Interpolation for B-splines. More...

#include <feibspline.h>

Inheritance diagram for oofem::BSplineInterpolation:

Collaboration diagram for oofem::BSplineInterpolation:

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

virtual const char *	giveClassName () const

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...

Surface interpolation services
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
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	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 B-splines.

Definition at line 60 of file feibspline.h.

Constructor & Destructor Documentation

oofem::BSplineInterpolation::BSplineInterpolation ( int nsd )

inline

Definition at line 82 of file feibspline.h.

oofem::BSplineInterpolation::~BSplineInterpolation ( )

virtual

Definition at line 42 of file feibspline.C.

References degree, knotMultiplicity, knotValues, knotVector, nsd, numberOfControlPoints, and numberOfKnotSpans.

Member Function Documentation

void oofem::BSplineInterpolation::basisFuns	(	FloatArray &	N,
		int	span,
		double	u,
		int	p,
		const double *	U
	)

protected

Evaluates the nonvanishing basis functions of 1d BSpline (algorithm A2.2 from NURBS book)

Parameters

span	Knot span index (zero based).
u	Value at which to evaluate.
p	Degree.
U	Knot vector.
N	Computed p+1 nonvanishing functions (N_{span-p,p}-N_{span,p})

Warning: Parameter u and span must be in a valid range.

Definition at line 660 of file feibspline.C.

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

Referenced by oofem::TSplineInterpolation::basisFunction(), oofem::NURBSInterpolation::evalN(), evalN(), oofem::NURBSInterpolation::local2global(), and local2global().

virtual void oofem::BSplineInterpolation::boundaryEdgeEvalN	(	FloatArray &	answer,
		int	boundary,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo
	)

inlinevirtual

Evaluates the basis functions on the requested boundary.

Only basis functions that are nonzero anywhere on the boundary are given. Ordering can be obtained from giveBoundaryNodes. Boundaries are defined as the corner nodes for 1D geometries, edges for 2D geometries and surfaces for 3D geometries.

Parameters

answer	Basis functions Array to be filled with the boundary nodes.
boundary	Boundary number.
lcoords	The local coordinates (on the boundary local coordinate system).
cellgeo	Underlying cell geometry.

Todo:

Implements oofem::FEInterpolation.

Definition at line 135 of file feibspline.h.

References OOFEM_ERROR.

virtual void oofem::BSplineInterpolation::boundaryEdgeGiveNodes	(	IntArray &	answer,
		int	boundary
	)

inlinevirtual

Gives the boundary nodes for requested boundary number.

Parameters

answer	Array to be filled with the boundary nodes.
boundary	Boundary number.

Implements oofem::FEInterpolation.

Definition at line 133 of file feibspline.h.

References OOFEM_ERROR.

virtual double oofem::BSplineInterpolation::boundaryEdgeGiveTransformationJacobian	(	int	boundary,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo
	)

inlinevirtual

Evaluates the determinant of the transformation Jacobian on the requested boundary.

Boundaries are defined as the corner nodes for 1D geometries, edges for 2D geometries and surfaces for 3D geometries.

Parameters

boundary	Boundary number.
lcoords	The local coordinates (on the boundary local coordinate system).
cellgeo	Underlying cell geometry.

Returns: The determinant of the boundary transformation Jacobian.

Implements oofem::FEInterpolation.

Definition at line 137 of file feibspline.h.

References OOFEM_ERROR.

virtual void oofem::BSplineInterpolation::boundaryEdgeLocal2Global	(	FloatArray &	answer,
		int	boundary,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo
	)

inlinevirtual

Maps the local boundary coordinates to global.

Boundaries are defined as the corner nodes for 1D geometries, edges for 2D geometries and surfaces for 3D geometries.

Parameters

answer	Global coordinates.
boundary	Boundary number.
lcoords	The local coordinates (on the boundary local coordinate system).
cellgeo	Underlying cell geometry.

Implements oofem::FEInterpolation.

Definition at line 140 of file feibspline.h.

References OOFEM_ERROR.

virtual void oofem::BSplineInterpolation::boundaryEvalN	(	FloatArray &	answer,
		int	boundary,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo
	)

inlinevirtual

Evaluates the basis functions on the requested boundary.

Only basis functions that are nonzero anywhere on the boundary are given. Ordering can be obtained from giveBoundaryNodes. Boundaries are defined as the corner nodes for 1D geometries, edges for 2D geometries and surfaces for 3D geometries.

Parameters

answer	Basis functions Array to be filled with the boundary nodes.
boundary	Boundary number.
lcoords	The local coordinates (on the boundary local coordinate system).
cellgeo	Underlying cell geometry.

Implements oofem::FEInterpolation.

Definition at line 169 of file feibspline.h.

References OOFEM_ERROR.

virtual double oofem::BSplineInterpolation::boundaryEvalNormal	(	FloatArray &	answer,
		int	boundary,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo
	)

inlinevirtual

Evaluates the normal on the requested boundary.

Parameters

answer	The evaluated normal.
boundary	Boundary number.
lcoords	The local coordinates (on the boundary local coordinate system).
cellgeo	Underlying cell geometry.

Returns: The boundary transformation Jacobian.

Implements oofem::FEInterpolation.

Definition at line 171 of file feibspline.h.

References OOFEM_ERROR.

virtual void oofem::BSplineInterpolation::boundaryGiveNodes	(	IntArray &	answer,
		int	boundary
	)

inlinevirtual

Gives the boundary nodes for requested boundary number.

Boundaries are defined as the corner nodes for 1D geometries, edges for 2D geometries and surfaces for 3D geometries.

Parameters

answer	Array to be filled with the boundary nodes.
boundary	Boundary number.

Implements oofem::FEInterpolation.

Definition at line 167 of file feibspline.h.

References OOFEM_ERROR.

virtual double oofem::BSplineInterpolation::boundaryGiveTransformationJacobian	(	int	boundary,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo
	)

inlinevirtual

Evaluates the determinant of the transformation Jacobian on the requested boundary.

Boundaries are defined as the corner nodes for 1D geometries, edges for 2D geometries and surfaces for 3D geometries.

Parameters

boundary	Boundary number.
lcoords	The local coordinates (on the boundary local coordinate system).
cellgeo	Underlying cell geometry.

Returns: The determinant of the boundary transformation Jacobian.

Implements oofem::FEInterpolation.

Definition at line 174 of file feibspline.h.

References OOFEM_ERROR.

virtual void oofem::BSplineInterpolation::boundaryLocal2Global	(	FloatArray &	answer,
		int	boundary,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo
	)

inlinevirtual

Maps the local boundary coordinates to global.

Boundaries are defined as the corner nodes for 1D geometries, edges for 2D geometries and surfaces for 3D geometries.

Parameters

answer	Global coordinates.
boundary	Boundary number.
lcoords	The local coordinates (on the boundary local coordinate system).
cellgeo	Underlying cell geometry.

Implements oofem::FEInterpolation.

Definition at line 177 of file feibspline.h.

References OOFEM_ERROR.

virtual void oofem::BSplineInterpolation::boundarySurfaceEvaldNdx	(	FloatMatrix &	answer,
		int	isurf,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo
	)

inlinevirtual

Evaluates the matrix of derivatives of edge 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 dNj/dxi.
isurf	Determines the surface number.
lcoords	Array containing (local) coordinates.
cellgeo	Underlying cell geometry.

Implements oofem::FEInterpolation.

Definition at line 147 of file feibspline.h.

References OOFEM_ERROR.

virtual void oofem::BSplineInterpolation::boundarySurfaceEvalN	(	FloatArray &	answer,
		int	isurf,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo
	)

inlinevirtual

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

Parameters

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

Implements oofem::FEInterpolation.

Definition at line 146 of file feibspline.h.

References OOFEM_ERROR.

virtual double oofem::BSplineInterpolation::boundarySurfaceEvalNormal	(	FloatArray &	answer,
		int	isurf,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo
	)

inlinevirtual

Evaluates the normal out of the surface at given point.

Parameters

answer	Contains resulting normal vector.
isurf	Determines the surface number.
lcoords	Array containing (local) coordinates.
cellgeo	Underlying cell geometry.

Returns: Surface mapping jacobian.

Implements oofem::FEInterpolation.

Definition at line 150 of file feibspline.h.

References OOFEM_ERROR.

virtual void oofem::BSplineInterpolation::boundarySurfaceGiveNodes	(	IntArray &	answer,
		int	boundary
	)

inlinevirtual

Gives the boundary nodes for requested boundary number.

Parameters

answer	Array to be filled with the boundary nodes.
boundary	Boundary number.

Implements oofem::FEInterpolation.

Definition at line 159 of file feibspline.h.

References OOFEM_ERROR.

virtual double oofem::BSplineInterpolation::boundarySurfaceGiveTransformationJacobian	(	int	isurf,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo
	)

inlinevirtual

Evaluates the edge jacobian of transformation between local and global coordinates.

Parameters

isurf	Determines the surface number.
lcoords	Array containing (local) coordinates.
cellgeo	Underlying cell geometry.

Returns: Determinant of the transformation.

Implements oofem::FEInterpolation.

Definition at line 156 of file feibspline.h.

References OOFEM_ERROR.

virtual void oofem::BSplineInterpolation::boundarySurfaceLocal2global	(	FloatArray &	answer,
		int	isurf,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo
	)

inlinevirtual

Evaluates edge global coordinates from given local ones.

These derivatives are in global coordinate system (where the nodal coordinates are defined).

Parameters

answer	Contains resulting global coordinates.
isurf	Determines the surface number.
lcoords	Array containing (local) coordinates.
cellgeo	Underlying cell geometry.

Implements oofem::FEInterpolation.

Definition at line 153 of file feibspline.h.

References OOFEM_ERROR.

void oofem::BSplineInterpolation::dersBasisFuns	(	int	n,
		double	u,
		int	span,
		int	p,
		double *const	U,
		FloatMatrix &	ders
	)

protected

Computes nonzero basis functions and their derivatives at u.

For information on the algorithm, see A2.3 on p72 of the NURBS book. The result is stored in the ders matrix, where ders is of size (n+1,p+1) and the derivative

$\begin{align*} N(u) &= \mathit{ders}(0,span-p+j) \quad\text{where } j=0...p \ \ N'(u) &= \mathit{ders}(1,span-p+j) \quad\text{where } j=0...p \ \ N''(u) &= \mathit{ders}(2,span-p+j) \quad\text{where } j=0...p \end{align*}$

Parameters

n	Degree of the derivation.
u	Parametric value.
span	Knot span index (zero based).
p	Degree.
U	Knot vector.
ders	Matrix containing the derivatives of the basis functions.

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

Definition at line 692 of file feibspline.C.

References oofem::FloatMatrix::resize().

Referenced by oofem::TSplineInterpolation::dersBasisFunction(), oofem::NURBSInterpolation::evaldNdx(), evaldNdx(), oofem::NURBSInterpolation::giveJacobianMatrixAt(), and giveJacobianMatrixAt().

double oofem::BSplineInterpolation::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.

Implements oofem::FEInterpolation.

Reimplemented in oofem::TSplineInterpolation, and oofem::NURBSInterpolation.

Definition at line 228 of file feibspline.C.

References oofem::FloatArray::at(), degree, dersBasisFuns(), findSpan(), oofem::FloatMatrix::giveDeterminant(), giveNumberOfKnotSpanBasisFunctions(), oofem::FEICellGeometry::giveVertexCoordinates(), oofem::FEIIGAElementGeometryWrapper::knotSpan, knotVector, nsd, numberOfControlPoints, OOFEM_ERROR, oofem::FloatMatrix::resize(), oofem::FloatArray::zero(), and oofem::FloatMatrix::zero().

void oofem::BSplineInterpolation::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.

Implements oofem::FEInterpolation.

Reimplemented in oofem::TSplineInterpolation, and oofem::NURBSInterpolation.

Definition at line 181 of file feibspline.C.

References oofem::FloatArray::at(), basisFuns(), degree, findSpan(), giveNumberOfKnotSpanBasisFunctions(), oofem::FEIIGAElementGeometryWrapper::knotSpan, knotVector, N, nsd, numberOfControlPoints, OOFEM_ERROR, and oofem::FloatArray::resize().

int oofem::BSplineInterpolation::findSpan	(	int	n,
		int	p,
		double	u,
		const double *	U
	)		const

protected

Determines the knot span index (Algorithm A2.1 from the NURBS book)

Determines the knot span for which there exists non-zero basis functions. The span is the index k for which the parameter u is valid in the (u_k,u_{k+1}] range.

Parameters

n	Number of control points - 1.
u	Parametric value.
p	Degree.
U	Knot vector.

Returns: Span index at u (zero based).

Warning: Parameter u must be in a valid range.

Definition at line 792 of file feibspline.C.

Referenced by oofem::TSplineInterpolation::basisFunction(), oofem::TSplineInterpolation::dersBasisFunction(), oofem::NURBSInterpolation::evaldNdx(), oofem::TSplineInterpolation::evaldNdx(), evaldNdx(), oofem::NURBSInterpolation::evalN(), oofem::TSplineInterpolation::evalN(), evalN(), oofem::NURBSInterpolation::giveJacobianMatrixAt(), oofem::TSplineInterpolation::giveJacobianMatrixAt(), giveJacobianMatrixAt(), oofem::NURBSInterpolation::local2global(), oofem::TSplineInterpolation::local2global(), and local2global().

virtual integrationDomain oofem::BSplineInterpolation::giveBoundaryEdgeIntegrationDomain ( int boundary ) const

inlinevirtual

Returns boundary integration domain.

Implements oofem::FEInterpolation.

Definition at line 120 of file feibspline.h.

References oofem::_Line, and oofem::_UnknownIntegrationDomain.

virtual IntegrationRule* oofem::BSplineInterpolation::giveBoundaryEdgeIntegrationRule	(	int	order,
		int	boundary
	)

inlinevirtual

Sets up a suitable integration rule for integrating over the requested boundary.

The required polynomial order for the determinant of the jacobian is added automatically.

Parameters

order	Polynomial order of the integrand (should NOT including determinant of jacobian).
boundary	Boundary number.

Reimplemented from oofem::FEInterpolation.

Definition at line 208 of file feibspline.h.

References N, and OOFEM_ERROR.

virtual integrationDomain oofem::BSplineInterpolation::giveBoundaryIntegrationDomain ( int boundary ) const

inlinevirtual

Returns boundary integration domain.

Implements oofem::FEInterpolation.

Definition at line 100 of file feibspline.h.

References oofem::_Line, oofem::_Point, oofem::_Square, and oofem::_UnknownIntegrationDomain.

virtual IntegrationRule* oofem::BSplineInterpolation::giveBoundaryIntegrationRule	(	int	order,
		int	boundary
	)

inlinevirtual

Sets up a suitable integration rule for integrating over the requested boundary.

The required polynomial order for the determinant of the jacobian is added automatically.

Parameters

order	Polynomial order of the integrand (should NOT including determinant of jacobian).
boundary	Boundary number.

Reimplemented from oofem::FEInterpolation.

Definition at line 205 of file feibspline.h.

References OOFEM_ERROR.

virtual integrationDomain oofem::BSplineInterpolation::giveBoundarySurfaceIntegrationDomain ( int boundary ) const

inlinevirtual

Returns boundary integration domain.

Implements oofem::FEInterpolation.

Definition at line 111 of file feibspline.h.

References oofem::_Square, and oofem::_UnknownIntegrationDomain.

virtual const char* oofem::BSplineInterpolation::giveClassName ( ) const

inlinevirtual

Reimplemented in oofem::TSplineInterpolation, and oofem::NURBSInterpolation.

Definition at line 199 of file feibspline.h.

virtual Element_Geometry_Type oofem::BSplineInterpolation::giveGeometryType ( ) const

inlinevirtual

Returns the geometry type fo the interpolator.

Implements oofem::FEInterpolation.

Definition at line 98 of file feibspline.h.

virtual integrationDomain oofem::BSplineInterpolation::giveIntegrationDomain ( ) const

inlinevirtual

Returns the integration domain of the interpolator.

Implements oofem::FEInterpolation.

Definition at line 87 of file feibspline.h.

References oofem::_Cube, oofem::_Line, oofem::_Square, and oofem::_UnknownIntegrationDomain.

virtual IntegrationRule* oofem::BSplineInterpolation::giveIntegrationRule ( int order )

inlinevirtual

Sets up a suitable integration rule for numerical integrating over volume.

The required polynomial order for the determinant of the jacobian is added automatically.

Parameters

order Polynomial order of integrand (should NOT including determinant of jacobian).

Reimplemented from oofem::FEInterpolation.

Definition at line 202 of file feibspline.h.

References OOFEM_ERROR.

void oofem::BSplineInterpolation::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::FEInterpolation.

Reimplemented in oofem::TSplineInterpolation, and oofem::NURBSInterpolation.

Definition at line 495 of file feibspline.C.

References oofem::FloatArray::add(), oofem::FloatArray::at(), degree, dersBasisFuns(), findSpan(), oofem::FEICellGeometry::giveVertexCoordinates(), oofem::FEIIGAElementGeometryWrapper::knotSpan, knotVector, nsd, numberOfControlPoints, OOFEM_ERROR, oofem::FloatMatrix::resize(), oofem::FloatArray::zero(), and oofem::FloatMatrix::zero().

virtual const IntArray* oofem::BSplineInterpolation::giveKnotMultiplicity ( int dim )

inlinevirtual

Returns the knot multiplicity of the receiver.

Reimplemented from oofem::FEInterpolation.

Definition at line 186 of file feibspline.h.

int oofem::BSplineInterpolation::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::FEInterpolation.

Reimplemented in oofem::TSplineInterpolation.

Definition at line 602 of file feibspline.C.

References oofem::IntArray::at(), degree, giveNumberOfKnotSpanBasisFunctions(), nsd, numberOfControlPoints, OOFEM_ERROR, and oofem::IntArray::resize().

virtual const FloatArray* oofem::BSplineInterpolation::giveKnotValues ( int dim )

inlinevirtual

Returns the knot values of the receiver.

Reimplemented from oofem::FEInterpolation.

Definition at line 187 of file feibspline.h.

Referenced by oofem::TSplineInterpolation::evaldNdx(), oofem::TSplineInterpolation::evalN(), oofem::TSplineInterpolation::giveJacobianMatrixAt(), and oofem::TSplineInterpolation::local2global().

virtual const double* const* oofem::BSplineInterpolation::giveKnotVector ( )

inlinevirtual

Returns the subdivision of patch parametric space.

Reimplemented from oofem::FEInterpolation.

Definition at line 183 of file feibspline.h.

void oofem::BSplineInterpolation::giveNonzeroBasisFuncInterval	(	int	span,
		int	deg,
		int &	s,
		int &	e
	)

inlineprotected

Returns the range of nonzero basis functions for given knot span and given degree.

Definition at line 263 of file feibspline.h.

virtual int oofem::BSplineInterpolation::giveNsd ( )

inlinevirtual

Returns number of spatial dimensions.

Implements oofem::FEInterpolation.

Definition at line 130 of file feibspline.h.

virtual int oofem::BSplineInterpolation::giveNumberOfControlPoints ( int dim )

inlinevirtual

Definition at line 182 of file feibspline.h.

Referenced by oofem::BsplinePlaneStressElement::checkConsistency(), oofem::NURBSPlaneStressElement::checkConsistency(), and oofem::NURBSSpace3dElement::checkConsistency().

int oofem::BSplineInterpolation::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::FEInterpolation.

Reimplemented in oofem::TSplineInterpolation.

Definition at line 641 of file feibspline.C.

References degree, and nsd.

Referenced by oofem::NURBSInterpolation::evaldNdx(), evaldNdx(), oofem::NURBSInterpolation::evalN(), evalN(), and giveKnotSpanBasisFuncMask().

virtual int oofem::BSplineInterpolation::giveNumberOfKnotSpans ( int dim )

inlinevirtual

Returns the number of knot spans of the receiver.

Reimplemented from oofem::FEInterpolation.

Definition at line 181 of file feibspline.h.

virtual int oofem::BSplineInterpolation::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