#include <feitspline.h>

Inheritance diagram for oofem::TSplineInterpolation:

Collaboration diagram for oofem::TSplineInterpolation:

Public Member Functions
	TSplineInterpolation (int nsd)
void	initializeFrom (InputRecord &ir, ParameterManager &pm, int elnum, int priority) override
	Initializes receiver according to object description stored in input record.
void	setNumberOfControlPoints (int num)
void	evalN (FloatArray &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
double	evaldNdx (FloatMatrix &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
void	local2global (FloatArray &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
int	global2local (FloatArray &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
void	giveJacobianMatrixAt (FloatMatrix &jacobianMatrix, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
int	giveKnotSpanBasisFuncMask (const IntArray &knotSpan, IntArray &mask) const override
int	giveNumberOfKnotSpanBasisFunctions (const IntArray &knotSpan) const override
const char *	giveClassName () const
Public Member Functions inherited from oofem::BSplineInterpolation
	BSplineInterpolation (int nsd)
integrationDomain	giveIntegrationDomain (const Element_Geometry_Type egt) const override
const Element_Geometry_Type	giveGeometryType () const override
const Element_Geometry_Type	giveBoundaryGeometryType (int boundary) const override
integrationDomain	giveBoundaryIntegrationDomain (int ib, const Element_Geometry_Type) const override
	Returns boundary integration domain.
integrationDomain	giveBoundarySurfaceIntegrationDomain (int isurf, const Element_Geometry_Type) const override
	Returns boundary integration domain.
integrationDomain	giveBoundaryEdgeIntegrationDomain (int iedge, const Element_Geometry_Type) const override
	Returns boundary integration domain.
int	giveNsd (const Element_Geometry_Type) const override
void	postInitialize (ParameterManager &pm, int elnum) override
IntArray	boundaryEdgeGiveNodes (int boundary, const Element_Geometry_Type, bool includeHierarchical=false) const override
void	boundaryEdgeEvalN (FloatArray &answer, int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
double	boundaryEdgeGiveTransformationJacobian (int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
void	boundaryEdgeLocal2Global (FloatArray &answer, int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
double	boundaryEdgeEvalNormal (FloatArray &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
void	boundarySurfaceEvalN (FloatArray &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
void	boundarySurfaceEvaldNdx (FloatMatrix &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
double	boundarySurfaceEvalNormal (FloatArray &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
void	boundarySurfaceLocal2global (FloatArray &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
double	boundarySurfaceGiveTransformationJacobian (int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
IntArray	boundarySurfaceGiveNodes (int boundary, const Element_Geometry_Type, bool includeHierarchical=false) const override
IntArray	boundaryGiveNodes (int boundary, const Element_Geometry_Type) const override
void	boundaryEvalN (FloatArray &answer, int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
double	boundaryEvalNormal (FloatArray &answer, int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
double	boundaryGiveTransformationJacobian (int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
void	boundaryLocal2Global (FloatArray &answer, int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
int	giveNumberOfKnotSpans (int dim) const override
virtual int	giveNumberOfControlPoints (int dim) const
const FloatArray *	giveKnotVector () const override
const IntArray *	giveKnotMultiplicity (int dim) const override
const FloatArray *	giveKnotValues (int dim) const override
const char *	giveClassName () const
bool	hasSubPatchFormulation () const override
std::unique_ptr< IntegrationRule >	giveIntegrationRule (int order, const Element_Geometry_Type) const override
std::unique_ptr< IntegrationRule >	giveBoundaryIntegrationRule (int order, int boundary, Element_Geometry_Type) const override
std::unique_ptr< IntegrationRule >	giveBoundaryEdgeIntegrationRule (int order, int boundary, Element_Geometry_Type) const override
Public Member Functions inherited from oofem::FEInterpolation
	FEInterpolation (int o)
virtual	~FEInterpolation ()=default
int	giveInterpolationOrder () const
virtual void	giveCellDofMans (IntArray &nodes, IntArray &internalDofMans, Element *elem) const
	Returns list of element nodes (and list of internal dof managers) (including on edges and surfaces) defining the approximation.
virtual void	evald2Ndx2 (FloatMatrix &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
virtual void	evaldNdxi (FloatMatrix &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
virtual void	giveLocalNodeCoords (FloatMatrix &answer, const Element_Geometry_Type) const
virtual double	giveTransformationJacobian (const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
virtual std::unique_ptr< IntegrationRule >	giveBoundarySurfaceIntegrationRule (int order, int boundary, const Element_Geometry_Type) const
virtual double	evalNXIntegral (int boundary, const FEICellGeometry &cellgeo) const
virtual void	surfaceEvaldNdxi (FloatMatrix &answer, const FloatArray &lcoords) const
virtual void	surfaceEvald2Ndxi2 (FloatMatrix &answer, const FloatArray &lcoords) const
virtual int	giveNumberOfEdges (const Element_Geometry_Type) const
virtual int	giveNumberOfNodes (const Element_Geometry_Type) const
virtual void	initializeCell (Element *e) const
std::string	errorInfo (const char *func) const

Protected Member Functions
double	basisFunction (double u, int p, const FloatArray &U, const IntArray &I) const
void	dersBasisFunction (int n, double u, int p, const FloatArray &U, const IntArray &I, FloatArray &ders) const
void	createLocalKnotVector (FloatArray &answer, int p, const FloatArray &U, const IntArray &I, int &prepend, int &append) const
int	giveKnotSpanBasisFuncMask (const IntArray &startKnotSpan, const IntArray &endKnotSpan, IntArray &mask) const
int	giveNumberOfKnotSpanBasisFunctions (const IntArray &startKnotSpan, const IntArray &endKnotSpan) const
void	basisFuns (FloatArray &N, int span, double u, int p, const FloatArray &U) const
void	dersBasisFuns (int n, double u, int span, int p, const FloatArray &U, FloatMatrix &ders) const
int	findSpan (int n, int p, double u, const FloatArray &U) const
void	giveNonzeroBasisFuncInterval (int span, int deg, int &s, int &e) const

Protected Attributes
std::vector< std::array< IntArray, 3 > >	localIndexKnotVector
	Local index knot vector of the dimensions [totalNumberOfControlPoints][nsd][degree+2].
int	totalNumberOfControlPoints = 0
FloatArray	weights
Protected Attributes inherited from oofem::BSplineInterpolation
int	nsd
	Number of spatial directions.
std::array< int, 3 >	degree
	Degree in each direction.
std::array< FloatArray, 3 >	knotValues
	Knot values [nsd].
std::array< IntArray, 3 >	knotMultiplicity
	Knot multiplicity [nsd].
std::array< int, 3 >	numberOfControlPoints
	numberOfControlPoints[nsd]
std::array< FloatArray, 3 >	knotVector
	Knot vectors [nsd][knot_vector_size].
std::array< int, 3 >	numberOfKnotSpans
	Nonzero spans in each directions [nsd].
Protected Attributes inherited from oofem::FEInterpolation
int	order = 0

Additional Inherited Members
Static Protected Attributes inherited from oofem::BSplineInterpolation
static ParamKey	IPK_BSplineInterpolation_degree
static ParamKey	IPK_BSplineInterpolation_knotVectorU
static ParamKey	IPK_BSplineInterpolation_knotVectorV
static ParamKey	IPK_BSplineInterpolation_knotVectorW
static ParamKey	IPK_BSplineInterpolation_knotMultiplicityU
static ParamKey	IPK_BSplineInterpolation_knotMultiplicityV
static ParamKey	IPK_BSplineInterpolation_knotMultiplicityW

Detailed Description

Interpolation for T-splines.

Definition at line 62 of file feitspline.h.

Constructor & Destructor Documentation

◆ TSplineInterpolation()

oofem::TSplineInterpolation::TSplineInterpolation ( int nsd )

inline

Temporary open local knot vector to enable use of BSpline algorithms (common for all directions) [3*max_degree+2].

Definition at line 74 of file feitspline.h.

References oofem::BSplineInterpolation::BSplineInterpolation(), and oofem::BSplineInterpolation::nsd.

Member Function Documentation

◆ basisFunction()

double oofem::TSplineInterpolation::basisFunction	(	double	u,
		int	p,
		const FloatArray &	U,
		const IntArray &	I ) const

protected

Evaluates the middle basis function on local knot vector at u.

Parameters

u	Value at which to evaluate.
p	Degree.
U	Global knot values.
I	Local index knot vector.

Returns: N Computed middle basis function.

Warning: Parameter u must be in a valid range.

Definition at line 607 of file feitspline.C.

References createLocalKnotVector(), and N.

Referenced by evalN(), and local2global().

◆ createLocalKnotVector()

void oofem::TSplineInterpolation::createLocalKnotVector	(	FloatArray &	answer,
		int	p,
		const FloatArray &	U,
		const IntArray &	I,
		int &	prepend,
		int &	append ) const

protected

Creates local open knot vector. This is generally done extracting knot values from global knot vector using the local index knot vector and by prepending p times the first knot and appending p times the last knot. However, existing knot multiplicity at the start and end must be accounted for.

Parameters

p	Degree.
U	Global knot values.
I	Local index knot vector
prepend	Number of prepended entries
append	Number of appended entries

Definition at line 643 of file feitspline.C.

References oofem::FloatArray::at(), oofem::BSplineInterpolation::degree, oofem::BSplineInterpolation::nsd, and oofem::FloatArray::resize().

Referenced by basisFunction(), and dersBasisFunction().

◆ dersBasisFunction()

void oofem::TSplineInterpolation::dersBasisFunction	(	int	n,
		double	u,
		int	p,
		const FloatArray &	U,
		const IntArray &	I,
		FloatArray &	ders ) const

protected

Computes the middle basis function and it derivatives on local knot vector at u. The result is stored in the ders vector

\begin{align*}N(u) &= ders(0) N'(u) &= ders(1) N''(u)&= ders(2) \end{align*}

Parameters

n	Degree of the derivation.
u	Parametric value.
p	Degree.
U	Global knot values.
I	Local index knot vector.
ders	Vector containing the derivatives of the middle basis function.

Warning: Parameters n and u must be in a valid range.

Definition at line 624 of file feitspline.C.

References createLocalKnotVector(), and oofem::FloatArray::resize().

Referenced by evaldNdx(), and giveJacobianMatrixAt().

◆ evaldNdx()

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

overridevirtual

Evaluates the matrix of derivatives of interpolation functions (shape functions) at given point. These derivatives are in global coordinate system (where the nodal coordinates are defined)

Parameters

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

Returns: Determinant of the Jacobian.

Reimplemented from oofem::BSplineInterpolation.

Definition at line 157 of file feitspline.C.

References oofem::BSplineInterpolation::degree, dersBasisFunction(), oofem::BSplineInterpolation::findSpan(), oofem::FloatMatrix::giveDeterminant(), giveKnotSpanBasisFuncMask(), oofem::BSplineInterpolation::giveKnotValues(), oofem::IntArray::giveSize(), oofem::FEICellGeometry::giveVertexCoordinates(), oofem::FEIIGAElementGeometryWrapper::knotSpan, oofem::BSplineInterpolation::knotVector, localIndexKnotVector, oofem::BSplineInterpolation::nsd, oofem::BSplineInterpolation::numberOfControlPoints, OOFEM_ERROR, oofem::product(), oofem::FloatMatrix::resize(), weights, and oofem::FloatMatrix::zero().

◆ evalN()

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

overridevirtual

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

Parameters

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

Reimplemented from oofem::BSplineInterpolation.

Definition at line 116 of file feitspline.C.

References basisFunction(), oofem::BSplineInterpolation::degree, oofem::BSplineInterpolation::findSpan(), giveKnotSpanBasisFuncMask(), oofem::BSplineInterpolation::giveKnotValues(), oofem::IntArray::giveSize(), oofem::FEIIGAElementGeometryWrapper::knotSpan, oofem::BSplineInterpolation::knotVector, localIndexKnotVector, N, oofem::BSplineInterpolation::nsd, oofem::BSplineInterpolation::numberOfControlPoints, OOFEM_ERROR, oofem::FloatArray::resize(), oofem::sum(), oofem::FloatArray::times(), and weights.

◆ giveClassName()

const char * oofem::TSplineInterpolation::giveClassName ( ) const

inline

Definition at line 90 of file feitspline.h.

◆ giveJacobianMatrixAt()

void oofem::TSplineInterpolation::giveJacobianMatrixAt	(	FloatMatrix &	jacobianMatrix,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo ) const

overridevirtual

Gives the jacobian matrix at the local coordinates.

Parameters

jacobianMatrix	The requested matrix.
lcoords	Local coordinates.
cellgeo	Element geometry.

Reimplemented from oofem::BSplineInterpolation.

Definition at line 340 of file feitspline.C.

References oofem::BSplineInterpolation::degree, dersBasisFunction(), oofem::BSplineInterpolation::findSpan(), giveKnotSpanBasisFuncMask(), oofem::BSplineInterpolation::giveKnotValues(), oofem::IntArray::giveSize(), oofem::FEICellGeometry::giveVertexCoordinates(), oofem::FEIIGAElementGeometryWrapper::knotSpan, oofem::BSplineInterpolation::knotVector, localIndexKnotVector, oofem::BSplineInterpolation::nsd, oofem::BSplineInterpolation::numberOfControlPoints, OOFEM_ERROR, oofem::product(), oofem::FloatMatrix::resize(), weights, and oofem::FloatMatrix::zero().

◆ giveKnotSpanBasisFuncMask() [1/2]

int oofem::TSplineInterpolation::giveKnotSpanBasisFuncMask	(	const IntArray &	knotSpan,
		IntArray &	mask ) const

overridevirtual

Returns indices (zero based) of nonzero basis functions for given knot span. The knot span identifies the sub-region of the finite element.

Returns: Nonzero if mask is provided, zero otherwise meaning that all basis functions are generally nonzero.

Reimplemented from oofem::BSplineInterpolation.

Definition at line 452 of file feitspline.C.

References oofem::BSplineInterpolation::degree, oofem::IntArray::followedBy(), oofem::BSplineInterpolation::knotValues, oofem::BSplineInterpolation::knotVector, localIndexKnotVector, oofem::BSplineInterpolation::nsd, OOFEM_ERROR, oofem::IntArray::preallocate(), and totalNumberOfControlPoints.

Referenced by evaldNdx(), evalN(), giveJacobianMatrixAt(), and local2global().

◆ giveKnotSpanBasisFuncMask() [2/2]

int oofem::TSplineInterpolation::giveKnotSpanBasisFuncMask	(	const IntArray &	startKnotSpan,
		const IntArray &	endKnotSpan,
		IntArray &	mask ) const

protected

Returns indices (zero based) of nonzero basis functions for given knot span interval.

Definition at line 531 of file feitspline.C.

References oofem::BSplineInterpolation::degree, oofem::IntArray::followedBy(), oofem::BSplineInterpolation::knotValues, oofem::BSplineInterpolation::knotVector, localIndexKnotVector, oofem::BSplineInterpolation::nsd, OOFEM_ERROR, oofem::IntArray::preallocate(), and totalNumberOfControlPoints.

◆ giveNumberOfKnotSpanBasisFunctions() [1/2]

int oofem::TSplineInterpolation::giveNumberOfKnotSpanBasisFunctions ( const IntArray & knotSpan ) const

overridevirtual

Returns the number of nonzero basis functions at individual knot span,

Returns: Zero in case of all basis functions generaedgeEvaldNdslly nonzero, answer otherwise.

Todo: This loop seems meaningless. It just returns degree[nsd-1]+1 in the end ?

Reimplemented from oofem::BSplineInterpolation.

Definition at line 497 of file feitspline.C.

References oofem::BSplineInterpolation::degree, oofem::BSplineInterpolation::knotValues, oofem::BSplineInterpolation::knotVector, localIndexKnotVector, oofem::BSplineInterpolation::nsd, and totalNumberOfControlPoints.

◆ giveNumberOfKnotSpanBasisFunctions() [2/2]

int oofem::TSplineInterpolation::giveNumberOfKnotSpanBasisFunctions	(	const IntArray &	startKnotSpan,
		const IntArray &	endKnotSpan ) const

protected

Returns the number of nonzero basis functions at given knot span interval.

Definition at line 576 of file feitspline.C.

References oofem::BSplineInterpolation::degree, oofem::BSplineInterpolation::knotValues, oofem::BSplineInterpolation::knotVector, localIndexKnotVector, oofem::BSplineInterpolation::nsd, and totalNumberOfControlPoints.

◆ global2local()

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

inlineoverridevirtual

Evaluates local coordinates from given global ones. If local coordinates cannot be found (generate elements, or point far outside geometry, then the center coordinate will be used as a last resort, and the return value will be zero.

Parameters

answer	Contains evaluated local coordinates.
gcoords	Array containing global coordinates.
cellgeo	Underlying cell geometry.

Returns: Nonzero is returned if point is within the element geometry, zero otherwise.

Reimplemented from oofem::BSplineInterpolation.

Definition at line 82 of file feitspline.h.

References OOFEM_ERROR.

◆ initializeFrom()

void oofem::TSplineInterpolation::initializeFrom	(	InputRecord &	ir,
		ParameterManager &	pm,
		int	elnum,
		int	priority )

overridevirtual

Initializes receiver according to object description stored in input record.

Reimplemented from oofem::BSplineInterpolation.

Definition at line 46 of file feitspline.C.

References _IFT_TSplineInterpolation_localIndexKnotVectorU, _IFT_TSplineInterpolation_localIndexKnotVectorV, _IFT_TSplineInterpolation_localIndexKnotVectorW, _IFT_TSplineInterpolation_weights, oofem::IntArray::clear(), oofem::BSplineInterpolation::degree, oofem::IntArray::giveSize(), IR_GIVE_FIELD, oofem::BSplineInterpolation::knotValues, localIndexKnotVector, oofem::BSplineInterpolation::nsd, totalNumberOfControlPoints, and weights.

Referenced by oofem::IGATSplineElement::initializeFrom().

◆ local2global()

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

overridevirtual

Evaluates global coordinates from given local ones.

Parameters

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

Reimplemented from oofem::BSplineInterpolation.

Definition at line 289 of file feitspline.C.

References basisFunction(), oofem::BSplineInterpolation::degree, oofem::BSplineInterpolation::findSpan(), giveKnotSpanBasisFuncMask(), oofem::BSplineInterpolation::giveKnotValues(), oofem::IntArray::giveSize(), oofem::FEICellGeometry::giveVertexCoordinates(), oofem::FEIIGAElementGeometryWrapper::knotSpan, oofem::BSplineInterpolation::knotVector, localIndexKnotVector, N, oofem::BSplineInterpolation::nsd, oofem::BSplineInterpolation::numberOfControlPoints, OOFEM_ERROR, oofem::product(), oofem::FloatArray::resize(), oofem::FloatArray::times(), weights, and oofem::FloatArray::zero().

◆ setNumberOfControlPoints()

void oofem::TSplineInterpolation::setNumberOfControlPoints ( int num )

inline

Definition at line 78 of file feitspline.h.

Referenced by oofem::IGATSplineElement::initializeFinish().

Member Data Documentation

◆ localIndexKnotVector

std::vector< std::array<IntArray, 3> > oofem::TSplineInterpolation::localIndexKnotVector

protected

Local index knot vector of the dimensions [totalNumberOfControlPoints][nsd][degree+2].

Definition at line 66 of file feitspline.h.

Referenced by evaldNdx(), evalN(), giveJacobianMatrixAt(), giveKnotSpanBasisFuncMask(), giveKnotSpanBasisFuncMask(), giveNumberOfKnotSpanBasisFunctions(), giveNumberOfKnotSpanBasisFunctions(), initializeFrom(), and local2global().

◆ totalNumberOfControlPoints

int oofem::TSplineInterpolation::totalNumberOfControlPoints = 0

protected

Definition at line 67 of file feitspline.h.

Referenced by giveKnotSpanBasisFuncMask(), giveKnotSpanBasisFuncMask(), giveNumberOfKnotSpanBasisFunctions(), giveNumberOfKnotSpanBasisFunctions(), and initializeFrom().

◆ weights

FloatArray oofem::TSplineInterpolation::weights

protected

Definition at line 68 of file feitspline.h.

Referenced by evaldNdx(), evalN(), giveJacobianMatrixAt(), initializeFrom(), and local2global().

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

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ TSplineInterpolation()

Member Function Documentation

◆ basisFunction()

◆ createLocalKnotVector()

◆ dersBasisFunction()

◆ evaldNdx()

◆ evalN()

◆ giveClassName()

◆ giveJacobianMatrixAt()

◆ giveKnotSpanBasisFuncMask() [1/2]

◆ giveKnotSpanBasisFuncMask() [2/2]

◆ giveNumberOfKnotSpanBasisFunctions() [1/2]

◆ giveNumberOfKnotSpanBasisFunctions() [2/2]

◆ global2local()

◆ initializeFrom()

◆ local2global()

◆ setNumberOfControlPoints()

Member Data Documentation

◆ localIndexKnotVector

◆ totalNumberOfControlPoints

◆ weights