KratosMultiphysics
KRATOS Multiphysics (Kratos) is a framework for building parallel, multi-disciplinary simulation software, aiming at modularity, extensibility, and high performance. Kratos is written in C++, and counts with an extensive Python interface.
Public Types | Public Member Functions | List of all members
Kratos::Tetrahedra3D4< TPointType > Class Template Reference

A four node tetrahedra geometry with linear shape functions. More...

#include <tetrahedra_3d_4.h>

Inheritance diagram for Kratos::Tetrahedra3D4< TPointType >:
Collaboration diagram for Kratos::Tetrahedra3D4< TPointType >:

Public Types

typedef Geometry< TPointType > BaseType
 
typedef Line3D2< TPointType > EdgeType
 
typedef Triangle3D3< TPointType > FaceType
 
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::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::NormalType NormalType
 
typedef BaseType::CoordinatesArrayType CoordinatesArrayType
 
typedef Matrix MatrixType
 
- 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< GeometryTypeGeometriesArrayType
 
typedef TPointType PointType
 
typedef std::size_t IndexType
 
typedef std::size_t SizeType
 
typedef PointType::CoordinatesArrayType CoordinatesArrayType
 
typedef IntegrationPoint< 3 > IntegrationPointType
 
typedef std::vector< IntegrationPointTypeIntegrationPointsArrayType
 
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< MatrixJacobiansType
 
typedef GeometryData::ShapeFunctionsGradientsType ShapeFunctionsGradientsType
 
typedef GeometryData::ShapeFunctionsSecondDerivativesType ShapeFunctionsSecondDerivativesType
 
typedef GeometryData::ShapeFunctionsThirdDerivativesType ShapeFunctionsThirdDerivativesType
 
typedef DenseVector< doubleNormalType
 
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< PointPointerTypePointPointerContainerType
 
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
 

Public Member Functions

 KRATOS_CLASS_POINTER_DEFINITION (Tetrahedra3D4)
 
 Tetrahedra3D4 (typename PointType::Pointer pPoint1, typename PointType::Pointer pPoint2, typename PointType::Pointer pPoint3, typename PointType::Pointer pPoint4)
 
 Tetrahedra3D4 (const PointsArrayType &ThisPoints)
 
 Tetrahedra3D4 (const IndexType GeometryId, const PointsArrayType &rThisPoints)
 Constructor with Geometry Id. More...
 
 Tetrahedra3D4 (const std::string &rGeometryName, const PointsArrayType &rThisPoints)
 Constructor with Geometry Name. More...
 
 Tetrahedra3D4 (Tetrahedra3D4 const &rOther)
 
template<class TOtherPointType >
 Tetrahedra3D4 (Tetrahedra3D4< TOtherPointType > const &rOther)
 
 ~Tetrahedra3D4 () override
 Destructor. Does nothing!!! More...
 
GeometryData::KratosGeometryFamily GetGeometryFamily () const override
 
GeometryData::KratosGeometryType GetGeometryType () const override
 
Tetrahedra3D4operator= (const Tetrahedra3D4 &rOther)
 
template<class TOtherPointType >
Tetrahedra3D4operator= (Tetrahedra3D4< 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
 It 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...
 
VectorLumpingFactors (Vector &rResult, const typename BaseType::LumpingMethods LumpingMethod=BaseType::LumpingMethods::ROW_SUM) const override
 Lumping factors for the calculation of the lumped mass matrix. More...
 
double Length () const override
 
double Area () const override
 
double Volume () const override
 
double DomainSize () const override
 This method calculate and return length, area or volume of this geometry depending to it's dimension. 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 ShortestToLongestEdgeQuality () const override
 
double RegularityQuality () const override
 
double VolumeToSurfaceAreaQuality () const override
 
double VolumeToEdgeLengthQuality () const override
 
double VolumeToAverageEdgeLength () const override
 
double VolumeToRMSEdgeLength () const override
 
double MinDihedralAngle () const override
 
double MaxDihedralAngle () const override
 
double MinSolidAngle () const override
 
void ComputeSolidAngles (Vector &rSolidAngles) const override
 
void ComputeDihedralAngles (Vector &rDihedralAngles) const override
 
MatrixPointsLocalCoordinates (Matrix &rResult) const override
 
CoordinatesArrayTypePointLocalCoordinates (CoordinatesArrayType &rResult, const CoordinatesArrayType &rPoint) const override
 Returns the local coordinates of a given arbitrary point. More...
 
bool IsInside (const CoordinatesArrayType &rPoint, CoordinatesArrayType &rResult, const double Tolerance=std::numeric_limits< double >::epsilon()) 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...
 
Face
SizeType FacesNumber () const override
 Returns the number of faces of the current geometry. More...
 
GeometriesArrayType GenerateFaces () const override
 Returns all faces of the current geometry. More...
 
void NumberNodesInFaces (DenseVector< unsigned int > &NumberNodesInFaces) const override
 
void NodesInFaces (DenseMatrix< unsigned int > &NodesInFaces) const override
 
double ShapeFunctionValue (IndexType ShapeFunctionIndex, const CoordinatesArrayType &rPoint) const override
 
VectorShapeFunctionsValues (Vector &rResult, const CoordinatesArrayType &rCoordinates) const override
 
MatrixShapeFunctionsLocalGradients (Matrix &rResult, const CoordinatesArrayType &rPoint) const override
 
void ShapeFunctionsIntegrationPointsGradients (ShapeFunctionsGradientsType &rResult, IntegrationMethod ThisMethod) const override
 
void ShapeFunctionsIntegrationPointsGradients (ShapeFunctionsGradientsType &rResult, Vector &determinants_of_jacobian, IntegrationMethod ThisMethod) const override
 
ShapeFunctionsSecondDerivativesTypeShapeFunctionsSecondDerivatives (ShapeFunctionsSecondDerivativesType &rResult, const CoordinatesArrayType &rPoint) const override
 
bool HasIntersection (const BaseType &rThisGeometry) const override
 Test if this geometry intersects with other geometry. More...
 
bool HasIntersection (const Point &rLowPoint, const Point &rHighPoint) const override
 
void SplitAndDecompose (const BaseType &tetra, Plane &plane, std::vector< BaseType > &inside) const
 
void GetPlanes (array_1d< Plane, 4 > &plane) const
 
Spatial Operations
double CalculateDistance (const CoordinatesArrayType &rPointGlobalCoordinates, const double Tolerance=std::numeric_limits< double >::epsilon()) const override
 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...
 
Input and output
std::string Info () const override
 
void PrintInfo (std::ostream &rOStream) const override
 
void PrintData (std::ostream &rOStream) 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...
 
Geometryoperator= (const Geometry &rOther)
 
template<class TOtherPointType >
Geometryoperator= (Geometry< TOtherPointType > const &rOther)
 
 operator PointsArrayType & ()
 
TPointType & operator[] (const SizeType &i)
 
TPointType const & operator[] (const SizeType &i) const
 
PointPointerTypeoperator() (const SizeType &i)
 
ConstPointPointerTypeoperator() (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 ()
 
PointPointerContainerTypeGetContainer ()
 ‍** Gives a reference to underly normal container. *‍/ More...
 
const PointPointerContainerTypeGetContainer () const
 
DataValueContainerGetData ()
 
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 GeometryTypeGetGeometryParent (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 GeometryTypeGetGeometryPart (const IndexType Index)
 Used for composite geometries. It returns the the geometry part, corresponding to the Index. More...
 
virtual const GeometryTypeGetGeometryPart (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 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 (const CoordinatesArrayType &rPointLocalCoordinates) const
 It returns a vector that is normal to its corresponding geometry in the given local point. More...
 
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
 
const PointsArrayTypePoints () const
 
PointsArrayTypePoints ()
 
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...
 
SizeType IntegrationPointsNumber () const
 
SizeType IntegrationPointsNumber (IntegrationMethod ThisMethod) const
 
const IntegrationPointsArrayTypeIntegrationPoints () const
 
const IntegrationPointsArrayTypeIntegrationPoints (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 CoordinatesArrayTypeGlobalCoordinates (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 CoordinatesArrayTypeGlobalCoordinates (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...
 
JacobiansTypeJacobian (JacobiansType &rResult) const
 
virtual JacobiansTypeJacobian (JacobiansType &rResult, IntegrationMethod ThisMethod) const
 
virtual JacobiansTypeJacobian (JacobiansType &rResult, IntegrationMethod ThisMethod, Matrix &DeltaPosition) const
 
MatrixJacobian (Matrix &rResult, IndexType IntegrationPointIndex) const
 
virtual MatrixJacobian (Matrix &rResult, IndexType IntegrationPointIndex, IntegrationMethod ThisMethod) const
 
virtual MatrixJacobian (Matrix &rResult, IndexType IntegrationPointIndex, IntegrationMethod ThisMethod, const Matrix &rDeltaPosition) const
 
virtual MatrixJacobian (Matrix &rResult, const CoordinatesArrayType &rCoordinates) const
 
virtual MatrixJacobian (Matrix &rResult, const CoordinatesArrayType &rCoordinates, Matrix &rDeltaPosition) const
 
VectorDeterminantOfJacobian (Vector &rResult) const
 
virtual VectorDeterminantOfJacobian (Vector &rResult, IntegrationMethod ThisMethod) const
 
double DeterminantOfJacobian (IndexType IntegrationPointIndex) const
 
virtual double DeterminantOfJacobian (IndexType IntegrationPointIndex, IntegrationMethod ThisMethod) const
 
virtual double DeterminantOfJacobian (const CoordinatesArrayType &rPoint) const
 
JacobiansTypeInverseOfJacobian (JacobiansType &rResult) const
 
virtual JacobiansTypeInverseOfJacobian (JacobiansType &rResult, IntegrationMethod ThisMethod) const
 
MatrixInverseOfJacobian (Matrix &rResult, IndexType IntegrationPointIndex) const
 
virtual MatrixInverseOfJacobian (Matrix &rResult, IndexType IntegrationPointIndex, IntegrationMethod ThisMethod) const
 
virtual MatrixInverseOfJacobian (Matrix &rResult, const CoordinatesArrayType &rCoordinates) const
 
const MatrixShapeFunctionsValues () const
 
const MatrixShapeFunctionsValues (IntegrationMethod ThisMethod) const
 
double ShapeFunctionValue (IndexType IntegrationPointIndex, IndexType ShapeFunctionIndex) const
 
double ShapeFunctionValue (IndexType IntegrationPointIndex, IndexType ShapeFunctionIndex, IntegrationMethod ThisMethod) const
 
const ShapeFunctionsGradientsTypeShapeFunctionsLocalGradients () const
 
const ShapeFunctionsGradientsTypeShapeFunctionsLocalGradients (IntegrationMethod ThisMethod) const
 
const MatrixShapeFunctionLocalGradient (IndexType IntegrationPointIndex) const
 
const MatrixShapeFunctionLocalGradient (IndexType IntegrationPointIndex, IntegrationMethod ThisMethod) const
 
const MatrixShapeFunctionLocalGradient (IndexType IntegrationPointIndex, IndexType ShapeFunctionIndex, IntegrationMethod ThisMethod) const
 
const MatrixShapeFunctionDerivatives (IndexType DerivativeOrderIndex, IndexType IntegrationPointIndex, IntegrationMethod ThisMethod) const
 
const MatrixShapeFunctionDerivatives (IndexType DerivativeOrderIndex, IndexType IntegrationPointIndex) const
 
virtual ShapeFunctionsThirdDerivativesTypeShapeFunctionsThirdDerivatives (ShapeFunctionsThirdDerivativesType &rResult, const CoordinatesArrayType &rPoint) 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...
 

Serialization

class Serializer
 
template<class TOtherPointType >
class Tetrahedra3D4
 

Additional Inherited Members

- 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 AreaToEdgeLengthRatio () const
 
virtual double ShortestAltitudeToEdgeLengthRatio () 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::Tetrahedra3D4< TPointType >

A four node tetrahedra geometry with linear shape functions.

The node ordering corresponds with: v ,/ / 2 ,/|\ ,/ |\ ,/ '. \ ,/ |\ ,/ | ‘\ 0-----------’.-----—1 --> u \. | ,/ . | ,/ ‘. ’. ,/ \. |/ 3 \. w

Author
Riccardo Rossi
Janosch Stascheit
Felix Nagel

Member Typedef Documentation

◆ BaseType

template<class TPointType >
typedef Geometry<TPointType> Kratos::Tetrahedra3D4< TPointType >::BaseType

Type Definitions Geometry as base class.

◆ CoordinatesArrayType

template<class TPointType >
typedef BaseType::CoordinatesArrayType Kratos::Tetrahedra3D4< TPointType >::CoordinatesArrayType

Type of coordinates array

◆ EdgeType

template<class TPointType >
typedef Line3D2<TPointType> Kratos::Tetrahedra3D4< TPointType >::EdgeType

Type of edge and face geometries

◆ FaceType

template<class TPointType >
typedef Triangle3D3<TPointType> Kratos::Tetrahedra3D4< TPointType >::FaceType

◆ GeometriesArrayType

template<class TPointType >
typedef BaseType::GeometriesArrayType Kratos::Tetrahedra3D4< TPointType >::GeometriesArrayType

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

◆ IndexType

template<class TPointType >
typedef BaseType::IndexType Kratos::Tetrahedra3D4< 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::Tetrahedra3D4< TPointType >::IntegrationMethod

Integration methods implemented in geometry.

◆ 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

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::Tetrahedra3D4< 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::Tetrahedra3D4< TPointType >::JacobiansType

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

◆ MatrixType

template<class TPointType >
typedef Matrix Kratos::Tetrahedra3D4< TPointType >::MatrixType

Type of Matrix

◆ NormalType

template<class TPointType >
typedef BaseType::NormalType Kratos::Tetrahedra3D4< TPointType >::NormalType

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

◆ PointsArrayType

template<class TPointType >
typedef BaseType::PointsArrayType Kratos::Tetrahedra3D4< TPointType >::PointsArrayType

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

◆ PointType

template<class TPointType >
typedef TPointType Kratos::Tetrahedra3D4< TPointType >::PointType

Redefinition of template parameter TPointType.

◆ ShapeFunctionsGradientsType

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

◆ ShapeFunctionsLocalGradientsContainerType

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

◆ ShapeFunctionsSecondDerivativesType

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

◆ ShapeFunctionsValuesContainerType

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

◆ SizeType

template<class TPointType >
typedef BaseType::SizeType Kratos::Tetrahedra3D4< TPointType >::SizeType

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

Constructor & Destructor Documentation

◆ Tetrahedra3D4() [1/6]

template<class TPointType >
Kratos::Tetrahedra3D4< TPointType >::Tetrahedra3D4 ( typename PointType::Pointer  pPoint1,
typename PointType::Pointer  pPoint2,
typename PointType::Pointer  pPoint3,
typename PointType::Pointer  pPoint4 
)
inline

Life Cycle

◆ Tetrahedra3D4() [2/6]

template<class TPointType >
Kratos::Tetrahedra3D4< TPointType >::Tetrahedra3D4 ( const PointsArrayType ThisPoints)
inlineexplicit

◆ Tetrahedra3D4() [3/6]

template<class TPointType >
Kratos::Tetrahedra3D4< TPointType >::Tetrahedra3D4 ( const IndexType  GeometryId,
const PointsArrayType rThisPoints 
)
inlineexplicit

Constructor with Geometry Id.

◆ Tetrahedra3D4() [4/6]

template<class TPointType >
Kratos::Tetrahedra3D4< TPointType >::Tetrahedra3D4 ( const std::string &  rGeometryName,
const PointsArrayType rThisPoints 
)
inlineexplicit

Constructor with Geometry Name.

◆ Tetrahedra3D4() [5/6]

template<class TPointType >
Kratos::Tetrahedra3D4< TPointType >::Tetrahedra3D4 ( Tetrahedra3D4< TPointType > const &  rOther)
inline

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

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

◆ Tetrahedra3D4() [6/6]

template<class TPointType >
template<class TOtherPointType >
Kratos::Tetrahedra3D4< TPointType >::Tetrahedra3D4 ( Tetrahedra3D4< 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 don't copy the points and new geometry shares points with given source geometry. It's obvious that any change to this new geometry's point affect source geometry's points too.

◆ ~Tetrahedra3D4()

template<class TPointType >
Kratos::Tetrahedra3D4< TPointType >::~Tetrahedra3D4 ( )
inlineoverride

Destructor. Does nothing!!!

Member Function Documentation

◆ Area()

template<class TPointType >
double Kratos::Tetrahedra3D4< 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: might be necessary to reimplement

Reimplemented from Kratos::Geometry< TPointType >.

◆ AverageEdgeLength()

template<class TPointType >
double Kratos::Tetrahedra3D4< 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 >.

◆ CalculateDistance()

template<class TPointType >
double Kratos::Tetrahedra3D4< TPointType >::CalculateDistance ( const CoordinatesArrayType rPointGlobalCoordinates,
const double  Tolerance = std::numeric_limits<double>::epsilon() 
) const
inlineoverridevirtual

Computes the distance between an point in global coordinates and the closest point of this geometry. If projection fails, double::max will be returned.

Parameters
rPointGlobalCoordinatesthe point to which the closest point has to be found.
Toleranceaccepted orthogonal error.
Returns
Distance to geometry. positive -> outside of to the geometry (for 2D and solids) 0 -> on/ in the geometry.

Reimplemented from Kratos::Geometry< TPointType >.

◆ Circumradius()

template<class TPointType >
double Kratos::Tetrahedra3D4< TPointType >::Circumradius ( ) const
inlineoverridevirtual

This method calculates the circumradius of the geometry

Returns
The circumradius of the geometry

Reimplemented from Kratos::Geometry< TPointType >.

◆ ComputeDihedralAngles()

template<class TPointType >
void Kratos::Tetrahedra3D4< TPointType >::ComputeDihedralAngles ( Vector rDihedralAngles) const
inlineoverridevirtual

Implements the calculus of the 6 diheadral angles of the tetra Implements the calculus of the 6 diheadral angles of the tetra

Returns
The dihedral angles of the geometry

Reimplemented from Kratos::Geometry< TPointType >.

◆ ComputeSolidAngles()

template<class TPointType >
void Kratos::Tetrahedra3D4< TPointType >::ComputeSolidAngles ( Vector rSolidAngles) const
inlineoverridevirtual

Implements the calculus of the 4 solid angles of the tetra Implements the calculus of the 4 solid angles of the tetra

Returns
The solid angles of the geometry

Reimplemented from Kratos::Geometry< TPointType >.

◆ Create() [1/4]

template<class TPointType >
BaseType::Pointer Kratos::Tetrahedra3D4< TPointType >::Create ( const BaseType rGeometry) const
inlineoverride

Creates a new geometry pointer.

Parameters
rGeometryreference to an existing geometry
Returns
Pointer to the new geometry

◆ Create() [2/4]

template<class TPointType >
BaseType::Pointer Kratos::Tetrahedra3D4< TPointType >::Create ( const IndexType  NewGeometryId,
const BaseType rGeometry 
) const
inlineoverride

Creates a new geometry pointer.

Parameters
NewGeometryIdthe ID of the new geometry
rGeometryreference to an existing geometry
Returns
Pointer to the new geometry

◆ Create() [3/4]

template<class TPointType >
BaseType::Pointer Kratos::Tetrahedra3D4< TPointType >::Create ( const IndexType  NewGeometryId,
PointsArrayType const &  rThisPoints 
) const
inlineoverridevirtual

It creates a new geometry pointer.

Parameters
NewIdthe ID of the new geometry
rThisPointsthe nodes of the new geometry
Returns
a Pointer to the new geometry

Reimplemented from Kratos::Geometry< TPointType >.

◆ Create() [4/4]

template<class TPointType >
BaseType::Pointer Kratos::Tetrahedra3D4< TPointType >::Create ( PointsArrayType const &  rThisPoints) const
inlineoverridevirtual

Creates a new geometry pointer.

Parameters
rThisPointsthe nodes of the new geometry
Returns
Pointer to the new geometry

Reimplemented from Kratos::Geometry< TPointType >.

◆ DomainSize()

template<class TPointType >
double Kratos::Tetrahedra3D4< TPointType >::DomainSize ( ) const
inlineoverridevirtual

This method calculate and return 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()

Reimplemented from Kratos::Geometry< TPointType >.

◆ EdgesNumber()

template<class TPointType >
SizeType Kratos::Tetrahedra3D4< 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::Tetrahedra3D4< 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::Tetrahedra3D4< 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 >.

◆ GenerateFaces()

template<class TPointType >
GeometriesArrayType Kratos::Tetrahedra3D4< TPointType >::GenerateFaces ( ) const
inlineoverridevirtual

Returns all faces of the current geometry.

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

Returns
GeometriesArrayType containes this geometry faces.
See also
EdgesNumber
GenerateEdges
FacesNumber

Reimplemented from Kratos::Geometry< TPointType >.

◆ GetGeometryFamily()

template<class TPointType >
GeometryData::KratosGeometryFamily Kratos::Tetrahedra3D4< TPointType >::GetGeometryFamily ( ) const
inlineoverridevirtual

Reimplemented from Kratos::Geometry< TPointType >.

◆ GetGeometryType()

template<class TPointType >
GeometryData::KratosGeometryType Kratos::Tetrahedra3D4< TPointType >::GetGeometryType ( ) const
inlineoverridevirtual

Reimplemented from Kratos::Geometry< TPointType >.

◆ GetPlanes()

template<class TPointType >
void Kratos::Tetrahedra3D4< TPointType >::GetPlanes ( array_1d< Plane, 4 > &  plane) const
inline

◆ HasIntersection() [1/2]

template<class TPointType >
bool Kratos::Tetrahedra3D4< TPointType >::HasIntersection ( const BaseType rThisGeometry) const
inlineoverride

Test if this geometry intersects with other geometry.

Parameters
ThisGeometryGeometry 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::Tetrahedra3D4< TPointType >::HasIntersection ( const Point rLowPoint,
const Point rHighPoint 
) const
inlineoverridevirtual

Test intersection of the geometry with a box

Tests the intersection of the geometry with a 3D box defined by rLowPoint and rHighPoint

Parameters
rLowPointLower point of the box to test the intersection
rHighPointHigher point of the box to test the intersection
Returns
True if the geometry intersects the box, False in any other case.

Reimplemented from Kratos::Geometry< TPointType >.

◆ Info()

template<class TPointType >
std::string Kratos::Tetrahedra3D4< 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::Tetrahedra3D4< TPointType >::Inradius ( ) const
inlineoverridevirtual

This method calculates the inradius of the geometry

Returns
The inradius of the geometry

Reimplemented from Kratos::Geometry< TPointType >.

◆ InradiusToCircumradiusQuality()

template<class TPointType >
double Kratos::Tetrahedra3D4< 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

\( \frac{r}{\rho} \)

Returns
The inradius to circumradius quality metric.

Reimplemented from Kratos::Geometry< TPointType >.

◆ InradiusToLongestEdgeQuality()

template<class TPointType >
double Kratos::Tetrahedra3D4< 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

\( \frac{r}{L} \)

Returns
The inradius to longest edge quality metric.

Reimplemented from Kratos::Geometry< TPointType >.

◆ IsInside()

template<class TPointType >
bool Kratos::Tetrahedra3D4< 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
rPointThe point to be checked if is inside o note in global coordinates
rResultThe local coordinates of the point
ToleranceThe 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::Tetrahedra3D4< TPointType >::KRATOS_CLASS_POINTER_DEFINITION ( Tetrahedra3D4< TPointType >  )

Pointer definition of Tetrahedra3D4

◆ Length()

template<class TPointType >
double Kratos::Tetrahedra3D4< TPointType >::Length ( ) const
inlineoverridevirtual

Informations 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.

Returns
double value contains length or Characteristic length
See also
Area()
Volume()
DomainSize()

:TODO: might be necessary to reimplement

Reimplemented from Kratos::Geometry< TPointType >.

◆ LumpingFactors()

template<class TPointType >
Vector& Kratos::Tetrahedra3D4< 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
rResultVector containing the lumping factors
LumpingMethodThe 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 >.

◆ MaxDihedralAngle()

template<class TPointType >
double Kratos::Tetrahedra3D4< TPointType >::MaxDihedralAngle ( ) const
inlineoverridevirtual

Calculates the max dihedral angle quality metric. Calculates the max dihedral angle quality metric. The max dihedral angle is max angle between two faces of the element In radians

Returns
[description]

Reimplemented from Kratos::Geometry< TPointType >.

◆ MaxEdgeLength()

template<class TPointType >
double Kratos::Tetrahedra3D4< 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 >.

◆ MinDihedralAngle()

template<class TPointType >
double Kratos::Tetrahedra3D4< TPointType >::MinDihedralAngle ( ) const
inlineoverridevirtual

Calculates the min dihedral angle quality metric. Calculates the min dihedral angle quality metric. The min dihedral angle is min angle between two faces of the element In radians

Returns
[description]

Reimplemented from Kratos::Geometry< TPointType >.

◆ MinEdgeLength()

template<class TPointType >
double Kratos::Tetrahedra3D4< 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 >.

◆ MinSolidAngle()

template<class TPointType >
double Kratos::Tetrahedra3D4< TPointType >::MinSolidAngle ( ) const
inlineoverridevirtual

Calculates the min solid angle quality metric. Calculates the min solid angle quality metric. The min solid angle [stereoradians] is the lowest solid angle "seen" from any of the 4 nodes of the geometry In stereo radians

Returns
[description]

Reimplemented from Kratos::Geometry< TPointType >.

◆ NodesInFaces()

template<class TPointType >
void Kratos::Tetrahedra3D4< TPointType >::NodesInFaces ( DenseMatrix< unsigned int > &  NodesInFaces) const
inlineoverridevirtual

Reimplemented from Kratos::Geometry< TPointType >.

◆ NumberNodesInFaces()

template<class TPointType >
void Kratos::Tetrahedra3D4< TPointType >::NumberNodesInFaces ( DenseVector< unsigned int > &  NumberNodesInFaces) const
inlineoverridevirtual

Reimplemented from Kratos::Geometry< TPointType >.

◆ operator=() [1/2]

template<class TPointType >
Tetrahedra3D4& Kratos::Tetrahedra3D4< TPointType >::operator= ( const Tetrahedra3D4< TPointType > &  rOther)
inline

Operators 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 >
Tetrahedra3D4& Kratos::Tetrahedra3D4< TPointType >::operator= ( Tetrahedra3D4< 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::Tetrahedra3D4< TPointType >::PointLocalCoordinates ( CoordinatesArrayType rResult,
const CoordinatesArrayType rPoint 
) const
inlineoverridevirtual

Returns the local coordinates of a given arbitrary point.

Parameters
rResultThe vector containing the local coordinates of the point
rPointThe 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::Tetrahedra3D4< TPointType >::PointsLocalCoordinates ( Matrix rResult) const
inlineoverridevirtual

Returns a matrix of the local coordinates of all points

Parameters
rResulta Matrix that will be overwritten by the results
Returns
the coordinates of all points of the current geometry

Reimplemented from Kratos::Geometry< TPointType >.

◆ PrintData()

template<class TPointType >
void Kratos::Tetrahedra3D4< 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
rOStreamStream to print into it.
See also
PrintInfo()
Info()

Reimplemented from Kratos::Geometry< TPointType >.

◆ PrintInfo()

template<class TPointType >
void Kratos::Tetrahedra3D4< TPointType >::PrintInfo ( std::ostream &  rOStream) const
inlineoverridevirtual

Print information about this object.

Parameters
rOStreamStream to print into it.
See also
PrintData()
Info()

Reimplemented from Kratos::Geometry< TPointType >.

◆ RegularityQuality()

template<class TPointType >
double Kratos::Tetrahedra3D4< TPointType >::RegularityQuality ( ) const
inlineoverridevirtual

Calculates the Regularity quality metric. Calculates the Regularity quality metric. 1 -> Optimal value 0 -> Worst value

\( \frac{4r}{H} \)

Returns
regularity quality.

Reimplemented from Kratos::Geometry< TPointType >.

◆ ShapeFunctionsIntegrationPointsGradients() [1/2]

template<class TPointType >
void Kratos::Tetrahedra3D4< 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
rResulta container which takes the calculated gradients
ThisMethodthe given IntegrationMethod
Returns
the gradients of all shape functions with regard to the global coordinates

KLUDGE: method call only works with explicit JacobiansType rather than creating JacobiansType within argument list

:TODO: TESTING!!!

Reimplemented from Kratos::Geometry< TPointType >.

◆ ShapeFunctionsIntegrationPointsGradients() [2/2]

template<class TPointType >
void Kratos::Tetrahedra3D4< TPointType >::ShapeFunctionsIntegrationPointsGradients ( ShapeFunctionsGradientsType rResult,
Vector determinants_of_jacobian,
IntegrationMethod  ThisMethod 
) const
inlineoverridevirtual

Reimplemented from Kratos::Geometry< TPointType >.

◆ ShapeFunctionsLocalGradients()

template<class TPointType >
Matrix& Kratos::Tetrahedra3D4< TPointType >::ShapeFunctionsLocalGradients ( Matrix rResult,
const CoordinatesArrayType rPoint 
) const
inlineoverridevirtual

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

Parameters
rPointthe current point at which the gradients are calculated
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::Tetrahedra3D4< TPointType >::ShapeFunctionsSecondDerivatives ( ShapeFunctionsSecondDerivativesType rResult,
const CoordinatesArrayType rPoint 
) const
inlineoverridevirtual

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

Parameters
rResulta third order tensor which contains the second derivatives
rPointthe given point the second order derivatives are calculated in

Reimplemented from Kratos::Geometry< TPointType >.

◆ ShapeFunctionsValues()

template<class TPointType >
Vector& Kratos::Tetrahedra3D4< 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::Tetrahedra3D4< TPointType >::ShapeFunctionValue ( IndexType  ShapeFunctionIndex,
const CoordinatesArrayType rPoint 
) const
inlineoverridevirtual

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

Parameters
ShapeFunctionIndexThe number of the desired shape function
rPointthe 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 >.

◆ ShortestToLongestEdgeQuality()

template<class TPointType >
double Kratos::Tetrahedra3D4< TPointType >::ShortestToLongestEdgeQuality ( ) const
inlineoverridevirtual

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

\( \frac{l}{L} \)

Returns
[description]

Reimplemented from Kratos::Geometry< TPointType >.

◆ SplitAndDecompose()

template<class TPointType >
void Kratos::Tetrahedra3D4< TPointType >::SplitAndDecompose ( const BaseType tetra,
Plane plane,
std::vector< BaseType > &  inside 
) const
inline

◆ Volume()

template<class TPointType >
double Kratos::Tetrahedra3D4< TPointType >::Volume ( ) const
inlineoverridevirtual

This method calculates and returns the volume of this geometry. This method calculates and returns the volume of this geometry.

This method uses the V = (A x B) * C / 6 formula.

Returns
double value contains length, area or volume.
See also
Length()
Area()
Volume()

:TODO: might be necessary to reimplement

Reimplemented from Kratos::Geometry< TPointType >.

◆ VolumeToAverageEdgeLength()

template<class TPointType >
double Kratos::Tetrahedra3D4< TPointType >::VolumeToAverageEdgeLength ( ) const
inlineoverridevirtual

Calculates the volume to average edge lenght quality metric. Calculates the volume to average edge lenght quality metric. 1 -> Optimal value 0 -> Worst value

\( \frac{V}{\frac{1}{6}\sum{l_i}} \)

Returns
[description]

Reimplemented from Kratos::Geometry< TPointType >.

◆ VolumeToEdgeLengthQuality()

template<class TPointType >
double Kratos::Tetrahedra3D4< TPointType >::VolumeToEdgeLengthQuality ( ) const
inlineoverridevirtual

Calculates the Volume to edge length quaility metric. Calculates the Volume to edge length quaility metric. 1 -> Optimal value 0 -> Worst value

\( \frac{V^{2/3}}{\sum{l_{i}^{2}}} \)

Returns
Volume to edge length quality.

Reimplemented from Kratos::Geometry< TPointType >.

◆ VolumeToRMSEdgeLength()

template<class TPointType >
double Kratos::Tetrahedra3D4< TPointType >::VolumeToRMSEdgeLength ( ) const
inlineoverridevirtual

Calculates the volume to average edge length quality metric. Calculates the volume to average edge length quality metric. The average edge lenght is calculated using the RMS. This metric is bounded by the interval (0,1) being: 1 -> Optimal value 0 -> Worst value

\( \frac{V}{\sqrt{\frac{1}{6}\sum{A_{i}^{2}}}} \)

Returns
[description]

Reimplemented from Kratos::Geometry< TPointType >.

◆ VolumeToSurfaceAreaQuality()

template<class TPointType >
double Kratos::Tetrahedra3D4< TPointType >::VolumeToSurfaceAreaQuality ( ) const
inlineoverridevirtual

Calculates the volume to surface area quality metric. Calculates the volume to surface area quality metric. 1 -> Optimal value 0 -> Worst value

\( \frac{V^4}{(\sum{A_{i}^{2}})^{3}} \)

Returns
volume to surface quality.

Reimplemented from Kratos::Geometry< TPointType >.

Friends And Related Function Documentation

◆ Serializer

template<class TPointType >
friend class Serializer
friend

◆ Tetrahedra3D4

template<class TPointType >
template<class TOtherPointType >
friend class Tetrahedra3D4
friend

Private Friends


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