Detailed Description

template<class T>
class gismo::gsMultiPatch< T >

Container class for a set of geometry patches and their topology, that is, the interface connections and outer boundary faces.

Template Parameters

T	coefficient type

Inheritance diagram for gsMultiPatch< T >:

Collaboration diagram for gsMultiPatch< T >:

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

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

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.

virtual void	active_into (const gsMatrix< T > &u, gsMatrix< index_t > &result) const
	Indices of active (non-zero) function(s) for each point.

void	addAutoBoundaries ()
	Make all patch sides which are not yet declared as interface or boundary to a boundary.

void	addBoundary (const patchSide &ps)
	Set patch side ps to a boundary.

void	addBoundary (index_t p, boxSide s, std::string l="")
	Set side s of box p to a boundary.

void	addBox (index_t i=1)
	Add i new boxes.

template<class T >
gsProperty< T >	addBoxProperty (const std::string &name, T t=T())
	Adds a box property.

void	addInterface (const boundaryInterface &bi)
	Add an interface described by bi.

GISMO_DEPRECATED void	addInterface (gsGeometry< T > g1, boxSide s1, gsGeometry< T > g2, boxSide s2)
	Add an interface joint between side s1 of geometry g1 side s2 of geometry g2.

void	addInterface (index_t p1, boxSide s1, index_t p2, boxSide s2, std::string l="")
	Add an interface between side s1 of box p1 and side s2 of box p2.

index_t	addPatch (const gsGeometry< T > &g)
	Add a patch by copying argument.

index_t	addPatch (typename gsGeometry< T >::uPtr g)
	Add a patch from a gsGeometry<T>::uPtr.

void	addPatchBoundary (gsGeometry< T > *g, boxSide s)
	Add side s of patch g to the outer boundary of the domain.

std::vector< std::vector< patchComponent > >	allComponents (bool combineCorners=false) const
	Returns all components representing the topology.

gsMultiPatch< T >	approximateLinearly (index_t nsamples) const
	Computes linear approximation of the patches using nsamples per direction.

std::vector< gsBasis< T > * >	basesCopy (bool numeratorOnly=false) const
	Makes a deep copy of all bases and puts them in a vector.

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.

gsBasis< T > &	basis (const size_t i) const
	Return the basis of the i-th patch.

biterator	bBegin ()

const_biterator	bBegin () const

iterator	begin ()

const_iterator	begin () const

biterator	bEnd ()

const_biterator	bEnd () const

std::map< std::array< size_t, 4 >, internal::ElementBlock >	BezierOperator () const
	Performs Bezier extraction on the multipatch.

const boundaryInterface &	bInterface (int i) const
	Access i-th boundary interface.

const bContainer &	boundaries () const
	Return the vector of boundaries.

bContainer	boundaries (const std::string l) const
	Return the vector of boundaries with label l.

void	boundingBox (gsMatrix< T > &result) const
	Returns a bounding box for the multipatch domain. The output result is a matrix with two columns, corresponding to two points: the lower and upper corner of the bounding box.

void	checkConsistency () const
	Check that boundaries and interfaces are consistent.

void	clear ()
	Clear (delete) all patches.

void	clearAll ()
	Clear all boxes, boundary and interface data.

void	clearTopology ()
	Clear all boundary and interface data.

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

gsBoxTopology *	clone () const
	Clone function. Used to make a copy of the object.

void	closeGaps (T tol=1e-4)
	Attempt to close gaps between the interfaces. Assumes that the topology is computed, ie. computeTopology() has been called.

short_t	coDim () const
	Co-dimension of the geometry (must match for all patches).

gsMatrix< T >	coefs () const
	Returns the coefficient matrix of the multi-patch geometry.

index_t	coefsSize () const
	Return the number of coefficients (control points)

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

bool	computeTopology (T tol=1e-4, bool cornersOnly=false, bool tjunctions=false)
	Attempt to compute interfaces and boundaries automatically.

void	constructBoundaryRep ()
	Construct the boundary representation.

void	constructBoundaryRep (const std::string l)
	Construct the boundary representation of sides with label l.

void	constructInterfaceRep (const std::string l)
	Construct the interface representation of sides with label l.

void	degreeDecrease (int elevationSteps=1)
	Decrease the degree of all patches by elevationSteps.

void	degreeElevate (short_t const elevationSteps=1, short_t const dir=-1)
	Elevate the degree of all patches by elevationSteps, preserves smoothness.

void	degreeIncrease (short_t const elevationSteps=1, short_t const dir=-1)
	Increase the degree of all patches by elevationSteps, preserves multiplicity.

void	degreeReduce (int elevationSteps=1)
	Reduce the degree of all patches by elevationSteps.

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

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

virtual void	deriv2_into (const gsMatrix< T > &u, gsMatrix< T > &result) const
	Second derivatives.

virtual void	deriv_into (const gsMatrix< T > &u, gsMatrix< T > &result) const
	First derivatives.

std::string	detail () const
	Prints the object as a string with extended details.

short_t	dim () const
	Dimension of the boxes.

short_t	domainDim () const
	Dimension of the (source) domain.

bool	empty () const
	Returns true if gsMultiPatch is empty.

iterator	end ()

const_iterator	end () const

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

virtual void	eval_into (const gsMatrix< T > &u, gsMatrix< T > &result) const
	Evaluates the function(s).

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

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

gsMultiPatch< T >	extractBezier () const
	Extracts a Bezier representation of the current gsMultiPatch object.

InterfacePtr	findInterface (const index_t b1, const index_t b2) const

size_t	findPatchIndex (gsGeometry< T > *g) const
	Search for the given geometry and return its patch index.

void	fixOrientation ()
	Provides positive orientation for all patches.

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.

short_t	geoDim () const
	Dimension of the geometry (must match for all patches).

BoundaryPtr	getBoundary (const patchSide &ps)
	Returns a pointer to the boundary stored in this class, given ps.

template<class T >
gsProperty< T >	getBoxProperty (const std::string &name) const
	Adds a box property.

bool	getCornerList (const patchCorner &start, std::vector< patchCorner > &cornerList) const

void	getEVs (std::vector< std::vector< patchCorner > > &cornerLists, bool boundaries=false) const

bool	getInterface (const patchSide &ps, boundaryInterface &result) const

gsAffineFunction< T >	getMapForInterface (const boundaryInterface &bi, T scaling=0) const
	construct the affine map that places bi.first() next to bi.second() and identifies the two matching sides. The optional scaling specifies the scaling of first() in the direction orthogonal to the interface. By default it preserves the size of bi.first() in that direction

gsDofMapper	getMapper (T tol) const
	Used to get a mapper with unique vertices.

int	getMaxValence () const
	returns the maximal valence of a vertex of this topology.

bool	getNeighbour (const patchSide &ps, patchSide &result) const

bool	getNeighbour (const patchSide &ps, patchSide &result, int &ii) const

void	getOVs (std::vector< std::vector< patchCorner > > &cornerLists) const

	gsMultiPatch ()
	Default empty constructor.

	gsMultiPatch (const gsGeometry< T > &geo)
	Create a single-patch instance.

	gsMultiPatch (const gsMultiPatch &other)
	Copy constructor (makes deep copy)

	gsMultiPatch (PatchContainer &patches)
	Create from a vector of patches.

	gsMultiPatch (PatchContainer &patches, const std::vector< patchSide > &boundary, const std::vector< boundaryInterface > &interfaces)
	Create from patches and boundary/interface information.

std::vector< T >	HausdorffDistance (const gsMultiPatch< T > &other, const index_t nsamples=1000, const T accuracy=1e-6, const bool directed=false)
	Construct the interface representation.

iiterator	iBegin ()

const_iiterator	iBegin () const

iiterator	iEnd ()

const_iiterator	iEnd () const

const ifContainer &	interfaces () const
	Return the vector of interfaces.

ifContainer	interfaces (const std::string l) const
	Return the vector of interfaces with label l.

bool	isBoundary (const patchSide &ps) const
	Is the given patch side ps set to a boundary?

bool	isBoundary (index_t p, boxSide s)
	Returns true if side s on patch p is a boundary.

bool	isClosed ()
	Returns true if the multipatch object is a closed manifold (ie. it has no boundaries)

bool	isInterface (const patchSide &ps) const
	Is the given patch side ps set to an interface?

void	locatePoints (const gsMatrix< T > &points, gsVector< index_t > &pids, gsMatrix< T > &preim, const T accuracy=1e-6) const
	For each point in points, locates the parametric coordinates of the point.

void	locatePoints (const gsMatrix< T > &points, index_t pid1, gsVector< index_t > &pid2, gsMatrix< T > &preim) const
	For each point in points located on patch pid1, locates the parametric coordinates of the point.

size_t	nBoundary () const
	Number of boundaries.

index_t	nBoxes () const
	Number of boxes.

size_t	nInterfaces () const
	Number of interfaces.

size_t	nPatches () const
	Number of patches.

index_t	nPieces () const
	Number of pieces in the domain of definition.

index_t	numBoxProperties () const
	Returns the number of assigned box properties.

gsMultiPatch &	operator= (gsMultiPatch other)
	Assignment operator (uses copy-and-swap idiom)

const gsGeometry< T > &	operator[] (size_t i) const
	Return the i-th patch.

gsMatrix< T >	parameterRange (int i=0) const
	Returns the range of parameter.

short_t	parDim () const
	Dimension of the parameter domain (must match for all patches).

gsGeometry< T > &	patch (size_t i) const
	Return the i-th patch.

PatchContainer const &	patches () const
	Returns a vector of patches // to do : replace by copies.

void	permute (const std::vector< short_t > &perm)
	Permutes the patches according to perm.

const gsGeometry< T > &	piece (const index_t i) const
	Returns the piece(s) of the function(s) at subdomain k.

gsMatrix< T >	pointOn (const patchCorner &pc)
	Get coordinates of the patchCorner pc in the physical domain.

gsMatrix< T >	pointOn (const patchSide &ps)
	Get coordinates of a central point of the the patchSide ps in the physical domain.

std::ostream &	print (std::ostream &os) const
	Prints the object as a string.

bool	repairInterface (const boundaryInterface &bi)
	Checks if the interface is fully matching, and if not, repairs it.

void	repairInterfaces ()
	Checks if all patch-interfaces are fully matching, and if not, repairs them, i.e., makes them fully matching.

void	setDim (short_t i)
	Set the dimension of the boxes.

index_t	size () const
	size

void	swap (gsBoxTopology &other)
	Swap with another gsBoxTopology.

void	swap (gsMultiPatch &other)
	Swap with another gsMultiPatch.

short_t	targetDim () const
	Dimension of the target space.

gsSurfMesh	toMesh () const
	Creates a surface mesh out of this multipatch.

void	uniformCoarsen (int numKnots=1)
	Coarsen uniformly all patches by removing numKnots in each knot-span.

void	uniformRefine (int numKnots=1, int mul=1, short_t const dir=-1)
	Refine uniformly all patches by inserting numKnots in each knot-span with multipliplicity mul.

gsMultiPatch< T >	uniformSplit (index_t dir=-1) const
	Splits each patch uniformly in each direction (if dir = -1) into two new patches, giving a total number of 2^d new patches per patch. If dir is a parametric direction, then it only splits in that one direction. This method allocated new space for each new geometry, the original one stays unchanged.

	~gsMultiPatch ()
	Destructor.

Protected Attributes
bContainer	m_boundary
	List of boundaries of the boxes.

gsProperty_container	m_boxProp
	List of properties for each box.

short_t	m_dim
	Dimension of the boxes held.

ifContainer	m_interfaces
	List of intefaces between boxes.

index_t	nboxes
	Number of boxes held.

Member Function Documentation

◆ active()

template<typename T >

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()

◆ active_into()

template<typename T >

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

virtualinherited

Indices of active (non-zero) function(s) for each point.

The columns are sorted in increasing order, if on a point there are less active then the number of rows in the result matrix (some other point has more actives) then the rest of the column is filled with 0s.

Parameters

u
result

Reimplemented in gsBasis< SrcT::Scalar_t >, gsLagrangeBasis< T >, gsLegendreBasis< T >, gsMonomialBasis< T >, gsMvLegendreBasis< T >, gsBasis< T >, gsConstantBasis< T >, gsFunction< T >, gsHTensorBasis< d, T >, gsTHBSplineBasis< d, T >, gsMappedSingleBasis< d, T >, gsTensorBSplineBasis< 1, T >, gsTensorBSplineBasis< d, T >, gsTensorBSplineBasis< domainDim+1, T >, gsTensorBasis< d, T >, and gsTensorBasis< 1, T >.

◆ addBoxProperty()

template<class T >

gsProperty< T > addBoxProperty	(	const std::string &	name,
		T	t = `T()`
	)

inlineinherited

Adds a box property.

Parameters

[in]	name	The name of the property
[in]	t	The value of the property

Template Parameters

T	The type of the property

Returns: The property as a gsProperty object

◆ addInterface()

template<class T >

void addInterface	(	gsGeometry< T > *	g1,
		boxSide	s1,
		gsGeometry< T > *	g2,
		boxSide	s2
	)

Add an interface joint between side s1 of geometry g1 side s2 of geometry g2.

Todo:: add orientation information

◆ allComponents()

std::vector< std::vector< patchComponent > > allComponents ( bool combineCorners = false ) const

inherited

Returns all components representing the topology.

Each entry of the outer vector represents one component (patch-interior, face, edge, corner, etc.). Since the components refering to one interface can be addressed as belonging to different patches, each component itself is represented by an inner vector which contains all patchComponent objects that refer to the particular component.

Parameters

combineCorners If this is set, all corners are treated as one component

◆ basesCopy()

template<class T >

std::vector< gsBasis< T > * > basesCopy ( bool numeratorOnly = false ) const

Makes a deep copy of all bases and puts them in a vector.

Parameters

numeratorOnly If true, and the bases are derived from gsRationalBasis, then only the source bases (numerators) are returned

◆ bBegin() [1/2]

biterator bBegin ( )

inlineinherited

Get an iterator to the beginning of the boundaries

Returns: an iterator to the beginning of the boundaries

◆ bBegin() [2/2]

const_biterator bBegin ( ) const

inlineinherited

Get a const-iterator to the beginning of the boundaries

Returns: an iterator to the beginning of the boundaries

◆ begin() [1/2]

template<class T >

iterator begin ( )

inline

Get an iterator to the beginning of the patches

Returns: an iterator to the beginning of the patches

◆ begin() [2/2]

template<class T >

const_iterator begin ( ) const

inline

Get a const-iterator to the patches

Returns: an iterator to the beginning of the patches

◆ bEnd() [1/2]

biterator bEnd ( )

inlineinherited

Get an iterator to the end of the boundaries

Returns: an iterator to the end of the knotvector

◆ bEnd() [2/2]

const_biterator bEnd ( ) const

inlineinherited

Get a const-iterator to the end of the boundaries

Returns: an iterator to the end of the boundaries

◆ BezierOperator()

template<class T >

std::map< std::array< size_t, 4 >, internal::ElementBlock > BezierOperator ( ) const

Performs Bezier extraction on the multipatch.

Returns: The ElementBlock structure of the Bezier extraction, which contains the Bezier coefficients and the active nodes for each bezier patch;

◆ compute()

template<typename T >

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 gsConstantFunction< T >, and gsGeometry< T >.

◆ computeTopology()

template<class T >

bool computeTopology	(	T	tol = `1e-4`,
		bool	cornersOnly = `false`,
		bool	tjunctions = `false`
	)

Attempt to compute interfaces and boundaries automatically.

Parameters

tol	The tolerance to test for matching points
cornersOnly	When set to true an interface is accepted if the patch corners match, even if the parameterization does not agree

◆ deriv()

template<class T >

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

inherited

Evaluate the derivatives,.

See also: deriv_into()

◆ deriv2()

template<class T >

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.

◆ deriv2_into()

template<typename T >

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

virtualinherited

Second derivatives.

For scalar valued functions \(f_1, \ldots, f_S\) from \(\mathbb{R}^n\rightarrow\mathbb{R}\) format is:

\[ \left[ \begin{array}{ccccc} \partial_{1}\partial_{1}f_1(\mathbf{u}_1) & \partial_{1}\partial_{1}f_1(\mathbf{u}_2) & \ldots & \partial_{1}\partial_{1}f_1(\mathbf{u}_N)\\ \partial_{2}\partial_{2}f_1(\mathbf{u}_1) & \partial_{2}\partial_{2}f_1(\mathbf{u}_2) & \ldots & \partial_{2}\partial_{2}f_1(\mathbf{u}_N)\\ \vdots & \vdots & & \vdots \\ \partial_{n}\partial_{n}f_1(\mathbf{u}_1) & \partial_{n}\partial_{n}f_1(\mathbf{u}_2) & \ldots & \partial_{n}\partial_{n}f_1(\mathbf{u}_N)\\ \partial_{1}\partial_{2}f_1(\mathbf{u}_1) & \partial_{1}\partial_{2}f_1(\mathbf{u}_2) & \ldots & \partial_{1}\partial_{2}f_1(\mathbf{u}_N)\\ \partial_{1}\partial_{3}f_1(\mathbf{u}_1) & \partial_{1}\partial_{3}f_1(\mathbf{u}_2) & \ldots & \partial_{1}\partial_{3}f_1(\mathbf{u}_N)\\ \vdots & \vdots & & \vdots \\ \partial_{1}\partial_{n}f_1(\mathbf{u}_1) & \partial_{1}\partial_{n}f_1(\mathbf{u}_2) & \ldots & \partial_{1}\partial_{n}f_1(\mathbf{u}_N)\\ \partial_{2}\partial_{3}f_1(\mathbf{u}_1) & \partial_{2}\partial_{3}f_1(\mathbf{u}_2) & \ldots & \partial_{2}\partial_{3}f_1(\mathbf{u}_N)\\ \vdots & \vdots & & \vdots\\ \partial_{2}\partial_{n}f_1(\mathbf{u}_1) & \partial_{2}\partial_{n}f_1(\mathbf{u}_2) & \ldots & \partial_{2}\partial_{n}f_1(\mathbf{u}_N)\\ \partial_{3}\partial_{4}f_1(\mathbf{u}_1) & \partial_{3}\partial_{4}f_1(\mathbf{u}_2) & \ldots & \partial_{3}\partial_{4}f_1(\mathbf{u}_N)\\ \vdots & \vdots & & \vdots \\ \partial_{n-1}\partial_{n}f_1(\mathbf{u}_1) & \partial_{n-1}\partial_{n}f_1(\mathbf{u}_2) & \ldots & \partial_{n-1}\partial_{n}f_1(\mathbf{u}_N)\\ \vdots & \vdots & & \vdots \\ \partial_{1}\partial_{1}f_S(\mathbf{u}_1) & \partial_{1}\partial_{1}f_S(\mathbf{u}_2) & \ldots & \partial_{1}\partial_{1}f_S(\mathbf{u}_N)\\ \vdots & \vdots & & \vdots \\ \partial_{n-1}\partial_{n}f_S(\mathbf{u}_1) & \partial_{n-1}\partial_{n}f_S(\mathbf{u}_2) & \ldots & \partial_{n-1}\partial_{n}f_S(\mathbf{u}_N)\\ \end{array} \right] \]

For vector valued functions function \(f_1, \ldots, f_S\) from \(\mathbb{R}^n\rightarrow\mathbb{R}^{m}\) the format is:

\[ \left[ \begin{array}{ccccc} \partial_{1}\partial_{1}f_1^{(1)}(\mathbf{u}_1) & \partial_{1}\partial_{1}f_1^{(1)}(\mathbf{u}_2) & \ldots & \partial_{1}\partial_{1}f_1^{(1)}(\mathbf{u}_N)\\ \partial_{2}\partial_{2}f_1^{(1)}(\mathbf{u}_1) & \partial_{2}\partial_{2}f_1^{(1)}(\mathbf{u}_2) & \ldots & \partial_{2}\partial_{2}f_1^{(1)}(\mathbf{u}_N)\\ \vdots & \vdots & & \vdots \\ \partial_{n}\partial_{n}f_1^{(1)}(\mathbf{u}_1) & \partial_{n}\partial_{n}f_1^{(1)}(\mathbf{u}_2) & \ldots & \partial_{n}\partial_{n}f_1^{(1)}(\mathbf{u}_N)\\ \partial_{1}\partial_{2}f_1^{(1)}(\mathbf{u}_1) & \partial_{1}\partial_{2}f_1^{(1)}(\mathbf{u}_2) & \ldots & \partial_{1}\partial_{2}f_1^{(1)}(\mathbf{u}_N)\\ \partial_{1}\partial_{3}f_1^{(1)}(\mathbf{u}_1) & \partial_{1}\partial_{3}f_1^{(1)}(\mathbf{u}_2) & \ldots & \partial_{1}\partial_{3}f_1^{(1)}(\mathbf{u}_N)\\ \vdots & \vdots & & \vdots \\ \partial_{1}\partial_{n}f_1^{(1)}(\mathbf{u}_1) & \partial_{1}\partial_{n}f_1^{(1)}(\mathbf{u}_2) & \ldots & \partial_{1}\partial_{n}f_1^{(1)}(\mathbf{u}_N)\\ \partial_{2}\partial_{3}f_1^{(1)}(\mathbf{u}_1) & \partial_{2}\partial_{3}f_1^{(1)}(\mathbf{u}_2) & \ldots & \partial_{2}\partial_{3}f_1^{(1)}(\mathbf{u}_N)\\ \vdots & \vdots & & \vdots\\ \partial_{2}\partial_{n}f_1^{(1)}(\mathbf{u}_1) & \partial_{2}\partial_{n}f_1^{(1)}(\mathbf{u}_2) & \ldots & \partial_{2}\partial_{n}f_1^{(1)}(\mathbf{u}_N)\\ \partial_{3}\partial_{4}f_1^{(1)}(\mathbf{u}_1) & \partial_{3}\partial_{4}f_1^{(1)}(\mathbf{u}_2) & \ldots & \partial_{3}\partial_{4}f_1^{(1)}(\mathbf{u}_N)\\ \vdots & \vdots & & \vdots \\ \partial_{n-1}\partial_{n}f_1^{(1)}(\mathbf{u}_1) & \partial_{n-1}\partial_{n}f_1^{(1)}(\mathbf{u}_2) & \ldots & \partial_{n-1}\partial_{n}f_1^{(1)}(\mathbf{u}_N)\\ \vdots & \vdots & & \vdots \\ \partial_{1}\partial_{1}f_1^{(m)}(\mathbf{u}_1) & \partial_{1}\partial_{1}f_1^{(m)}(\mathbf{u}_2) & \ldots & \partial_{1}\partial_{1}f_1^{(m)}(\mathbf{u}_N)\\ \vdots & \vdots & & \vdots \\ \partial_{n-1}\partial_{n}f_1^{(m)}(\mathbf{u}_1) & \partial_{n-1}\partial_{n}f_1^{(m)}(\mathbf{u}_2) & \ldots & \partial_{n-1}\partial_{n}f_1^{(m)}(\mathbf{u}_N)\\ \vdots & \vdots & & \vdots \\ \partial_{1}\partial_{1}f_S^{(1)}(\mathbf{u}_1) & \partial_{1}\partial_{1}f_S^{(1)}(\mathbf{u}_2) & \ldots & \partial_{1}\partial_{1}f_S^{(1)}(\mathbf{u}_N)\\ \vdots & \vdots & & \vdots \\ \partial_{n-1}\partial_{n}f_S^{(1)}(\mathbf{u}_1) & \partial_{n-1}\partial_{n}f_S^{(1)}(\mathbf{u}_2) & \ldots & \partial_{n-1}\partial_{n}f_S^{(1)}(\mathbf{u}_N)\\ \vdots & \vdots & & \vdots \\ \partial_{1}\partial_{1}f_S^{(m)}(\mathbf{u}_1) & \partial_{1}\partial_{1}f_S^{(m)}(\mathbf{u}_2) & \ldots & \partial_{1}\partial_{1}f_S^{(m)}(\mathbf{u}_N)\\ \vdots & \vdots & & \vdots \\ \partial_{n-1}\partial_{n}f_S^{(m)}(\mathbf{u}_1) & \partial_{n-1}\partial_{n}f_S^{(m)}(\mathbf{u}_2) & \ldots & \partial_{n-1}\partial_{n}f_S^{(m)}(\mathbf{u}_N)\\ \end{array} \right] \]

where \( f^{(i)}_j\) is the \(i\)-th component of function \( f_j\) of the set.

Parameters

u
result

Reimplemented in gsFunction< real_t >, gsBasis< SrcT::Scalar_t >, gsGeometryTransform< T >, gsLagrangeBasis< T >, gsLegendreBasis< T >, gsMonomialBasis< T >, gsMvLegendreBasis< T >, gsAffineFunction< T >, gsBasis< T >, gsConstantFunction< T >, gsFuncCoordinate< T >, gsFunction< T >, gsFunctionExpr< T >, gsGeometry< T >, gsHBSplineBasis< d, T >, gsTHBSplineBasis< d, T >, gsMappedSingleBasis< d, T >, gsMappedSingleSpline< d, T >, gsTensorBSplineBasis< 1, T >, gsTensorBasis< d, T >, and gsTensorBasis< 1, T >.

◆ deriv_into()

template<typename T >

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

virtualinherited

First derivatives.

For scalar valued functions \(f_1, \ldots, f_S\) from \(\mathbb{R}^n\rightarrow\mathbb{R}\) format is:

\[ \left[ \begin{array}{ccccc} \partial_{1}f_1(\mathbf{u}_1) & \partial_{1}f_1(\mathbf{u}_2) & \ldots & \partial_{1}f_1(\mathbf{u}_N) \\ \vdots & \vdots & & \vdots \\ \partial_{n}f_1(\mathbf{u}_1) & \partial_{n}f_1(\mathbf{u}_2) & \ldots & \partial_{n}f_1(\mathbf{u}_N) \\ \vdots & \vdots & & \vdots \\ \partial_{1}f_S(\mathbf{u}_S) & \partial_{1}f_S(\mathbf{u}_2) & \ldots & \partial_{1}f_S(\mathbf{u}_N) \\ \vdots & \vdots & & \vdots \\ \partial_{n}f_S(\mathbf{u}_S) & \partial_{n}f_S(\mathbf{u}_2) & \ldots & \partial_{n}f_S(\mathbf{u}_N) \\ \end{array} \right], \]

For vector valued functions function \(f_1, \ldots, f_S\) from \(\mathbb{R}^n\rightarrow\mathbb{R}^{m}\) the format is:

\[ \left[ \begin{array}{ccccc} \partial_{1}f_1^{(1)}(\mathbf{u}_1) & \partial_{1}f_1^{(1)}(\mathbf{u}_2) & \ldots & \partial_{1}f_1^{(1)}(\mathbf{u}_N)\\ \vdots & \vdots & & \vdots \\ \partial_{n}f_1^{(1)}(\mathbf{u}_1) & \partial_{n}f_1^{(1)}(\mathbf{u}_2) & \ldots & \partial_{n}f_1^{(1)}(\mathbf{u}_N)\\ \partial_{1}f_1^{(2)}(\mathbf{u}_1) & \partial_{1}f_1^{(2)}(\mathbf{u}_2) & \ldots & \partial_{1}f_1^{(2)}(\mathbf{u}_N)\\ \vdots & \vdots & & \vdots \\ \partial_{n}f_1^{(2)}(\mathbf{u}_1) & \partial_{n}f_1^{(2)}(\mathbf{u}_2) & \ldots & \partial_{n}f_1^{(2)}(\mathbf{u}_N)\\ \partial_{1}f_1^{(m)}(\mathbf{u}_1) & \partial_{1}f_1^{(m)}(\mathbf{u}_2) & \ldots & \partial_{1}f_1^{(m)}(\mathbf{u}_N)\\ \vdots & \vdots & & \vdots \\ \partial_{n}f_1^{(m)}(\mathbf{u}_1) & \partial_{n}f_1^{(m)}(\mathbf{u}_2) & \ldots & \partial_{n}f_1^{(m)}(\mathbf{u}_N)\\ \vdots & \vdots & & \vdots \\ \partial_{1}f_S^{(1)}(\mathbf{u}_S) & \partial_{1}f_S^{(1)}(\mathbf{u}_2) & \ldots & \partial_{1}f_S^{(1)}(\mathbf{u}_N)\\ \vdots & \vdots & & \vdots \\ \partial_{n}f_S^{(1)}(\mathbf{u}_S) & \partial_{n}f_S^{(1)}(\mathbf{u}_2) & \ldots & \partial_{n}f_S^{(1)}(\mathbf{u}_N)\\ \partial_{1}f_S^{(2)}(\mathbf{u}_S) & \partial_{1}f_S^{(2)}(\mathbf{u}_2) & \ldots & \partial_{1}f_S^{(2)}(\mathbf{u}_N)\\ \vdots & \vdots & & \vdots \\ \partial_{n}f_S^{(2)}(\mathbf{u}_S) & \partial_{n}f_S^{(2)}(\mathbf{u}_2) & \ldots & \partial_{n}f_S^{(2)}(\mathbf{u}_N)\\ \partial_{1}f_S^{(m)}(\mathbf{u}_S) & \partial_{1}f_S^{(m)}(\mathbf{u}_2) & \ldots & \partial_{1}f_S^{(m)}(\mathbf{u}_N)\\ \vdots & \vdots & & \vdots \\ \partial_{n}f_S^{(m)}(\mathbf{u}_S) & \partial_{n}f_S^{(m)}(\mathbf{u}_2) & \ldots & \partial_{n}f_S^{(m)}(\mathbf{u}_N)\\ \end{array} \right], \]

where \(f^{(i)}_j\) is the \(i\)-th component of function \(f_j\) of the set.

Parameters

u
result

Reimplemented in gsFunction< real_t >, gsBasis< SrcT::Scalar_t >, gsLagrangeBasis< T >, gsLegendreBasis< T >, gsMonomialBasis< T >, gsMvLegendreBasis< T >, gsAffineFunction< T >, gsBasis< T >, gsBasisFun< T >, gsConstantBasis< T >, gsConstantFunction< T >, gsFuncCoordinate< T >, gsFunction< T >, gsFunctionExpr< T >, gsGeometry< T >, gsSquaredDistance< T >, gsGeometrySlice< T >, gsGeometryTransform< T >, gsHBSplineBasis< d, T >, gsTHBSplineBasis< d, T >, gsMappedSingleBasis< d, T >, gsMappedSingleSpline< d, T >, gsTensorBSplineBasis< 1, T >, gsTensorBasis< d, T >, and gsTensorBasis< 1, T >.

◆ domainDim()

template<class T >

short_t domainDim ( ) const

inlinevirtual

Dimension of the (source) domain.

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

Implements gsFunctionSet< T >.

◆ end() [1/2]

template<class T >

iterator end ( )

inline

Get an iterator to the end of the patches

Returns: an iterator to the end of the patches

◆ end() [2/2]

template<class T >

const_iterator end ( ) const

inline

Get a const iterator to the end of the patches

Returns: an iterator to the end of the patches

◆ eval()

template<class T >

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

inherited

Evaluate the function,.

See also: eval_into()

◆ eval_into()

template<typename T >

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

virtualinherited

Evaluates the function(s).

For scalar valued functions \(f_1, \ldots, f_S\) from \(\mathbb{R}^n\rightarrow\mathbb{R}\) format is:

\[ \left[ \begin{array}{ccccc} f_1(\mathbf{u}_1) & f_1(\mathbf{u}_2) & \ldots & f_1(\mathbf{u}_N)\\ f_2(\mathbf{u}_1) & f_2(\mathbf{u}_2) & \ldots & f_2(\mathbf{u}_N)\\ \vdots & \vdots & & \vdots\\ f_S(\mathbf{u}_1) & f_S(\mathbf{u}_2) & \ldots & f_S(\mathbf{u}_N) \end{array} \right] \]

For vector valued functions function \(f_1, \ldots, f_S\) from \(\mathbb{R}^n\rightarrow\mathbb{R}^m\) the format is:

\[ \left[ \begin{array}{ccccc} f_1^{(1)}(\mathbf{u}_1) & f_1^{(1)}(\mathbf{u}_2) & \ldots & f_1^{(1)}(\mathbf{u}_N) \\ \vdots & \vdots & & \vdots \\ f_1^{(m)}(\mathbf{u}_1) & f_1^{(m)}(\mathbf{u}_2) & \ldots & f_1^{(m)}(\mathbf{u}_N)\\ \vdots & \vdots & & \vdots \\ f_S^{(1)}(\mathbf{u}_1) & f_S^{(1)}(\mathbf{u}_2) & \ldots & f_S^{(1)}(\mathbf{u}_N) \\ \vdots & \vdots & & \vdots \\ f_S^{(m)}(\mathbf{u}_1) & f_S^{(m)}(\mathbf{u}_2) & \ldots & f_S^{(m)}(\mathbf{u}_N) \end{array} \right] \]

where \(f^{(i)}_j\) is the \(i\)-th component of function \(f_j\) of the set.

Parameters

u
result

Reimplemented in gsBasis< SrcT::Scalar_t >, gsPiecewiseFunction< T >, gsElementErrorPlotter< T >, gsCauchyStressFunction< T >, gsDetFunction< T >, gsFsiLoad< T >, gsMaterialMatrixEvalSingle< T, out >, gsMaterialMatrixIntegrateSingle< T, out >, gsShellStressFunction< T >, gsLagrangeBasis< T >, gsLegendreBasis< T >, gsMonomialBasis< T >, gsMvLegendreBasis< T >, gsCPPInterface< T >, gsRemapInterface< T >, gsAffineFunction< T >, gsBasis< T >, gsBasisFun< T >, gsConstantBasis< T >, gsConstantFunction< T >, gsAbsError< T >, gsGradientField< T >, gsJacDetField< T >, gsNormalField< T >, gsParamField< T >, gsPatchIdField< T >, gsFuncCoordinate< T >, gsFunctionExpr< T >, gsGeometry< T >, gsSquaredDistance< T >, gsGeometrySlice< T >, gsGeometryTransform< T >, gsHBSplineBasis< d, T >, gsTHBSplineBasis< d, T >, gsMappedSingleBasis< d, T >, gsMappedSingleSpline< d, T >, gsTensorBSplineBasis< 1, T >, gsTensorBasis< d, T >, gsTensorBasis< 1, T >, and gsFunction< T >.

◆ evalAllDers()

template<class T >

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

◆ evalAllDers_into()

template<typename T >

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

virtualinherited

Evaluate the nonzero functions and their derivatives up to order n at points u into result.

The derivatives (the 0-th derivative is the function value) are stored in a result. result is a std::vector, where result[i] is a gsMatrix which contains the i-th derivatives.

The entries in result[0], result[1], and result[2] are ordered as in eval_into(), deriv_into(), and deriv2_into(), respectively. For i > 2, the derivatives are stored in lexicographical order, e.g. for order i = 3 and dimension 2 the derivatives are stored as follows: \( \partial_{xxx}, \, \partial_{xxy}, \, \partial_{xyy}, \, \partial_{yyy}.\, \)

Parameters

[in]	u	Evaluation points, each column corresponds to one evaluation point.
[in]	n	All derivatives up to order n are computed and stored in result.
[in,out]	result	See above for format.

Reimplemented in gsConstantFunction< T >, gsGeometry< T >, gsSquaredDistance< T >, gsTHBSplineBasis< d, T >, gsMappedSingleBasis< d, T >, gsMappedSingleSpline< d, T >, gsTensorBSplineBasis< 1, T >, gsTensorBasis< d, T >, and gsTensorBasis< 1, T >.

◆ extractBezier()

template<class T >

gsMultiPatch< T > extractBezier ( ) const

Extracts a Bezier representation of the current gsMultiPatch object.

This function extracts the Bezier representation of the current gsMultiPatch object.

Template Parameters

T	The numerical type used for the definition of the gsMultiPatch object.

Returns: A gsMultiPatch object containing the Bezier representation of the original object.

Note: Currently, only bivariate splines are supported.

◆ findInterface()

const boundaryInterface * findInterface	(	const index_t	b1,
		const index_t	b2
	)		const

inherited

Returns a pointer to the interface between boxes b1 and b2, if one exists, otherwise it returns a null pointer

◆ getBoxProperty()

template<class T >

gsProperty< T > getBoxProperty ( const std::string & name ) const

inlineinherited

Adds a box property.

Parameters

[in] name The name of the property

Template Parameters

T	The type of the property

Returns: The property as a gsProperty<T> object

◆ getCornerList()

bool getCornerList	(	const patchCorner &	start,
		std::vector< patchCorner > &	cornerList
	)		const

inherited

takes a patchCorner start and gives back all other patchCorners, that represent the same point in the vector cornerList

◆ getEVs()

void getEVs	(	std::vector< std::vector< patchCorner > > &	cornerLists,
		bool	boundaries = `false`
	)		const

inherited

gives back all the extraordinary vertices (3 faces or more than 4) of the topology each EV is represented by a vector of patchCorners, which represent the same vertex all the vectors are put in the vector cornerLists. It will only find vertices on the inside. CAREFUL: works only for 2D

◆ getInterface()

bool getInterface	(	const patchSide &	ps,
		boundaryInterface &	result
	)		const

inlineinherited

set result to the associated interface of ps, returns false if it is a boundary patchSide

◆ getMapForInterface()

template<class T >

gsAffineFunction< T > getMapForInterface	(	const boundaryInterface &	bi,
		T	scaling = `0`
	)		const

construct the affine map that places bi.first() next to bi.second() and identifies the two matching sides. The optional scaling specifies the scaling of first() in the direction orthogonal to the interface. By default it preserves the size of bi.first() in that direction

Parameters

bi
scaling

Returns

◆ getNeighbour() [1/2]

bool getNeighbour	(	const patchSide &	ps,
		patchSide &	result
	)		const

inherited

set result to the associated patchSide of ps, returns false if it is a boundary patchSide

◆ getNeighbour() [2/2]

bool getNeighbour	(	const patchSide &	ps,
		patchSide &	result,
		int &	ii
	)		const

inherited

set result to the associated patchSide of ps, returns false if it is a boundary patchSide

◆ getOVs()

void getOVs ( std::vector< std::vector< patchCorner > > & cornerLists ) const

inherited

gives back all the ordinary vertices (4 faces) of the topology each OV is represented by a vector of patchCorners, which represent the same vertex all the vectors are put in the vector cornerLists It will only find vertices on the inside. CAREFUL: works only for 2D

◆ iBegin() [1/2]

iiterator iBegin ( )

inlineinherited

Get an iterator to the beginning of the interfaces

Returns: an iterator to the beginning of the interfaces

◆ iBegin() [2/2]

const_iiterator iBegin ( ) const

inlineinherited

Get a const-iterator to the interfaces

Returns: an iterator to the beginning of the interfaces

◆ iEnd() [1/2]

iiterator iEnd ( )

inlineinherited

Get an iterator to the end of the interfaces

Returns: an iterator to the end of the interfaces

◆ iEnd() [2/2]

const_iiterator iEnd ( ) const

inlineinherited

Get a const iterator to the end of the interfaces

Returns: an iterator to the end of the interfaces

◆ locatePoints() [1/2]

template<class T >

void locatePoints	(	const gsMatrix< T > &	points,
		gsVector< index_t > &	pids,
		gsMatrix< T > &	preim,
		const T	accuracy = `1e-6`
	)		const

For each point in points, locates the parametric coordinates of the point.

Parameters

points
pids	vector containing for each point the patch id where it belongs (or -1 if not found)
preim	in each column, the parametric coordinates of the corresponding point in the patch

◆ locatePoints() [2/2]

template<class T >

void locatePoints	(	const gsMatrix< T > &	points,
		index_t	pid1,
		gsVector< index_t > &	pid2,
		gsMatrix< T > &	preim
	)		const

For each point in points located on patch pid1, locates the parametric coordinates of the point.

Parameters

pid2	vector containing for each point the patch id where it belongs (or -1 if not found)
preim	in each column, the parametric coordinates of the corresponding point in the patch

◆ numBoxProperties()

index_t numBoxProperties ( ) const

inlineinherited

Returns the number of assigned box properties.

Returns: The number of assigned box properties

◆ pointOn()

template<class T >

gsMatrix< T > pointOn ( const patchSide & ps )

Get coordinates of a central point of the the patchSide ps in the physical domain.

The central point in the physical domain is the the midpoint on the parameter domain, mapped to the physical domain

◆ repairInterface()

template<class T >

bool repairInterface ( const boundaryInterface & bi )

Checks if the interface is fully matching, and if not, repairs it.

Remarks: Designed for gsHTensorBasis and derived bases. Assumes that the respective meshes on all levels of the gsHTensorBasis are fully matching.

Returns: true, if something was repaired, i.e., if the mesh on the interface was changed.

◆ repairInterfaces()

template<class T >

void repairInterfaces ( )

inline

Checks if all patch-interfaces are fully matching, and if not, repairs them, i.e., makes them fully matching.

Remarks: Designed for gsHTensorBasis and derived bases. Assumes that the meshes on all levels of the gsHTensorBasis are fully matching.

◆ size()

template<class T >

index_t size ( ) const

inlinevirtual

size

Warning: gsFunction and gsGeometry have size() == 1. This should not be confused with the size eg. of gsGeometry::basis(), which is the number of basis functions in the basis

Returns: the size of the function set: the total number of functions

Reimplemented from gsFunctionSet< T >.

◆ targetDim()

template<class T >

short_t targetDim ( ) const

inlinevirtual

Dimension of the target space.

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

Reimplemented from gsFunctionSet< T >.

Detailed Description

Public Types

Public Member Functions

Protected Attributes

Member Function Documentation

◆ active()

◆ active_into()

◆ addBoxProperty()

◆ addInterface()

◆ allComponents()

◆ basesCopy()

◆ bBegin() [1/2]

◆ bBegin() [2/2]

◆ begin() [1/2]

◆ begin() [2/2]

◆ bEnd() [1/2]

◆ bEnd() [2/2]

◆ BezierOperator()

◆ compute()

◆ computeTopology()

◆ deriv()

◆ deriv2()

◆ deriv2_into()

◆ deriv_into()

◆ domainDim()

◆ end() [1/2]

◆ end() [2/2]

◆ eval()

◆ eval_into()

◆ evalAllDers()

◆ evalAllDers_into()

◆ extractBezier()

◆ findInterface()

◆ getBoxProperty()

◆ getCornerList()

◆ getEVs()

◆ getInterface()

◆ getMapForInterface()

◆ getNeighbour() [1/2]

◆ getNeighbour() [2/2]

◆ getOVs()

◆ iBegin() [1/2]

◆ iBegin() [2/2]

◆ iEnd() [1/2]

◆ iEnd() [2/2]

◆ locatePoints() [1/2]

◆ locatePoints() [2/2]

◆ numBoxProperties()

◆ pointOn()

◆ repairInterface()

◆ repairInterfaces()

◆ size()

◆ targetDim()