gsMPBESBasis< d, T > Class Template Reference

Detailed Description

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

Purely abstract class gsMappedBasis, which gives means of combining basis functions to new, global ones.

This is done by having a set of basis functions (as a collection of basis patches) plus a topology, which specifies the relation of these patches. A mapping is then created, which combines basis functions with certain weights, to achieve a (predefined) increased smoothness degree over the interfaces.

The function getMappedSingleBasis() then provides a class implementing gsBasis, which can be used also as a basis for a geometry.

To split the gsMappedBasis into Patches again, the function exportToPatches() can be used.

The notion of a localIndex is used for the accumulated indizes of the basis functions of the patches, whereas the globalIndex is used for the new, combined 'global' basis functions. PatchIndex is the index of a local basis function in its patch, so: localIndex = patchIndex + _firstLocalIndex(patch).

Template Parameters

d	dimension of the parameter domains
T	coefficient type

Inheritance diagram for gsMPBESBasis< d, T >:

Classes
struct	distances
	Private stract that has the purpose of storing distance information of c^0 parts around special vertices. More...

Public Types
typedef memory::shared_ptr < gsMPBESBasis >	Ptr
	Shared pointer for gsMPBESBasis.
typedef memory::unique_ptr < gsMPBESBasis >	uPtr
	Unique pointer for gsMPBESBasis.

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...
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.
virtual unsigned	basisFunctionsOnSide (const patchSide &ps) const =0
	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) basis 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) 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
	gsMPBESBasis ()
	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
virtual 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.
virtual void	refine (const index_t patch, gsMatrix< T > const &boxes, bool updateBasis=true)=0
virtual void	refine_withCoefs (gsMatrix< T > &localCoefs, const index_t patch, gsMatrix< T > const &boxes, bool updateBasis=true)=0
virtual void	refineElements (const index_t patch, std::vector< index_t > const &boxes, bool updateBasis=true)=0
virtual void	refineElements_withCoefs (gsMatrix< T > &localCoefs, const index_t patch, std::vector< index_t > const &boxes, bool updateBasis=true)=0
virtual void	repairPatches (std::vector< gsMatrix< T > * > &coefs, index_t startFromPatch=-1)=0
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)
virtual	~gsMPBESBasis ()
	constructor, deletes all the bases and the mapper
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) 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.

Protected Member Functions
bool	_check () const
	Checks the gsMappedBasis for consistency.
virtual bool	_checkTopologyWithBases () const =0
	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
virtual void	_setMapping ()=0
	create a new mapping of the local basisfunctions
virtual T	findParameter (patchSide const &ps, patchCorner const &pc, unsigned nrBasisFuncs) const =0
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.

Static Private Attributes
static const short_t	Dim
	Dimension of the parameter domains.

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
	)

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
	)

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) basis 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

inline

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  ) 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

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

protectedpure virtual

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

Implemented in gsMPBESBSplineBasis< d, T >, and gsMPBESHSplineBasis< 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

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

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

pure 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

Implemented in gsMPBESBSplineBasis< d, T >, and gsMPBESHSplineBasis< d, T >.

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

pure 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

Implemented in gsMPBESBSplineBasis< d, T >, and gsMPBESHSplineBasis< d, T >.

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

pure 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

Implemented in gsMPBESBSplineBasis< d, T >, and gsMPBESHSplineBasis< d, T >.

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

pure 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

Implemented in gsMPBESBSplineBasis< d, T >, and gsMPBESHSplineBasis< d, T >.

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

pure virtual

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

Implemented in gsMPBESBSplineBasis< d, T >, and gsMPBESHSplineBasis< d, T >.

void repairPatches

(

index_t

startFromPatch = -1

)

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

void setC0

(

patchCorner

pc

)

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
	)

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
	)

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

(

)

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
	)

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
	)

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