Interpolation for T-splines. More...

#include <feitspline.h>

Inheritance diagram for oofem::TSplineInterpolation:

Collaboration diagram for oofem::TSplineInterpolation:

Public Member Functions
	TSplineInterpolation (int nsd)

virtual	~TSplineInterpolation ()

IRResultType	initializeFrom (InputRecord *ir)
	Initializes receiver according to object description stored in input record. More...

void	setNumberOfControlPoints (int num)

virtual void	evalN (FloatArray &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the array of interpolation functions (shape functions) at given point. More...

virtual double	evaldNdx (FloatMatrix &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the matrix of derivatives of interpolation functions (shape functions) at given point. More...

virtual void	local2global (FloatArray &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates global coordinates from given local ones. More...

virtual int	global2local (FloatArray &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates local coordinates from given global ones. More...

virtual void	giveJacobianMatrixAt (FloatMatrix &jacobianMatrix, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Gives the jacobian matrix at the local coordinates. More...

virtual int	giveKnotSpanBasisFuncMask (const IntArray &knotSpan, IntArray &mask)
	Returns indices (zero based) of nonzero basis functions for given knot span. More...

virtual int	giveNumberOfKnotSpanBasisFunctions (const IntArray &knotSpan)
	Returns the number of nonzero basis functions at individual knot span,. More...

const char *	giveClassName () const

Public Member Functions inherited from oofem::BSplineInterpolation
	BSplineInterpolation (int nsd)

virtual	~BSplineInterpolation ()

virtual integrationDomain	giveIntegrationDomain () const
	Returns the integration domain of the interpolator. More...

virtual Element_Geometry_Type	giveGeometryType () const
	Returns the geometry type fo the interpolator. More...

virtual integrationDomain	giveBoundaryIntegrationDomain (int ib) const
	Returns boundary integration domain. More...

virtual integrationDomain	giveBoundarySurfaceIntegrationDomain (int isurf) const
	Returns boundary integration domain. More...

virtual integrationDomain	giveBoundaryEdgeIntegrationDomain (int iedge) const
	Returns boundary integration domain. More...

virtual int	giveNsd ()
	Returns number of spatial dimensions. More...

virtual void	boundaryEdgeGiveNodes (IntArray &answer, int boundary)
	Gives the boundary nodes for requested boundary number. More...

virtual void	boundaryEdgeEvalN (FloatArray &answer, int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the basis functions on the requested boundary. More...

virtual double	boundaryEdgeGiveTransformationJacobian (int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the determinant of the transformation Jacobian on the requested boundary. More...

virtual void	boundaryEdgeLocal2Global (FloatArray &answer, int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Maps the local boundary coordinates to global. More...

virtual void	boundaryGiveNodes (IntArray &answer, int boundary)
	Gives the boundary nodes for requested boundary number. More...

virtual void	boundaryEvalN (FloatArray &answer, int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the basis functions on the requested boundary. More...

virtual double	boundaryEvalNormal (FloatArray &answer, int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the normal on the requested boundary. More...

virtual double	boundaryGiveTransformationJacobian (int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the determinant of the transformation Jacobian on the requested boundary. More...

virtual void	boundaryLocal2Global (FloatArray &answer, int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Maps the local boundary coordinates to global. More...

virtual int	giveNumberOfKnotSpans (int dim)
	Returns the number of knot spans of the receiver. More...

virtual int	giveNumberOfControlPoints (int dim)

virtual const double const	giveKnotVector ()
	Returns the subdivision of patch parametric space. More...

virtual const IntArray *	giveKnotMultiplicity (int dim)
	Returns the knot multiplicity of the receiver. More...

virtual const FloatArray *	giveKnotValues (int dim)
	Returns the knot values of the receiver. More...

virtual bool	hasSubPatchFormulation ()
	Returns true, if receiver is formulated on sub-patch basis. More...

virtual IntegrationRule *	giveIntegrationRule (int order)
	Sets up a suitable integration rule for numerical integrating over volume. More...

virtual IntegrationRule *	giveBoundaryIntegrationRule (int order, int boundary)
	Sets up a suitable integration rule for integrating over the requested boundary. More...

virtual IntegrationRule *	giveBoundaryEdgeIntegrationRule (int order, int boundary)
	Sets up a suitable integration rule for integrating over the requested boundary. More...

virtual void	boundarySurfaceEvalN (FloatArray &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the array of edge interpolation functions (shape functions) at given point. More...

virtual void	boundarySurfaceEvaldNdx (FloatMatrix &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the matrix of derivatives of edge interpolation functions (shape functions) at given point. More...

virtual double	boundarySurfaceEvalNormal (FloatArray &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the normal out of the surface at given point. More...

virtual void	boundarySurfaceLocal2global (FloatArray &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates edge global coordinates from given local ones. More...

virtual double	boundarySurfaceGiveTransformationJacobian (int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the edge jacobian of transformation between local and global coordinates. More...

virtual void	boundarySurfaceGiveNodes (IntArray &answer, int boundary)
	Gives the boundary nodes for requested boundary number. More...

Public Member Functions inherited from oofem::FEInterpolation
	FEInterpolation (int o)

virtual	~FEInterpolation ()

virtual int	giveNumberOfNodes () const
	Returns the number of geometric nodes of the receiver. More...

std::string	errorInfo (const char *func) const

int	giveInterpolationOrder ()
	Returns the interpolation order. More...

virtual void	evald2Ndx2 (FloatMatrix &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the matrix of second derivatives of interpolation functions (shape functions) at given point. More...

virtual void	evaldNdxi (FloatMatrix &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the matrix of derivatives of interpolation functions (shape functions) at given point. More...

virtual void	giveLocalNodeCoords (FloatMatrix &answer)
	Returns a matrix containing the local coordinates for each node corresponding to the interpolation. More...

virtual double	giveTransformationJacobian (const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the determinant of the transformation. More...

virtual IntegrationRule *	giveBoundarySurfaceIntegrationRule (int order, int boundary)
	Sets up a suitable integration rule for integrating over the requested boundary. More...

virtual double	evalNXIntegral (int boundary, const FEICellGeometry &cellgeo)
	Computes the integral $\int_S n \cdot x \mathrm{d}s$ . More...

virtual int	giveNumberOfEdges () const
	Returns number of edges. More...

Protected Member Functions
double	basisFunction (double u, int p, const FloatArray &U, const int *I)
	Evaluates the middle basis function on local knot vector at u. More...

void	dersBasisFunction (int n, double u, int p, const FloatArray &U, const int *I, FloatArray &ders)
	Computes the middle basis function and it derivatives on local knot vector at u. More...

void	createLocalKnotVector (int p, const FloatArray &U, const int I, int prepend, int *append)
	Creates local open knot vector. More...

int	giveKnotSpanBasisFuncMask (const IntArray &startKnotSpan, const IntArray &endKnotSpan, IntArray &mask)
	Returns indices (zero based) of nonzero basis functions for given knot span interval. More...

int	giveNumberOfKnotSpanBasisFunctions (const IntArray &startKnotSpan, const IntArray &endKnotSpan)
	Returns the number of nonzero basis functions at given knot span interval. More...

Protected Member Functions inherited from oofem::BSplineInterpolation
void	basisFuns (FloatArray &N, int span, double u, int p, const double *U)
	Evaluates the nonvanishing basis functions of 1d BSpline (algorithm A2.2 from NURBS book) More...

void	dersBasisFuns (int n, double u, int span, int p, double *const U, FloatMatrix &ders)
	Computes nonzero basis functions and their derivatives at u. More...

int	findSpan (int n, int p, double u, const double *U) const
	Determines the knot span index (Algorithm A2.1 from the NURBS book) More...

void	giveNonzeroBasisFuncInterval (int span, int deg, int &s, int &e)
	Returns the range of nonzero basis functions for given knot span and given degree. More...

Protected Attributes
int ***	localIndexKnotVector
	Local index knot vector of the dimensions [totalNumberOfControlPoints][nsd][degree+2]. More...

int	totalNumberOfControlPoints

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

Protected Attributes inherited from oofem::BSplineInterpolation
int	nsd
	Number of spatial directions. More...

int *	degree
	Degree in each direction. More...

FloatArray *	knotValues
	Knot values [nsd]. More...

IntArray *	knotMultiplicity
	Knot multiplicity [nsd]. More...

int *	numberOfControlPoints
	numberOfControlPoints[nsd] More...

double **	knotVector
	Knot vectors [nsd][knot_vector_size]. More...

int *	numberOfKnotSpans
	Nonzero spans in each directions [nsd]. More...

Protected Attributes inherited from oofem::FEInterpolation
int	order

Detailed Description

Interpolation for T-splines.

Definition at line 61 of file feitspline.h.

Constructor & Destructor Documentation

oofem::TSplineInterpolation::TSplineInterpolation ( int nsd )

inline

Definition at line 72 of file feitspline.h.

oofem::TSplineInterpolation::~TSplineInterpolation ( )

virtual

Definition at line 46 of file feitspline.C.

References localIndexKnotVector, oofem::BSplineInterpolation::nsd, oofem::BSplineInterpolation::numberOfControlPoints, and openLocalKnotVector.

Member Function Documentation

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

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 640 of file feitspline.C.

References oofem::BSplineInterpolation::basisFuns(), createLocalKnotVector(), oofem::BSplineInterpolation::findSpan(), N, and openLocalKnotVector.

Referenced by evalN(), and local2global().

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

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 675 of file feitspline.C.

References oofem::FloatArray::at(), and openLocalKnotVector.

Referenced by basisFunction(), and dersBasisFunction().

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

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 657 of file feitspline.C.

References createLocalKnotVector(), oofem::BSplineInterpolation::dersBasisFuns(), oofem::BSplineInterpolation::findSpan(), openLocalKnotVector, and oofem::FloatArray::resize().

Referenced by evaldNdx(), and giveJacobianMatrixAt().

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

virtual

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 188 of file feitspline.C.

References oofem::FloatArray::at(), 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::FloatMatrix::resize(), and oofem::FloatMatrix::zero().

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

virtual

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 145 of file feitspline.C.

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

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

inlinevirtual

Reimplemented from oofem::BSplineInterpolation.

Definition at line 89 of file feitspline.h.

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

virtual

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 372 of file feitspline.C.

References oofem::FloatArray::at(), 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::FloatMatrix::resize(), and oofem::FloatMatrix::zero().

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

virtual

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 485 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().

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

protected

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

Definition at line 564 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.

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

virtual

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

Returns: Zero in case of all basis functions generally 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 530 of file feitspline.C.

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

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

protected

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

Definition at line 609 of file feitspline.C.

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

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

inlinevirtual

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