointType >

SizeType Kratos::Triangle2D3< TPointType >::EdgesNumber ( ) const

inlineoverridevirtual

This method gives you number of all edges of this geometry.

For example, for a hexahedron, this would be 12

Returns: SizeType containes number of this geometry edges.

See also: EdgesNumber(); Edges(); GenerateEdges(); FacesNumber(); Faces(); GenerateFaces()

Reimplemented from Kratos::Geometry< TPointType >.

◆ FacesNumber()

template<class TPointType >

SizeType Kratos::Triangle2D3< TPointType >::FacesNumber ( ) const

inlineoverridevirtual

Returns the number of faces of the current geometry.

This is only implemented for 3D geometries, since 2D geometries only have edges but no faces

See also: EdgesNumber; Edges; Faces

Reimplemented from Kratos::Geometry< TPointType >.

◆ GenerateEdges()

template<class TPointType >

GeometriesArrayType Kratos::Triangle2D3< TPointType >::GenerateEdges ( ) const

inlineoverridevirtual

This method gives you all edges of this geometry.

This method will gives you all the edges with one dimension less than this geometry. For example a triangle would return three lines as its edges or a tetrahedral would return four triangle as its edges but won't return its six edge lines by this method.

Returns: GeometriesArrayType containes this geometry edges.

See also: EdgesNumber(); Edge()

Reimplemented from Kratos::Geometry< TPointType >.

◆ GetGeometryFamily()

template<class TPointType >

GeometryData::KratosGeometryFamily Kratos::Triangle2D3< TPointType >::GetGeometryFamily ( ) const

inlineoverridevirtual

Reimplemented from Kratos::Geometry< TPointType >.

◆ GetGeometryType()

template<class TPointType >

GeometryData::KratosGeometryType Kratos::Triangle2D3< TPointType >::GetGeometryType ( ) const

inlineoverridevirtual

Reimplemented from Kratos::Geometry< TPointType >.

◆ HasIntersection() [1/2]

template<class TPointType >

bool Kratos::Triangle2D3< TPointType >::HasIntersection ( const BaseType & rThisGeometry ) const

inlineoverride

Detect if this triangle is intersected with another geometry.

Parameters

ThisGeometry Geometry to intersect with

Returns: True if the geometries intersect, False in any other case

We always check the intersection from the higher LocalSpaceDimension to the lower one

◆ HasIntersection() [2/2]

template<class TPointType >

bool Kratos::Triangle2D3< TPointType >::HasIntersection	(	const Point &	rLowPoint,
		const Point &	rHighPoint
	)		const

inlineoverridevirtual

Check if an axis-aliged bounding box (AABB) intersects a triangle

Based on code develop by Moller: http://fileadmin.cs.lth.se/cs/personal/tomas_akenine-moller/code/tribox3.txt and the article "A Fast Triangle-Triangle Intersection Test", SIGGRAPH '05 ACM, Art.8, 2005: http://fileadmin.cs.lth.se/cs/personal/tomas_akenine-moller/code/tribox_tam.pdf

Returns: bool if the triangle overlaps a box

Parameters

rLowPoint	first corner of the box
rHighPoint	second corner of the box

Reimplemented from Kratos::Geometry< TPointType >.

◆ Info()

template<class TPointType >

std::string Kratos::Triangle2D3< TPointType >::Info ( ) const

inlineoverridevirtual

Turn back information as a string.

Returns: String contains information about this geometry.

See also: PrintData(); PrintInfo()

Reimplemented from Kratos::Geometry< TPointType >.

◆ Inradius()

template<class TPointType >

double Kratos::Triangle2D3< TPointType >::Inradius ( ) const

inlineoverridevirtual

Calculates the inradius of the geometry. Calculates the inradius of the geometry.

Returns: Inradius of the geometry.

See also: Circumradius()

Reimplemented from Kratos::Geometry< TPointType >.

◆ InradiusToCircumradiusQuality()

template<class TPointType >

double Kratos::Triangle2D3< TPointType >::InradiusToCircumradiusQuality ( ) const

inlineoverridevirtual

Quality functions.

Calculates the inradius to circumradius quality metric. Calculates the inradius to circumradius quality metric. This metric is bounded by the interval (0,1) being: 1 -> Optimal value 0 -> Worst value

@formulae $$ \frac{r_K}{\rho_K} $$

Returns: The inradius to circumradius quality metric.

Reimplemented from Kratos::Geometry< TPointType >.

◆ InradiusToLongestEdgeQuality()

template<class TPointType >

double Kratos::Triangle2D3< TPointType >::InradiusToLongestEdgeQuality ( ) const

inlineoverridevirtual

Calculates the inradius to longest edge quality metric. Calculates the inradius to longest edge quality metric. This metric is bounded by the interval (0,1) being: 1 -> Optimal value 0 -> Worst value

@formulae $$ \frac{r_K}{h_{max}} $$

Returns: The inradius to longest edge quality metric.

Reimplemented from Kratos::Geometry< TPointType >.

◆ IsInside()

template<class TPointType >

bool Kratos::Triangle2D3< TPointType >::IsInside	(	const CoordinatesArrayType &	rPoint,
		CoordinatesArrayType &	rResult,
		const double	Tolerance = `std::numeric_limits<double>::epsilon()`
	)		const

inlineoverridevirtual

Returns whether given arbitrary point is inside the Geometry and the respective local point for the given global point

Parameters

rPoint	The point to be checked if is inside o note in global coordinates
rResult	The local coordinates of the point
Tolerance	The tolerance that will be considered to check if the point is inside or not

Returns: True if the point is inside, false otherwise

Reimplemented from Kratos::Geometry< TPointType >.

◆ KRATOS_CLASS_POINTER_DEFINITION()

template<class TPointType >

Kratos::Triangle2D3< TPointType >::KRATOS_CLASS_POINTER_DEFINITION ( Triangle2D3< TPointType > )

Pointer definition of Triangle2D3

◆ Length()

template<class TPointType >

double Kratos::Triangle2D3< TPointType >::Length ( ) const

inlineoverridevirtual

This method calculates and returns Length or charactereistic length of this geometry depending on it's dimension. For one dimensional geometry for example Line it returns length of it and for the other geometries it gives Characteristic length otherwise. In the current geometry this function returns the determinant of jacobian

Returns: double value contains length or Characteristic length

See also: Area(); Volume(); DomainSize() :TODO: could be replaced by something more suitable (comment by janosch)

Reimplemented from Kratos::Geometry< TPointType >.

◆ LumpingFactors()

template<class TPointType >

Vector& Kratos::Triangle2D3< TPointType >::LumpingFactors	(	Vector &	rResult,
		const typename BaseType::LumpingMethods	LumpingMethod = `BaseType::LumpingMethods::ROW_SUM`
	)		const

inlineoverridevirtual

Lumping factors for the calculation of the lumped mass matrix.

Parameters

rResult	Vector containing the lumping factors
LumpingMethod	The lumping method considered. The three methods available are: The row sum method Diagonal scaling Evaluation of M using a quadrature involving only the nodal points and thus automatically yielding a diagonal matrix for standard element shape function

Reimplemented from Kratos::Geometry< TPointType >.

◆ MaxEdgeLength()

template<class TPointType >

double Kratos::Triangle2D3< TPointType >::MaxEdgeLength ( ) const

inlineoverridevirtual

This method calculates and returns the maximum edge length of the geometry

Returns: double value with the maximum edge length

See also: MinEdgeLength(); AverageEdgeLength()

Reimplemented from Kratos::Geometry< TPointType >.

◆ MinEdgeLength()

template<class TPointType >

double Kratos::Triangle2D3< TPointType >::MinEdgeLength ( ) const

inlineoverridevirtual

This method calculates and returns the minimum edge length of the geometry

Returns: double value with the minimum edge length

See also: MaxEdgeLength(); AverageEdgeLength()

Reimplemented from Kratos::Geometry< TPointType >.

◆ NodesInFaces()

template<class TPointType >

void Kratos::Triangle2D3< TPointType >::NodesInFaces ( DenseMatrix< unsigned int > & NodesInFaces ) const

inlineoverridevirtual

Reimplemented from Kratos::Geometry< TPointType >.

◆ Normal()

template<class TPointType >

array_1d<double, 3> Kratos::Triangle2D3< TPointType >::Normal ( const CoordinatesArrayType & rPointLocalCoordinates ) const

inlineoverridevirtual

It returns a vector that is normal to its corresponding geometry in the given local point.

Parameters

rPointLocalCoordinates Reference to the local coordinates of the point in where the normal is to be computed

Returns: The normal in the given point

Reimplemented from Kratos::Geometry< TPointType >.

◆ NumberNodesInFaces()

template<class TPointType >

void Kratos::Triangle2D3< TPointType >::NumberNodesInFaces ( DenseVector< unsigned int > & NumberNodesInFaces ) const

inlineoverridevirtual

Reimplemented from Kratos::Geometry< TPointType >.

◆ operator=() [1/2]

template<class TPointType >

Triangle2D3& Kratos::Triangle2D3< TPointType >::operator= ( const Triangle2D3< TPointType > & rOther )

inline

Assignment operator.

Note: This operator don't copy the points and this geometry shares points with given source geometry. It's obvious that any change to this geometry's point affect source geometry's points too.

See also: Clone; ClonePoints

◆ operator=() [2/2]

template<class TPointType >

template<class TOtherPointType >

Triangle2D3& Kratos::Triangle2D3< TPointType >::operator= ( Triangle2D3< TOtherPointType > const & rOther )

inline

Assignment operator for geometries with different point type.

Note: This operator don't copy the points and this geometry shares points with given source geometry. It's obvious that any change to this geometry's point affect source geometry's points too.

See also: Clone; ClonePoints

◆ PointLocalCoordinates()

template<class TPointType >

CoordinatesArrayType& Kratos::Triangle2D3< TPointType >::PointLocalCoordinates	(	CoordinatesArrayType &	rResult,
		const CoordinatesArrayType &	rPoint
	)		const

inlineoverridevirtual

Returns the local coordinates of a given arbitrary point The local coordinates are computed solving for xi and eta the system given by the linear transformation: x = (1-xi-eta)*x1 + xi*x2 + eta*x3 y = (1-xi-eta)*y1 + xi*y2 + eta*y3

Parameters

rResult	The vector containing the local coordinates of the point
rPoint	The point in global coordinates

Returns: The vector containing the local coordinates of the point

Reimplemented from Kratos::Geometry< TPointType >.

◆ PointsLocalCoordinates()

template<class TPointType >

Matrix& Kratos::Triangle2D3< TPointType >::PointsLocalCoordinates ( Matrix & rResult ) const

inlineoverridevirtual

returns the local coordinates of all nodes of the current geometry

Parameters

rResult a Matrix object that will be overwritten by the result

Returns: the local coordinates of all nodes

Reimplemented from Kratos::Geometry< TPointType >.

◆ PrintData()

template<class TPointType >

void Kratos::Triangle2D3< TPointType >::PrintData ( std::ostream & rOStream ) const

inlineoverridevirtual

Print geometry's data into given stream. Prints it's points by the order they stored in the geometry and then center point of geometry.

Parameters

rOStream Stream to print into it.

See also: PrintInfo(); Info() :TODO: needs to be reviewed because it is not properly implemented yet (comment by janosch)

Reimplemented from Kratos::Geometry< TPointType >.

◆ PrintInfo()

template<class TPointType >

void Kratos::Triangle2D3< TPointType >::PrintInfo ( std::ostream & rOStream ) const

inlineoverridevirtual

Print information about this object.

Parameters

rOStream Stream to print into it.

See also: PrintData(); Info()

Reimplemented from Kratos::Geometry< TPointType >.

◆ Semiperimeter()

template<class TPointType >

virtual double Kratos::Triangle2D3< TPointType >::Semiperimeter ( ) const

inlinevirtual

Class Interface.

This method calculates and returns the semiperimeter of the geonetry.

Returns: double value with the minimum edge length

◆ ShapeFunctionsGradients()

template<class TPointType >

virtual Matrix& Kratos::Triangle2D3< TPointType >::ShapeFunctionsGradients	(	Matrix &	rResult,
		PointType &	rPoint
	)

inlinevirtual

returns the shape function gradients in an arbitrary point, given in local coordinates

Parameters

rResult	the matrix of gradients, will be overwritten with the gradients for all shape functions in given point
rPoint	the given point the gradients are calculated in

◆ ShapeFunctionsIntegrationPointsGradients() [1/2]

template<class TPointType >

void Kratos::Triangle2D3< TPointType >::ShapeFunctionsIntegrationPointsGradients	(	ShapeFunctionsGradientsType &	rResult,
		IntegrationMethod	ThisMethod
	)		const

inlineoverridevirtual

Calculates the Gradients of the shape functions. Calculates the gradients of the shape functions with regard to the global coordinates in all integration points ( $ \frac{\partial N^i}{\partial X_j} $)

Parameters

rResult	a container which takes the calculated gradients
ThisMethod	the given IntegrationMethod

Returns: the gradients of all shape functions with regard to the global coordinates

Reimplemented from Kratos::Geometry< TPointType >.

◆ ShapeFunctionsIntegrationPointsGradients() [2/2]

template<class TPointType >

void Kratos::Triangle2D3< TPointType >::ShapeFunctionsIntegrationPointsGradients	(	ShapeFunctionsGradientsType &	rResult,
		Vector &	determinants_of_jacobian,
		IntegrationMethod	ThisMethod
	)		const

inlineoverridevirtual

Reimplemented from Kratos::Geometry< TPointType >.

◆ ShapeFunctionsLocalGradients() [1/3]

template<class TPointType >

virtual ShapeFunctionsGradientsType Kratos::Triangle2D3< TPointType >::ShapeFunctionsLocalGradients ( )

inlinevirtual

Calculates the local gradients for all integration points for the default integration method

◆ ShapeFunctionsLocalGradients() [2/3]

template<class TPointType >

virtual ShapeFunctionsGradientsType Kratos::Triangle2D3< TPointType >::ShapeFunctionsLocalGradients ( IntegrationMethod ThisMethod )

inlinevirtual

Calculates the local gradients for all integration points for given integration method

◆ ShapeFunctionsLocalGradients() [3/3]

template<class TPointType >

Matrix& Kratos::Triangle2D3< TPointType >::ShapeFunctionsLocalGradients	(	Matrix &	rResult,
		const CoordinatesArrayType &	rPoint
	)		const

inlineoverridevirtual

Calculates the gradients in terms of local coordinates of all shape functions in a given point.

Parameters

rPoint the current point at which the gradients are calculated in local coordinates

Returns: the gradients of all shape functions $ \frac{\partial N^i}{\partial \xi_j} $

Reimplemented from Kratos::Geometry< TPointType >.

◆ ShapeFunctionsSecondDerivatives()

template<class TPointType >

ShapeFunctionsSecondDerivativesType& Kratos::Triangle2D3< TPointType >::ShapeFunctionsSecondDerivatives	(	ShapeFunctionsSecondDerivativesType &	rResult,
		const CoordinatesArrayType &	rPoint
	)		const

inlineoverridevirtual

returns the second order derivatives of all shape functions in given arbitrary pointers

Parameters

rResult	a third order tensor which contains the second derivatives
rPoint	the given point the second order derivatives are calculated in

Reimplemented from Kratos::Geometry< TPointType >.

◆ ShapeFunctionsThirdDerivatives()

template<class TPointType >

ShapeFunctionsThirdDerivativesType& Kratos::Triangle2D3< TPointType >::ShapeFunctionsThirdDerivatives	(	ShapeFunctionsThirdDerivativesType &	rResult,
		const CoordinatesArrayType &	rPoint
	)		const

inlineoverridevirtual

returns the third order derivatives of all shape functions in given arbitrary pointers

Parameters

rResult	a fourth order tensor which contains the third derivatives
rPoint	the given point the third order derivatives are calculated in

Reimplemented from Kratos::Geometry< TPointType >.

◆ ShapeFunctionsValues()

template<class TPointType >

Vector& Kratos::Triangle2D3< TPointType >::ShapeFunctionsValues	(	Vector &	rResult,
		const CoordinatesArrayType &	rCoordinates
	)		const

inlineoverridevirtual

This method gives all non-zero shape functions values evaluated at the rCoordinates provided

Note: There is no control if the return vector is empty or not!

Returns: Vector of values of shape functions $ F_{i} $ where i is the shape function index (for NURBS it is the index of the local enumeration in the element).

See also: ShapeFunctionValue; ShapeFunctionsLocalGradients; ShapeFunctionLocalGradient

Reimplemented from Kratos::Geometry< TPointType >.

◆ ShapeFunctionValue()

template<class TPointType >

double Kratos::Triangle2D3< TPointType >::ShapeFunctionValue	(	IndexType	ShapeFunctionIndex,
		const CoordinatesArrayType &	rPoint
	)		const

inlineoverridevirtual

Calculates the value of a given shape function at a given point.

Parameters

ShapeFunctionIndex	The number of the desired shape function
rPoint	the given point in local coordinates at which the value of the shape function is calculated

Returns: the value of the shape function at the given point

Reimplemented from Kratos::Geometry< TPointType >.

◆ ShortestAltitudeToEdgeLengthRatio()

template<class TPointType >

double Kratos::Triangle2D3< TPointType >::ShortestAltitudeToEdgeLengthRatio ( ) const

inlineoverridevirtual

Calculates the shortest altitude to edge length quality metric. Calculates the shortest altitude to edge length quality metric. This metric is bounded by the interval (0,1) being: 1 -> Optimal value 0 -> Worst value -1 -> Optimal value with inverted volume.

@formulae $$ \frac{h_{min}}{h_{max}} $$

Returns: The shortest altitude to edge length quality metric.

Reimplemented from Kratos::Geometry< TPointType >.

Friends And Related Function Documentation

◆ Serializer

template<class TPointType >

friend class Serializer

friend

◆ Triangle2D3

template<class TPointType >

template<class TOtherPointType >

friend class Triangle2D3

friend

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

/home/runner/work/Documentation/Documentation/master/kratos/geometries/triangle_2d_3.h

Public Member Functions

Friends

Type Definitions

Serialization

Additional Inherited Members

Detailed Description

template<class TPointType> class Kratos::Triangle2D3< TPointType >

Member Typedef Documentation

◆ BaseType

◆ CoordinatesArrayType

◆ EdgeType

◆ GeometriesArrayType

◆ IndexType

◆ IntegrationMethod

◆ IntegrationPointsArrayType

◆ IntegrationPointsContainerType

◆ IntegrationPointType

◆ JacobiansType

◆ NormalType

◆ PointsArrayType

◆ PointType

◆ ShapeFunctionsGradientsType

◆ ShapeFunctionsLocalGradientsContainerType

◆ ShapeFunctionsSecondDerivativesType

◆ ShapeFunctionsThirdDerivativesType

◆ ShapeFunctionsValuesContainerType

◆ SizeType

Constructor & Destructor Documentation

◆ Triangle2D3() [1/6]

◆ Triangle2D3() [2/6]

◆ Triangle2D3() [3/6]

◆ Triangle2D3() [4/6]

◆ Triangle2D3() [5/6]

◆ Triangle2D3() [6/6]

◆ ~Triangle2D3()

Member Function Documentation

◆ Area()

◆ AreaToEdgeLengthRatio()

◆ AverageEdgeLength()

◆ Circumradius()

◆ Create() [1/4]

◆ Create() [2/4]

◆ Create() [3/4]

◆ Create() [4/4]

◆ DeterminantOfJacobian() [1/3]

◆ DeterminantOfJacobian() [2/3]

◆ DeterminantOfJacobian() [3/3]

◆ DomainSize()

◆ EdgesNumber()

◆ FacesNumber()

◆ GenerateEdges()

◆ GetGeometryFamily()

◆ GetGeometryType()

◆ HasIntersection() [1/2]

◆ HasIntersection() [2/2]

◆ Info()

◆ Inradius()

◆ InradiusToCircumradiusQuality()

◆ InradiusToLongestEdgeQuality()

◆ IsInside()

◆ KRATOS_CLASS_POINTER_DEFINITION()

◆ Length()

◆ LumpingFactors()

◆ MaxEdgeLength()

◆ MinEdgeLength()

◆ NodesInFaces()

◆ Normal()

◆ NumberNodesInFaces()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ PointLocalCoordinates()

◆ PointsLocalCoordinates()

◆ PrintData()

◆ PrintInfo()

◆ Semiperimeter()

◆ ShapeFunctionsGradients()

◆ ShapeFunctionsIntegrationPointsGradients() [1/2]

◆ ShapeFunctionsIntegrationPointsGradients() [2/2]

◆ ShapeFunctionsLocalGradients() [1/3]

◆ ShapeFunctionsLocalGradients() [2/3]

template<class TPointType>
class Kratos::Triangle2D3< TPointType >