#include <nurbs_curve_geometry.h>

Inheritance diagram for Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >:

Collaboration diagram for Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >:

Public Member Functions
Life Cycle
	NurbsCurveGeometry (const PointsArrayType &rThisPoints, const SizeType PolynomialDegree, const Vector &rKnots)
	Conctructor for B-Spline curves. More...

	NurbsCurveGeometry (const PointsArrayType &rThisPoints, const SizeType PolynomialDegree, const Vector &rKnots, const Vector &rWeights)
	Conctructor for NURBS curves. More...

	NurbsCurveGeometry (const PointsArrayType &ThisPoints)

	NurbsCurveGeometry (NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType > const &rOther)
	Copy constructor. More...

template<class TOtherContainerPointType >
	NurbsCurveGeometry (NurbsCurveGeometry< TWorkingSpaceDimension, TOtherContainerPointType > const &rOther)
	Copy constructor from a geometry with different point type. More...

	~NurbsCurveGeometry () override=default
	Destructor. More...

Operators
NurbsCurveGeometry &	operator= (const NurbsCurveGeometry &rOther)
	Assignment operator. More...

template<class TOtherContainerPointType >
NurbsCurveGeometry &	operator= (NurbsCurveGeometry< TWorkingSpaceDimension, TOtherContainerPointType > const &rOther)
	Assignment operator for geometries with different point type. More...

Operations
BaseType::Pointer	Create (PointsArrayType const &ThisPoints) const override

Geometrical Information
SizeType	PointsNumberInDirection (IndexType LocalDirectionIndex) const override
	Returns number of points per direction. More...

Mathematical Informations
SizeType	PolynomialDegree (IndexType LocalDirectionIndex) const override
	Return polynomial degree of the curve. More...

Get and Set functions
const Vector &	Knots () const

SizeType	NumberOfKnots () const

SizeType	NumberOfNonzeroControlPoints () const

bool	IsRational () const

const Vector &	Weights () const

NurbsInterval	DomainInterval () const

std::vector< NurbsInterval >	KnotSpanIntervals () const

SizeType	NumberOfKnotSpans (IndexType DirectionIndex=0) const
	Returns the number of spans. More...

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

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

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

Projection Point
int	ProjectionPointGlobalToLocalSpace (const CoordinatesArrayType &rPointGlobalCoordinates, CoordinatesArrayType &rProjectedPointLocalCoordinates, const double Tolerance=std::numeric_limits< double >::epsilon()) const override
	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...

Geometrical Informations
double	Length () const override
	Computes the length of a nurbs curve. More...

Jacobian
Matrix &	Jacobian (Matrix &rResult, const CoordinatesArrayType &rCoordinates) const override
	Computes the Jacobian with coordinates. More...

Integration Info
IntegrationInfo	GetDefaultIntegrationInfo () const override
	Provides the default integration dependent on the polynomial degree. More...

Integration Points
void	CreateIntegrationPoints (IntegrationPointsArrayType &rIntegrationPoints, IntegrationInfo &rIntegrationInfo) const override

Quadrature Points
void	CreateQuadraturePointGeometries (GeometriesArrayType &rResultGeometries, IndexType NumberOfShapeFunctionDerivatives, const IntegrationPointsArrayType &rIntegrationPoints, IntegrationInfo &rIntegrationInfo) override

Operation within Global Space
CoordinatesArrayType &	GlobalCoordinates (CoordinatesArrayType &rResult, const CoordinatesArrayType &rLocalCoordinates) const override

void	GlobalSpaceDerivatives (std::vector< CoordinatesArrayType > &rGlobalSpaceDerivatives, const CoordinatesArrayType &rLocalCoordinates, const SizeType DerivativeOrder) const override
	This method maps from dimension space to working space and computes the number of derivatives at the dimension parameter. From Piegl and Tiller, The NURBS Book, Algorithm A3.2/ A4.2. More...

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

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

Geometry Family
GeometryData::KratosGeometryFamily	GetGeometryFamily () const override

GeometryData::KratosGeometryType	GetGeometryType () const override

Information
std::string	Info () const override
	Turn back information as a string. More...

void	PrintInfo (std::ostream &rOStream) const override
	Print information about this object. More...

void	PrintData (std::ostream &rOStream) const override
	Print object's data. More...

Public Member Functions inherited from Kratos::Geometry< TContainerPointType::value_type >
	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...

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

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

Geometry &	operator= (const Geometry &rOther)

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

	operator PointsArrayType & ()

TContainerPointType::value_type &	operator[] (const SizeType &i)

TContainerPointType::value_type 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

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)

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

void	SetValue (const TVariableType &rThisVariable, typename TVariableType::Type const &rValue)

TVariableType::Type &	GetValue (const TVariableType &rThisVariable)

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...

virtual Pointer	Create (PointsArrayType const &rThisPoints) const
	Creates a new geometry pointer. More...

virtual Pointer	Create (const IndexType NewGeometryId, PointsArrayType const &rThisPoints) const
	Creates a new geometry pointer. 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 ()

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

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 double	Area () const
	This method calculate and return area or surface area of this geometry depending to it's dimension. More...

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

virtual double	DomainSize () const
	This method calculate and return length, area or volume of this geometry depending to it's dimension. More...

virtual double	MinEdgeLength () const

virtual double	MaxEdgeLength () const

virtual double	AverageEdgeLength () const

virtual double	Circumradius () const

virtual double	Inradius () const

virtual bool	HasIntersection (const GeometryType &ThisGeometry) const

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

virtual void	BoundingBox (TContainerPointType::value_type &rLowPoint, TContainerPointType::value_type &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

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)

TContainerPointType::value_type const &	GetPoint (const int Index) const

TContainerPointType::value_type &	GetPoint (const int Index)

virtual Matrix &	PointsLocalCoordinates (Matrix &rResult) const

virtual CoordinatesArrayType &	PointLocalCoordinates (CoordinatesArrayType &rResult, const CoordinatesArrayType &rPoint) const
	Returns the local coordinates of a given arbitrary point. More...

virtual bool	IsInside (const CoordinatesArrayType &rPointGlobalCoordinates, CoordinatesArrayType &rResult, const double Tolerance=std::numeric_limits< double >::epsilon()) const
	Checks if given point in global space coordinates is inside the geometry boundaries. This function computes the local coordinates and checks then if this point lays within the boundaries. More...

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...

virtual SizeType	EdgesNumber () const
	This method gives you number of all edges 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...

virtual GeometriesArrayType	GenerateEdges () const
	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 SizeType	FacesNumber () const
	Returns the number of faces of the current geometry. More...

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

virtual void	NumberNodesInFaces (DenseVector< unsigned int > &rNumberNodesInFaces) const

virtual void	NodesInFaces (DenseMatrix< unsigned int > &rNodesInFaces) const

SizeType	IntegrationPointsNumber () const

SizeType	IntegrationPointsNumber (IntegrationMethod ThisMethod) const

const IntegrationPointsArrayType &	IntegrationPoints () const

const IntegrationPointsArrayType &	IntegrationPoints (IntegrationMethod ThisMethod) const

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

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, 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	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	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, Matrix &rDeltaPosition) const

Vector &	DeterminantOfJacobian (Vector &rResult) const

virtual Vector &	DeterminantOfJacobian (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

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

virtual double	ShapeFunctionValue (IndexType ShapeFunctionIndex, const CoordinatesArrayType &rCoordinates) 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

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

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

void	ShapeFunctionsIntegrationPointsGradients (ShapeFunctionsGradientsType &rResult) const

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

virtual void	ShapeFunctionsIntegrationPointsGradients (ShapeFunctionsGradientsType &rResult, Vector &rDeterminantsOfJacobian, IntegrationMethod ThisMethod) 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 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...

Type Definitions
typedef TContainerPointType::value_type	NodeType

typedef Geometry< NodeType >	BaseType

typedef NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >	GeometryType

typedef BaseType::IndexType	IndexType

typedef BaseType::SizeType	SizeType

typedef BaseType::CoordinatesArrayType	CoordinatesArrayType

typedef BaseType::PointsArrayType	PointsArrayType

typedef BaseType::GeometriesArrayType	GeometriesArrayType

typedef BaseType::IntegrationPointsArrayType	IntegrationPointsArrayType

	KRATOS_CLASS_POINTER_DEFINITION (NurbsCurveGeometry)
	Counted pointer of NurbsCurveGeometry. More...

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

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

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)

Private Serialization
class	Serializer

Additional Inherited Members
Public Types inherited from Kratos::Geometry< TContainerPointType::value_type >
enum class	QualityCriteria

enum class	LumpingMethods
	This defines the different methods to compute the lumping methods. More...

typedef Geometry< TContainerPointType::value_type >	GeometryType
	This Geometry type. More...

typedef PointerVector< TContainerPointType::value_type >	PointsArrayType

typedef GeometryData::IntegrationMethod	IntegrationMethod

typedef PointerVector< GeometryType >	GeometriesArrayType

typedef TContainerPointType::value_type	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 TContainerPointType::value_type &	PointReferenceType

typedef const TContainerPointType::value_type &	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< TContainerPointType::value_type >
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< TContainerPointType::value_type >
static constexpr IndexType	BACKGROUND_GEOMETRY_INDEX

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

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

virtual double	AreaToEdgeLengthRatio () const

virtual double	ShortestAltitudeToEdgeLengthRatio () const

virtual double	InradiusToLongestEdgeQuality () const

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...

Member Typedef Documentation

◆ BaseType

template<int TWorkingSpaceDimension, class TContainerPointType >

typedef Geometry<NodeType> Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::BaseType

◆ CoordinatesArrayType

template<int TWorkingSpaceDimension, class TContainerPointType >

typedef BaseType::CoordinatesArrayType Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::CoordinatesArrayType

◆ GeometriesArrayType

template<int TWorkingSpaceDimension, class TContainerPointType >

typedef BaseType::GeometriesArrayType Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::GeometriesArrayType

◆ GeometryType

template<int TWorkingSpaceDimension, class TContainerPointType >

typedef NurbsCurveGeometry<TWorkingSpaceDimension, TContainerPointType> Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::GeometryType

◆ IndexType

template<int TWorkingSpaceDimension, class TContainerPointType >

typedef BaseType::IndexType Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::IndexType

◆ IntegrationPointsArrayType

template<int TWorkingSpaceDimension, class TContainerPointType >

typedef BaseType::IntegrationPointsArrayType Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::IntegrationPointsArrayType

◆ NodeType

template<int TWorkingSpaceDimension, class TContainerPointType >

typedef TContainerPointType::value_type Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::NodeType

◆ PointsArrayType

template<int TWorkingSpaceDimension, class TContainerPointType >

typedef BaseType::PointsArrayType Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::PointsArrayType

◆ SizeType

template<int TWorkingSpaceDimension, class TContainerPointType >

typedef BaseType::SizeType Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::SizeType

Constructor & Destructor Documentation

◆ NurbsCurveGeometry() [1/5]

template<int TWorkingSpaceDimension, class TContainerPointType >

Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::NurbsCurveGeometry	(	const PointsArrayType &	rThisPoints,
		const SizeType	PolynomialDegree,
		const Vector &	rKnots
	)

inline

Conctructor for B-Spline curves.

◆ NurbsCurveGeometry() [2/5]

template<int TWorkingSpaceDimension, class TContainerPointType >

Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::NurbsCurveGeometry	(	const PointsArrayType &	rThisPoints,
		const SizeType	PolynomialDegree,
		const Vector &	rKnots,
		const Vector &	rWeights
	)

inline

Conctructor for NURBS curves.

◆ NurbsCurveGeometry() [3/5]

template<int TWorkingSpaceDimension, class TContainerPointType >

Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::NurbsCurveGeometry ( const PointsArrayType & ThisPoints )

inlineexplicit

◆ NurbsCurveGeometry() [4/5]

template<int TWorkingSpaceDimension, class TContainerPointType >

Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::NurbsCurveGeometry ( NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType > const & rOther )

inline

Copy constructor.

◆ NurbsCurveGeometry() [5/5]

template<int TWorkingSpaceDimension, class TContainerPointType >

template<class TOtherContainerPointType >

Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::NurbsCurveGeometry ( NurbsCurveGeometry< TWorkingSpaceDimension, TOtherContainerPointType > const & rOther )

inline

Copy constructor from a geometry with different point type.

◆ ~NurbsCurveGeometry()

template<int TWorkingSpaceDimension, class TContainerPointType >

Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::~NurbsCurveGeometry ( )

overridedefault

Destructor.

Member Function Documentation

◆ ClosestPointLocalToLocalSpace()

template<int TWorkingSpaceDimension, class TContainerPointType >

virtual int Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::ClosestPointLocalToLocalSpace	(	const CoordinatesArrayType &	rPointLocalCoordinates,
		CoordinatesArrayType &	rClosestPointLocalCoordinates,
		const double	Tolerance = `std::numeric_limits<double>::epsilon()`
	)		const

inlineoverridevirtual

Calculates the closes point projection This method calculates the closest point projection of a point in local space coordinates.

Parameters

rPointLocalCoordinates	Input local coordinates
rClosestPointLocalCoordinates	Closest point local coordinates. This should be initialized with the initial guess
Tolerance	Accepted orthogonal error

Returns: int -1 -> failed 0 -> outside 1 -> inside 2 -> on the boundary

Reimplemented from Kratos::Geometry< TContainerPointType::value_type >.

◆ Create()

template<int TWorkingSpaceDimension, class TContainerPointType >

BaseType::Pointer Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::Create ( PointsArrayType const & ThisPoints ) const

inlineoverride

◆ CreateIntegrationPoints()

template<int TWorkingSpaceDimension, class TContainerPointType >

void Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::CreateIntegrationPoints	(	IntegrationPointsArrayType &	rIntegrationPoints,
		IntegrationInfo &	rIntegrationInfo
	)		const

inlineoverridevirtual

Reimplemented from Kratos::Geometry< TContainerPointType::value_type >.

◆ CreateQuadraturePointGeometries() [1/3]

template<int TWorkingSpaceDimension, class TContainerPointType >

virtual void Kratos::Geometry< TPointType >::CreateQuadraturePointGeometries

inline

◆ CreateQuadraturePointGeometries() [2/3]

template<int TWorkingSpaceDimension, class TContainerPointType >

void Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::CreateQuadraturePointGeometries	(	GeometriesArrayType &	rResultGeometries,
		IndexType	NumberOfShapeFunctionDerivatives,
		const IntegrationPointsArrayType &	rIntegrationPoints,
		IntegrationInfo &	rIntegrationInfo
	)

inlineoverridevirtual

Get List of Control Points

Get Shape Functions N

Get Shape Function Derivatives DN_De, ...

Reimplemented from Kratos::Geometry< TContainerPointType::value_type >.

◆ CreateQuadraturePointGeometries() [3/3]

template<int TWorkingSpaceDimension, class TContainerPointType >

virtual void Kratos::Geometry< TPointType >::CreateQuadraturePointGeometries

inline

◆ DomainInterval()

template<int TWorkingSpaceDimension, class TContainerPointType >

NurbsInterval Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::DomainInterval ( ) const

inline

◆ GetDefaultIntegrationInfo()

template<int TWorkingSpaceDimension, class TContainerPointType >

IntegrationInfo Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::GetDefaultIntegrationInfo ( ) const

inlineoverridevirtual

Provides the default integration dependent on the polynomial degree.

Reimplemented from Kratos::Geometry< TContainerPointType::value_type >.

◆ GetGeometryFamily()

template<int TWorkingSpaceDimension, class TContainerPointType >

GeometryData::KratosGeometryFamily Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::GetGeometryFamily ( ) const

inlineoverridevirtual

Reimplemented from Kratos::Geometry< TContainerPointType::value_type >.

◆ GetGeometryType()

template<int TWorkingSpaceDimension, class TContainerPointType >

GeometryData::KratosGeometryType Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::GetGeometryType ( ) const

inlineoverridevirtual

Reimplemented from Kratos::Geometry< TContainerPointType::value_type >.

◆ GetPoint() [1/2]

template<int TWorkingSpaceDimension, class TContainerPointType >

TPointType& Kratos::Geometry< TPointType >::GetPoint

inline

An access method to the i'th points stored in this geometry.

Returns: A counted pointer to i'th point of geometry.

◆ GetPoint() [2/2]

template<int TWorkingSpaceDimension, class TContainerPointType >

TPointType const& Kratos::Geometry< TPointType >::GetPoint

inline

A constant access method to the i'th points stored in this geometry.

Returns: A constant counted pointer to i'th point of geometry.

◆ GlobalCoordinates()

template<int TWorkingSpaceDimension, class TContainerPointType >

CoordinatesArrayType& Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::GlobalCoordinates	(	CoordinatesArrayType &	rResult,
		const CoordinatesArrayType &	LocalCoordinates
	)		const

inlineoverridevirtual

This method provides the global coordinates corresponding to the local coordinates provided

Parameters

rResult	The array containing the global coordinates corresponding to the local coordinates provided
LocalCoordinates	The local coordinates provided

Returns: An array containing the global coordinates corresponding to the local coordinates provides

See also: PointLocalCoordinates

Reimplemented from Kratos::Geometry< TContainerPointType::value_type >.

◆ GlobalSpaceDerivatives()

template<int TWorkingSpaceDimension, class TContainerPointType >

void Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::GlobalSpaceDerivatives	(	std::vector< CoordinatesArrayType > &	rGlobalSpaceDerivatives,
		const CoordinatesArrayType &	rLocalCoordinates,
		const SizeType	DerivativeOrder
	)		const

inlineoverridevirtual

This method maps from dimension space to working space and computes the number of derivatives at the dimension parameter. From Piegl and Tiller, The NURBS Book, Algorithm A3.2/ A4.2.

Parameters

LocalCoordinates	The local coordinates in dimension space
Derivative	Number of computed derivatives

Returns: std::vector<array_1d<double, 3>> with the coordinates in working space

See also: PointLocalCoordinates

Reimplemented from Kratos::Geometry< TContainerPointType::value_type >.

◆ Info()

template<int TWorkingSpaceDimension, class TContainerPointType >

std::string Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::Info ( ) const

inlineoverridevirtual

Turn back information as a string.

Reimplemented from Kratos::Geometry< TContainerPointType::value_type >.

◆ IsInsideLocalSpace()

template<int TWorkingSpaceDimension, class TContainerPointType >

int Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::IsInsideLocalSpace	(	const CoordinatesArrayType &	rPointLocalCoordinates,
		const double	Tolerance = `std::numeric_limits<double>::epsilon()`
	)		const

inlineoverridevirtual

Checks if given point in local space coordinates of this geometry is inside the geometry boundaries.

Parameters

rPointLocalCoordinates	the point on the geometry, which shall be checked if it lays within the boundaries.
Tolerance	the tolerance to the boundary.

Returns: -1 -> failed 0 -> outside 1 -> inside 2 -> on the boundary

Reimplemented from Kratos::Geometry< TContainerPointType::value_type >.

◆ IsRational()

template<int TWorkingSpaceDimension, class TContainerPointType >

bool Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::IsRational ( ) const

inline

◆ Jacobian()

template<int TWorkingSpaceDimension, class TContainerPointType >

Matrix& Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::Jacobian	(	Matrix &	rResult,
		const CoordinatesArrayType &	rCoordinates
	)		const

inlineoverridevirtual

Computes the Jacobian with coordinates.

Compute shape functions

Compute Jacobian

Reimplemented from Kratos::Geometry< TContainerPointType::value_type >.

◆ Knots()

template<int TWorkingSpaceDimension, class TContainerPointType >

const Vector& Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::Knots ( ) const

inline

◆ KnotSpanIntervals()

template<int TWorkingSpaceDimension, class TContainerPointType >

std::vector<NurbsInterval> Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::KnotSpanIntervals ( ) const

inline

◆ KRATOS_CLASS_POINTER_DEFINITION()

template<int TWorkingSpaceDimension, class TContainerPointType >

Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::KRATOS_CLASS_POINTER_DEFINITION ( NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType > )

Counted pointer of NurbsCurveGeometry.

◆ Length()

template<int TWorkingSpaceDimension, class TContainerPointType >

double Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::Length ( ) const

inlineoverridevirtual

Computes the length of a nurbs curve.

Reimplemented from Kratos::Geometry< TContainerPointType::value_type >.

◆ NumberOfKnots()

template<int TWorkingSpaceDimension, class TContainerPointType >

SizeType Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::NumberOfKnots ( ) const

inline

◆ NumberOfKnotSpans()

template<int TWorkingSpaceDimension, class TContainerPointType >

SizeType Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::NumberOfKnotSpans ( IndexType DirectionIndex = 0 ) const

inline

Returns the number of spans.

◆ NumberOfNonzeroControlPoints()

template<int TWorkingSpaceDimension, class TContainerPointType >

SizeType Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::NumberOfNonzeroControlPoints ( ) const

inline

◆ operator=() [1/2]

template<int TWorkingSpaceDimension, class TContainerPointType >

NurbsCurveGeometry& Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::operator= ( const NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType > & rOther )

inline

Assignment operator.

◆ operator=() [2/2]

template<int TWorkingSpaceDimension, class TContainerPointType >

template<class TOtherContainerPointType >

NurbsCurveGeometry& Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::operator= ( NurbsCurveGeometry< TWorkingSpaceDimension, TOtherContainerPointType > const & rOther )

inline

Assignment operator for geometries with different point type.

◆ pGetPoint() [1/2]

template<int TWorkingSpaceDimension, class TContainerPointType >

TPointType::Pointer Kratos::Geometry< TPointType >::pGetPoint

inline

An access method to the i'th points stored in this geometry.

Returns: A counted pointer to i'th point of geometry.

◆ pGetPoint() [2/2]

template<int TWorkingSpaceDimension, class TContainerPointType >

const TPointType::Pointer Kratos::Geometry< TPointType >::pGetPoint

inline

A constant access method to the i'th points stored in this geometry.

Returns: A constant counted pointer to i'th point of geometry.

◆ PointsNumberInDirection()

template<int TWorkingSpaceDimension, class TContainerPointType >

SizeType Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::PointsNumberInDirection ( IndexType LocalDirectionIndex ) const

inlineoverridevirtual

Returns number of points per direction.

Reimplemented from Kratos::Geometry< TContainerPointType::value_type >.

◆ PolynomialDegree()

template<int TWorkingSpaceDimension, class TContainerPointType >

SizeType Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::PolynomialDegree ( IndexType LocalDirectionIndex ) const

inlineoverridevirtual

Return polynomial degree of the curve.

Reimplemented from Kratos::Geometry< TContainerPointType::value_type >.

◆ PrintData()

template<int TWorkingSpaceDimension, class TContainerPointType >

void Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::PrintData ( std::ostream & rOStream ) const

inlineoverridevirtual

Print object's data.

Reimplemented from Kratos::Geometry< TContainerPointType::value_type >.

◆ PrintInfo()

template<int TWorkingSpaceDimension, class TContainerPointType >

void Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::PrintInfo ( std::ostream & rOStream ) const

inlineoverridevirtual

Print information about this object.

Reimplemented from Kratos::Geometry< TContainerPointType::value_type >.

◆ ProjectionPointGlobalToLocalSpace()

template<int TWorkingSpaceDimension, class TContainerPointType >

int Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::ProjectionPointGlobalToLocalSpace	(	const CoordinatesArrayType &	rPointGlobalCoordinates,
		CoordinatesArrayType &	rProjectionPointLocalCoordinates,
		const double	Tolerance = `std::numeric_limits<double>::epsilon()`
	)		const

inlineoverridevirtual

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.

Parameters

rPointLocalCoordinates	Global coordinates of the point to be projected
rProjectionPointLocalCoordinates	Projection point local coordinates. This should be initialized with the initial guess
Tolerance	Accepted orthogonal error

Returns: int 0 -> failed 1 -> converged

Reimplemented from Kratos::Geometry< TContainerPointType::value_type >.

◆ ShapeFunctionsLocalGradients()

template<int TWorkingSpaceDimension, class TContainerPointType >

Matrix& Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::ShapeFunctionsLocalGradients	(	Matrix &	rResult,
		const CoordinatesArrayType &	rPoint
	)		const

inlineoverridevirtual

This method gives gradient of all shape functions evaluated in given point. There is no calculation and it just give it from shape functions values container if they are existing. Otherwise it gives you error which this value is not exist.

Parameters

rResult	the given Container that will be overwritten by the solution
rPoint	the given local coordinates the gradients will be evaluated for

Returns: a matrix of gradients for each shape function

Reimplemented from Kratos::Geometry< TContainerPointType::value_type >.

◆ ShapeFunctionsValues()

template<int TWorkingSpaceDimension, class TContainerPointType >

Vector& Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::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< TContainerPointType::value_type >.

◆ SpansLocalSpace()

template<int TWorkingSpaceDimension, class TContainerPointType >

void Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::SpansLocalSpace	(	std::vector< double > &	rSpans,
		IndexType	DirectionIndex = `0`
	)		const

inlineoverridevirtual

Reimplemented from Kratos::Geometry< TContainerPointType::value_type >.

◆ Weights()

template<int TWorkingSpaceDimension, class TContainerPointType >

const Vector& Kratos::NurbsCurveGeometry< TWorkingSpaceDimension, TContainerPointType >::Weights ( ) const

inline

Friends And Related Function Documentation

◆ Serializer

template<int TWorkingSpaceDimension, class TContainerPointType >

friend class Serializer

friend

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

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

Public Member Functions

Type Definitions

Private Serialization

Additional Inherited Members

Member Typedef Documentation

◆ BaseType

◆ CoordinatesArrayType

◆ GeometriesArrayType

◆ GeometryType

◆ IndexType

◆ IntegrationPointsArrayType

◆ NodeType

◆ PointsArrayType

◆ SizeType

Constructor & Destructor Documentation

◆ NurbsCurveGeometry() [1/5]

◆ NurbsCurveGeometry() [2/5]

◆ NurbsCurveGeometry() [3/5]

◆ NurbsCurveGeometry() [4/5]

◆ NurbsCurveGeometry() [5/5]

◆ ~NurbsCurveGeometry()

Member Function Documentation

◆ ClosestPointLocalToLocalSpace()

◆ Create()

◆ CreateIntegrationPoints()

◆ CreateQuadraturePointGeometries() [1/3]

◆ CreateQuadraturePointGeometries() [2/3]

◆ CreateQuadraturePointGeometries() [3/3]

◆ DomainInterval()

◆ GetDefaultIntegrationInfo()

◆ GetGeometryFamily()

◆ GetGeometryType()

◆ GetPoint() [1/2]

◆ GetPoint() [2/2]

◆ GlobalCoordinates()

◆ GlobalSpaceDerivatives()

◆ Info()

◆ IsInsideLocalSpace()

◆ IsRational()

◆ Jacobian()

◆ Knots()

◆ KnotSpanIntervals()

◆ KRATOS_CLASS_POINTER_DEFINITION()

◆ Length()

◆ NumberOfKnots()

◆ NumberOfKnotSpans()

◆ NumberOfNonzeroControlPoints()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ pGetPoint() [1/2]

◆ pGetPoint() [2/2]

◆ PointsNumberInDirection()

◆ PolynomialDegree()

◆ PrintData()

◆ PrintInfo()

◆ ProjectionPointGlobalToLocalSpace()

◆ ShapeFunctionsLocalGradients()

◆ ShapeFunctionsValues()

◆ SpansLocalSpace()

◆ Weights()

Friends And Related Function Documentation

◆ Serializer