Detailed Description

template<short_t d, class T>
class gismo::gsMPBESHSplineBasis< d, T >

A univariate Lagrange basis.

Template Parameters

T	coefficient type

Inheritance diagram for gsMPBESHSplineBasis< d, T >:

Collaboration diagram for gsMPBESHSplineBasis< d, T >:

Public Types
typedef memory::shared_ptr < gsMPBESHSplineBasis >	Ptr
	Shared pointer for gsMPBESHSplineBasis.

typedef memory::unique_ptr < gsMPBESHSplineBasis >	uPtr
	Unique pointer for gsMPBESHSplineBasis.

Public Member Functions
gsMatrix< index_t >	active (const gsMatrix< T > &u) const
	Returns the indices of active (nonzero) functions at points u, as a list of indices. More...

void	active_into (const index_t patch, const gsMatrix< T > &u, gsMatrix< index_t > &result) const
	Returns the indices of active (non-zero) basis functions of patch at points u, as a list of indices, in result. More...

gsHTensorBasis< d, T > &	basis (size_t i)
	Clone function. Used to make a copy of a derived basis.

const gsBasis< T > &	basis (const index_t k) const
	Helper which casts and returns the k-th piece of this function set as a gsBasis.

unsigned	basisFunctionsOnSide (const patchSide &ps) const
	Returns the amount of basis functions on a given side of a given patch.

void	boundary (std::vector< index_t > &indices, index_t offset=0) const

uPtr	clone ()
	Clone methode. Produceds a deep copy inside a uPtr.

virtual void	compute (const gsMatrix< T > &in, gsFuncData< T > &out) const
	Computes function data. More...

short_t	degree (const index_t patch, const short_t i) const
	Returns the polynomial degree of direction i of patch.

void	degreeElevate (index_t amount=1, bool updateBasis=true)

void	degreeIncrease (index_t amount=1, index_t dir=-1, bool updateBasis=true)

gsMatrix< T >	deriv (const gsMatrix< T > &u) const
	Evaluate the derivatives,. More...

gsMatrix< T >	deriv2 (const gsMatrix< T > &u) const
	Evaluates the second derivatives of active (i.e., non-zero) functions at points u. More...

std::string	detail () const
	Clone function. Used to make a copy of a derived basis. More...

short_t	dim () const
	Returns the dimension d of the parameter space.

short_t	domainDim () const
	Clone function. Used to make a copy of a derived basis.

gsMatrix< T >	eval (const gsMatrix< T > &u) const
	Evaluate the function,. More...

std::vector< gsMatrix< T > >	evalAllDers (const gsMatrix< T > &u, int n, bool sameElement=false) const
	Evaluate all derivatives upto order n,. More...

gsGeometry< T > *	exportPatch (const index_t i, gsMatrix< T > const &localCoef) const

gsMultiPatch< T >	exportToPatches (gsMatrix< T > const &localCoef) const

const gsFunction< T > &	function (const index_t k) const
	Helper which casts and returns the k-th piece of this function set as a gsFunction.

BasisType const &	getBase (index_t i) const
	getter for (const) m_bases[i]

BasisType &	getBase (index_t i)
	getter for m_bases[i]

const std::vector< BasisType * >	getBases () const
	getter for m_bases

std::vector< BasisType * >	getBasesCopy () const
	getter for m_bases

index_t	getIncrSmoothnessDegree () const
	getter for m_incrSmoothnessDegree

gsMappedSingleBasis< d, T > &	getMappedSingleBasis (const index_t i) const

gsWeightMapper< T > const &	getMapper () const
	getter for m_mapper

gsWeightMapper< T > *	getMapPointer () const
	getter for m_mapper

T	getParametricDistanceOfVertex (const patchCorner &pc, const patchSide &ps) const
	gives back the parametric c^0 distance of the edge ps starting from corner pc

index_t	getPatch (index_t const localIndex)
	See gsMappedBasis::_getPatchIndex.

gsBoxTopology const &	getTopol () const
	getter for m_topol

T	getWeight (const patchSide &ps) const

void	global_coef_to_local_coef (gsMatrix< T > const &globalCoefs, gsMatrix< T > &localCoefs) const

	gsMPBESHSplineBasis ()
	Default empty constructor.

void	innerBoundaries (std::vector< index_t > &indices, index_t offset=0) const

bool	isSpecialVertex (const patchCorner &pc) const
	gives back true, if the given patchCorner is a special vertex

void	local_coef_to_global_coef (gsMatrix< T > const &localCoefs, gsMatrix< T > &globalCoefs) const

index_t	localSize () const
	Returns the number of local basis functions in the basis.

index_t	localSize (const index_t index) const
	Returns the number of local basis functions of the patch with given index in the basis.

domainIter	makeDomainIterator (const index_t patch, const boxSide &s) const
	gives back the domain iterator of the boundary side s of a given patch

short_t	maxDegree () const
	Returns the maximal polynomial degree of the patches.

size_t	nPatches () const
	returns the amount of patches of the multi patch

void	numActive_into (const index_t patch, const gsMatrix< T > &u, gsVector< index_t > &result) const
	Returns the number of active (nonzero) basis functions at points u in result.

std::ostream &	print (std::ostream &os) const
	Prints the object to the stream.

void	refine (const index_t patch, gsMatrix< T > const &boxes, bool updateBasis=true)

void	refine_withCoefs (gsMatrix< T > &localCoef, const index_t patch, gsMatrix< T > const &boxes, bool updateBasis=true)

void	refineElements (const index_t patch, std::vector< index_t > const &boxes, bool updateBasis=true)

void	refineElements_withCoefs (gsMatrix< T > &localCoef, const index_t patch, std::vector< index_t > const &boxes, bool updateBasis=true)

virtual void	refineWithExtension (const index_t patch, gsMatrix< T > const &boxes, index_t refExt=0, bool updateBasis=true)
	Refine the are defined by boxes on patch k with extension refExt. More...

void	repairPatches (std::vector< gsMatrix< T > * > &coefs, index_t startFromPatch=-1)

void	repairPatches (index_t startFromPatch=-1)

void	setC0 (patchCorner pc)

bool	setWeight (const patchSide &ps, const T weight)

index_t	size (const index_t index) const

void	smoothCornerEdge (const patchCorner &pc, const patchSide &ps, bool updateBasis=true)

void	smoothEverything ()

virtual short_t	targetDim () const
	Dimension of the target space. More...

void	uniformRefine (index_t numKnots=1, index_t mul=1, bool updateBasis=true)

void	uniformRefine_withCoefs (gsMatrix< T > &localCoefs, index_t numKnots=1, index_t mul=1, bool updateBasis=true)

void	updateTopol ()
	updates the mapping of this basis (f.e. after a knot insertion)

Evaluation functions
void	eval_into (const index_t patch, const gsMatrix< T > &u, gsMatrix< T > &result) const
	Evaluates nonzero basis functions of patch at point u into result. More...

void	deriv_into (const index_t patch, const gsMatrix< T > &u, gsMatrix< T > &result) const

void	deriv2_into (const index_t patch, const gsMatrix< T > &u, gsMatrix< T > &result) const

void	evalAllDers_into (const index_t patch, const gsMatrix< T > &u, const index_t n, std::vector< gsMatrix< T > > &result, bool sameElement=false) const
	Evaluate the nonzero basis functions of patch and their derivatives up to order n at points u into result.

gsPiecewiseFunction< T >	basisFunction (index_t global_BF)

void	evalSingle_into (const index_t patch, const index_t global_BF, const gsMatrix< T > &u, gsMatrix< T > &result) const
	Evaluate the global_BF-th basis function on patch at points u into result.

void	derivSingle_into (const index_t patch, const index_t global_BF, const gsMatrix< T > &u, gsMatrix< T > &result) const

void	deriv2Single_into (const index_t patch, const index_t global_BF, const gsMatrix< T > &u, gsMatrix< T > &result) const

gsMatrix< T >	evalSingle (const index_t patch, const index_t global_BF, const gsMatrix< T > &u) const
	Evaluate a single basis function i at points u.

gsMatrix< T >	derivSingle (const index_t patch, const index_t global_BF, const gsMatrix< T > &u) const
	Evaluate a single basis function i derivative at points u.

gsMatrix< T >	deriv2Single (const index_t patch, const index_t global_BF, const gsMatrix< T > &u) const
	Evaluate the second derivative of a single basis function i at points u.

void	evalAllDersSingle_into (const index_t patch, const index_t global_BF, const gsMatrix< T > &u, const index_t n, gsMatrix< T > &result) const
	Evaluate the basis function global_BF at patch and its derivatives up to order n at points u into result.

Static Public Attributes
static const index_t	Dim
	Dimension of the parameter domain.

Protected Member Functions
bool	_check () const
	Checks the gsMappedBasis for consistency.

index_t	_getFirstLocalIndex (index_t const patch) const

index_t	_getLastLocalIndex (index_t const patch) const

index_t	_getLocalIndex (index_t const patch, index_t const patchIndex) const

index_t	_getPatch (index_t const localIndex) const

index_t	_getPatchIndex (const index_t localIndex) const

void	_initVertices ()
	initializes the m_vertices field

void	_setDistanceOfAllVertices ()
	initializes the m_distances field

void	_setMapping ()
	create a new mapping of the local basisfunctions

T	findParameter (patchSide const &ps, patchCorner const &pc, unsigned nrBasisFuncs) const

BasisType *	getBasePointer (index_t i)
	getter for m_bases[i]

Protected Attributes
std::vector< BasisType * >	m_bases
	Vector of local bases.

std::vector< distances >	m_distances
	vector of distances objects, that store C^0 distances from special vertices on the edges

short_t	m_incrSmoothnessDegree
	smoothness degree that is tried to achive over patch interfaces

gsWeightMapper< T > *	m_mapper
	Map between the local basis functions and the newly created ones.

unsigned	m_minDist
	minimal C^0 distance from special (extraordinary) vertices, specified in basisfunctions

std::vector< std::pair < patchSide, T > >	m_patchSideWeights
	vector storing the weights for interfaces

std::vector < gsMappedSingleBasis< d, T > >	m_sb
	Underlying bases per patch.

gsBoxTopology	m_topol
	Topology, specifying the relation (connections) between the patches.

std::vector< std::pair < patchCorner, bool > >	m_vertices
	vector storing all the inner vertices, with a flag if it is an Extraordinary vertex or an ordinary vertex.

Private Member Functions
bool	_checkTopologyWithBases () const
	Checks the gsMappedBasis for consistency.

Member Function Documentation

index_t _getFirstLocalIndex ( index_t const patch ) const

protectedinherited

gets the local index of the first basis function of the patch with the given number.

Parameters

[in] patch : the number of the patch

index_t _getLastLocalIndex ( index_t const patch ) const

inlineprotectedinherited

gets the local index of the last basis function of the patch with the given number.

Parameters

[in] patch : the number of the patch

index_t _getLocalIndex	(	index_t const	patch,
		index_t const	patchIndex
	)		const

inlineprotectedinherited

gets the local index of the basis function of the patch with the given number.

Parameters

[in]	patch	: the number of the patch
[in]	patchIndex	: the index of the basis function on the patch

index_t _getPatch ( index_t const localIndex ) const

protectedinherited

gets the number of the patch, where the local basis function with the given index is on.

Parameters

[in] localIndex : the accumulated index of the basis function

index_t _getPatchIndex ( const index_t localIndex ) const

protectedinherited

gets the patchIndex of the basis function specified by its localIndex. This is the index of this basis function in the basis of this patch.

Parameters

[in] localIndex : the accumulated index of the basis function

gsMatrix<index_t> active ( const gsMatrix< T > & u ) const

inlineinherited

Returns the indices of active (nonzero) functions at points u, as a list of indices.

See Also: active_into()

void active_into	(	const index_t	patch,
		const gsMatrix< T > &	u,
		gsMatrix< index_t > &	result
	)		const

inherited

Returns the indices of active (non-zero) basis functions of patch at points u, as a list of indices, in result.

Parameters

[in]	u	gsMatrix containing evaluation points. Each column represents one evaluation point.
[out]	result	For every column i of u, a column containing the indices of the active basis functions at evaluation point u.col(i).

void boundary	(	std::vector< index_t > &	indices,
		index_t	offset = `0`
	)		const

inherited

gets all indices of global basis functions on the boundary upto a given offset

void compute	(	const gsMatrix< T > &	in,
		gsFuncData< T > &	out
	)		const

virtualinherited

Computes function data.

This function evaluates the functions and their derivatives at the points in and writes them in the corresponding fields of out. Which field to write (and what to compute) is controlled by the out.flags (see also gsFuncData).

The input points in are expected to be compatible with the implementation/representation of the function, i.e. they should be points inside the domain of definitition of the function

Parameters

[in]	in
[out]	out

Reimplemented in gsGeometry< T >, and gsConstantFunction< T >.

void degreeElevate	(	index_t	amount = `1`,
		bool	updateBasis = `true`
	)

inherited

degree elevates all the bases preserving smoothness

Parameters

[in]	amount	: the amount of elevation the bases will go through
[in]	updateBasis	: if true, a new mapping will be constructed for the new basis functions, only set to false if one wants to apply more changes to the bases before calculating a new mapping

void degreeIncrease	(	index_t	amount = `1`,
		index_t	dir = `-1`,
		bool	updateBasis = `true`
	)

inherited

degree elevates all the bases preserving multiplicity

Parameters

[in]	amount	: the amount of elevation the bases will go through
[in]	updateBasis	: if true, a new mapping will be constructed for the new basis functions, only set to false if one wants to apply more changes to the bases before calculating a new mapping

gsMatrix< T > deriv ( const gsMatrix< T > & u ) const

inherited

Evaluate the derivatives,.

See Also: deriv_into()

gsMatrix< T > deriv2 ( const gsMatrix< T > & u ) const

inherited

Evaluates the second derivatives of active (i.e., non-zero) functions at points u.

See documentation for deriv2_into() (the one without input parameter coefs) for details.

See Also: deriv2_into()

Parameters

[in] u Evaluation points in columns.

Returns: For every column of u, a column containing the second derivatives. See documentation for deriv2_into() (the one without input parameter coefs) for details.

std::string detail ( ) const

inlineinherited

Clone function. Used to make a copy of a derived basis.

Prints the object as a string with extended details.

gsMatrix< T > eval ( const gsMatrix< T > & u ) const

inherited

Evaluate the function,.

See Also: eval_into()

void eval_into	(	const index_t	patch,
		const gsMatrix< T > &	u,
		gsMatrix< T > &	result
	)		const

inherited

Evaluates nonzero basis functions of patch at point u into result.

Let...
d denote the dimension of the parameter domain.
k denote the number of active (i.e., non-zero) basis functions (see active_into()). n denote the number of evaluation points.
The n evaluation points u are given in a gsMatrix of size d x n. Each column of u represents one evaluation point.

The gsMatrix result contains the computed function values in the following form:
Column j of result corresponds to one evaluation point (specified by the j-th column of u). The column contains the values of all active functions "above" each other.
For example, for scalar basis functions Bi : (x,y,z)-> R, a colum represents
(B1, B2, ... , Bn)^T,
where the order the basis functions Bi is as returned by active() and active_into().

Parameters

[in]	u	Evaluation points given as gsMatrix of size d x n. See above for details.
[in,out]	result	gsMatrix of size k x n. See above for details.

std::vector< gsMatrix< T > > evalAllDers	(	const gsMatrix< T > &	u,
		int	n,
		bool	sameElement = `false`
	)		const

inherited

Evaluate all derivatives upto order n,.

See Also: evalAllDers_into

gsGeometry< T > * exportPatch	(	const index_t	i,
		gsMatrix< T > const &	localCoef
	)		const

inherited

exports the patch i of this geometry (with coefs) to a Geometry object of the underlying basis. The ownership of this Geometry will go to the caller of this function.

Parameters

[in] localCoef : the coefficients to the local basis functions

gsMultiPatch< T > exportToPatches ( gsMatrix< T > const & localCoef ) const

inherited

exports this geometry (with coefs) to a gsMultiPatch object.

Parameters

[in] localCoef : the coefficients to the local basis functions

T findParameter	(	patchSide const &	ps,
		patchCorner const &	pc,
		unsigned	nrBasisFuncs
	)		const

protectedvirtual

finds the parametric c^0 distance of the edge ps starting from corner pc if the number of c^0 basis functions is given in nrBasisFuncs

Implements gsMPBESBasis< d, T >.

gsMappedSingleBasis<d,T>& getMappedSingleBasis ( const index_t i ) const

inlineinherited

gives back the gsMappedSingleBasis object set to the patch i, which ressembles the composite basis on one patch

T getWeight ( const patchSide & ps ) const

inherited

gets the weight at the given patchSide.

Parameters

[in] ps : patchSide

void global_coef_to_local_coef	(	gsMatrix< T > const &	globalCoefs,
		gsMatrix< T > &	localCoefs
	)		const

inlineinherited

converts the global coefficients to the local ones

Parameters

[in]	globalCoefs	: the coefficients to the global basis functions
[out]	localCoefs	: the coefficients to the local basis functions

void innerBoundaries	(	std::vector< index_t > &	indices,
		index_t	offset = `0`
	)		const

inherited

gets all indices of global basis functions on the inner boundary upto a given offset

void local_coef_to_global_coef	(	gsMatrix< T > const &	localCoefs,
		gsMatrix< T > &	globalCoefs
	)		const

inlineinherited

converts the local coefficients to the global ones

Parameters

[in]	localCoefs	: the coefficients to the local basis functions
[out]	globalCoefs	: the coefficients to the global basis functions

void refine	(	const index_t	patch,
		gsMatrix< T > const &	boxes,
		bool	updateBasis = `true`
	)

virtual

inserts the given boxes in the specified patch. The concrete implementation is left to the implementing classes of this abstract parent class.

Parameters

[in]	patch	: the patch number we look at
[in]	boxes	: the boxes to be inserted
[in]	updateBasis	: if true, a new mapping will be constructed for the new basis functions, only set to false if one wants to insert more boxes

Implements gsMPBESBasis< d, T >.

void refine_withCoefs	(	gsMatrix< T > &	localCoefs,
		const index_t	patch,
		gsMatrix< T > const &	boxes,
		bool	updateBasis = `true`
	)

virtual

inserts the given boxes in the specified patch, while also updating the given coefficients. The concrete implementation is left to the implementing classes of this abstract parent class.

Parameters

[in,out]	localCoefs	: the coefficients to the local basis functions
[in]	patch	: the patch number we look at
[in]	boxes	: the boxes to be inserted
[in]	updateBasis	: if true, a new mapping will be constructed for the new basis functions, only set to false if one wants to insert more boxes

Implements gsMPBESBasis< d, T >.

void refineElements	(	const index_t	patch,
		std::vector< index_t > const &	boxes,
		bool	updateBasis = `true`
	)

virtual

inserts the given boxes in the specified patch. The concrete implementation is left to the implementing classes of this abstract parent class.

Parameters

[in]	patch	: the patch number we look at
[in]	boxes	: the boxes to be inserted
[in]	updateBasis	: if true, a new mapping will be constructed for the new basis functions, only set to false if one wants to insert more boxes

Implements gsMPBESBasis< d, T >.

void refineElements_withCoefs	(	gsMatrix< T > &	localCoefs,
		const index_t	patch,
		std::vector< index_t > const &	boxes,
		bool	updateBasis = `true`
	)

virtual

inserts the given boxes in the specified patch, while also updating the given coefficients. The concrete implementation is left to the implementing classes of this abstract parent class.

Parameters

[in,out]	localCoefs	: the coefficients to the local basis functions
[in]	patch	: the patch number we look at
[in]	boxes	: the boxes to be inserted
[in]	updateBasis	: if true, a new mapping will be constructed for the new basis functions, only set to false if one wants to insert more boxes

Implements gsMPBESBasis< d, T >.

void refineWithExtension	(	const index_t	patch,
		gsMatrix< T > const &	boxes,
		index_t	refExt = `0`,
		bool	updateBasis = `true`
	)

virtual

Refine the are defined by boxes on patch k with extension refExt.

See gsHTensorBasis::refine() for further documentation.

void repairPatches	(	std::vector< gsMatrix< T > * > &	coefs,
		index_t	startFromPatch = `-1`
	)

virtual

Adjusts the patches to match each other at the interfaces by knot insertion (will be called automatically by refinement functions)

Implements gsMPBESBasis< d, T >.

void repairPatches ( index_t startFromPatch = -1 )

inherited

Adjusts the patches to match each other at the interfaces by knot insertion (will be called automatically by refinement functions)

void setC0 ( patchCorner pc )

inherited

sets a patchCorner to be a special vertex, which means edges connected to this corner will have a c^0 continuity

bool setWeight	(	const patchSide &	ps,
		const T	weight
	)

inherited

sets the weight at the given patchSide to value weight

Parameters

[in]	ps	: patchSide
[in]	weight	: T

index_t size ( const index_t index ) const

inherited

Returns the approximate number of (global) basis functions in the patch with given index all the sizes summed up should give the total number of (global) basis functions the default argument -1 will give the total number of basis functions for all patches

void smoothCornerEdge	(	const patchCorner &	pc,
		const patchSide &	ps,
		bool	updateBasis = `true`
	)

inherited

smooths a given edge connected to the corner back to the the minimal amount of C^0 continuity, specified by m_minDist.

Parameters

[in]	pc	: patchCorner, specifying the corner which should be smoothed
[in]	ps	: patchSide, specifying the edge, connected to the corner, which should be smoothed along
[in]	updateBasis	: if true, a new mapping will be constructed for the new basis functions, only set to false if one wants to insert more boxes

void smoothEverything ( )

inherited

smooths all edges back to the the minimal amount of C^0 continuity, specified by m_minDist.

virtual short_t targetDim ( ) const

inlinevirtualinherited

Dimension of the target space.

Returns: For \(f:\mathbb{R}^n\rightarrow\mathbb{R}^m\), returns \(m\).

Reimplemented in gsPatchIdField< T >, gsGeometry< T >, gsParamField< T >, gsNormalField< T >, gsMultiBasis< T >, gsMultiBasis< real_t >, gsMultiPatch< T >, gsMultiPatch< real_t >, gsFsiLoad< T >, gsMaterialMatrixEvalSingle< T, out >, gsMaterialMatrixIntegrateSingle< T, out >, gsFunctionExpr< T >, gsJacDetField< T >, gsDetFunction< T >, gsConstantFunction< T >, gsShellStressFunction< T >, gsGradientField< T >, gsPiecewiseFunction< T >, gsSquaredDistance< T >, gsAffineFunction< T >, gsPreCICEFunction< T >, gsMappedSingleSpline< d, T >, gsBasisFun< T >, gsAbsError< T >, gsGeometrySlice< T >, gsGeometryTransform< T >, gsFuncCoordinate< T >, and gsCauchyStressFunction< T >.

void uniformRefine	(	index_t	numKnots = `1`,
		index_t	mul = `1`,
		bool	updateBasis = `true`
	)

inherited

makes a uniform refinement of all the bases, with a defined number of new knots inserted in every knot span.

Parameters

[in]	numKnots	: the amount of knots which are inserted in every knot span
[in]	updateBasis	: if true, a new mapping will be constructed for the new basis functions, only set to false if one wants to insert more boxes

void uniformRefine_withCoefs	(	gsMatrix< T > &	localCoefs,
		index_t	numKnots = `1`,
		index_t	mul = `1`,
		bool	updateBasis = `true`
	)

inherited

makes a uniform refinement of all the bases, with a defined number of new knots inserted in every knot span.

Parameters

[in,out]	localCoefs	: the coefficients to the local basis functions
[in]	numKnots	: the amount of knots which are inserted in every knot span
[in]	updateBasis	: if true, a new mapping will be constructed for the new basis functions, only set to false if one wants to insert more boxes

Detailed Description

template<short_t d, class T> class gismo::gsMPBESHSplineBasis< d, T >

Public Types

Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Private Member Functions

Member Function Documentation

template<short_t d, class T>
class gismo::gsMPBESHSplineBasis< d, T >