Detailed Description

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

Class gsMappedSingleSpline represents an individual .....of a.

Note that it does not own the underlying spline: if you delete the object the spline is not deleted. The lifetime of the underlying spline should be at least the lifetime of gsMappedSingleSpline.

Inheritance diagram for gsMappedSingleSpline< d, T >:

Collaboration diagram for gsMappedSingleSpline< d, T >:

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

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

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

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...

virtual void	computeMap (gsMapData< T > &InOut) const
	Computes map function data. More...

gsFuncCoordinate< T >	coord (const index_t c) const
	Returns the scalar function giving the i-th coordinate of this function.

short_t	degree (short_t i) const
	Returns the polynomial degree.

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...

void	deriv2_into (const gsMatrix< T > &u, gsMatrix< T > &result) const
	Evaluates the (partial) derivatives of the nonzero spline functions at points u into result.

void	deriv_into (const gsMatrix< T > &u, gsMatrix< T > &result) const
	Evaluates the (partial) derivatives of non-zero spline functions at (the columns of) u.

virtual T	distanceL2 (gsFunction< T > const &) const
	Computes the L2-distance between this function and the field and a function func.

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

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

void	eval_into (const gsMatrix< T > &u, gsMatrix< T > &result) const
	Evaluates the non-zero spline functions at value u.

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

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

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.

	gsMappedSingleSpline (gsMappedSpline< d, T > *spline, unsigned const &i=0)
	Construct a spline function by a pointer to a spline and an index i.

virtual void	invertPoints (const gsMatrix< T > &points, gsMatrix< T > &result, const T accuracy=1e-6, const bool useInitialPoint=false) const

int	newtonRaphson (const gsVector< T > &value, gsVector< T > &arg, bool withSupport=true, const T accuracy=1e-6, int max_loop=100, T damping_factor=1) const

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

virtual gsMatrix< T >	parameterCenter () const
	Returns a "central" point inside inside the parameter domain.

gsMatrix< T >	parameterCenter (const boxCorner &bc) const
	Get coordinates of the boxCorner bc in the parameter domain.

gsMatrix< T >	parameterCenter (const boxSide &bs) const
	Get coordinates of the midpoint of the boxSide bs in the parameter domain.

virtual const gsFunction &	piece (const index_t k) const
	Returns the piece(s) of the function(s) at subdomain k.

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

void	recoverPoints (gsMatrix< T > &xyz, gsMatrix< T > &uv, index_t k, const T accuracy=1e-6) const

void	setPiece (unsigned const &i)

index_t	size () const
	size More...

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

Evaluation functions
These functions allow one to evaluate the function as well as its derivatives at one or more points in the parameter space. See also Evaluation members.
virtual void	eval_component_into (const gsMatrix< T > &u, const index_t comp, gsMatrix< T > &result) const
	Evaluate the function for component comp in the target dimension at points u into result.

virtual void	jacobian_into (const gsMatrix< T > &u, gsMatrix< T > &result) const
	Computes for each point u a block of result containing the Jacobian matrix.

void	div_into (const gsMatrix< T > &u, gsMatrix< T > &result) const
	Computes for each point u a block of result containing the divergence matrix.

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

virtual void	hessian_into (const gsMatrix< T > &u, gsMatrix< T > &result, index_t coord=0) const

virtual gsMatrix< T >	hessian (const gsMatrix< T > &u, index_t coord=0) const

virtual gsMatrix< T >	laplacian (const gsMatrix< T > &u) const
	Evaluate the Laplacian at points u. More...

Private Member Functions
	gsMappedSingleSpline ()
	Default empty constructor.

Member Function Documentation

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 gsMatrix< T > &	u,
		gsMatrix< index_t > &	result
	)		const

inlinevirtualinherited

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 from gsFunctionSet< 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 gsGeometry< T >, and gsConstantFunction< T >.

void computeMap ( gsMapData< T > & InOut ) const

virtualinherited

Computes map function data.

This function evaluates the functions and their derivatives at the points InOut.points and writes them in the corresponding fields of InOut. Which field to write (and what to compute) is controlled by the InOut.flags (see also gsMapData). This is intended for parametrizations only and it works on functions sets of cardinality 1 only.

Parameters

[in,out] InOut

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.

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 >.

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

inherited

Evaluate the function,.

See Also: eval_into()

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

virtual gsMatrix<T> hessian	(	const gsMatrix< T > &	u,
		index_t	coord = `0`
	)		const

inlinevirtualinherited

Evaluates the Hessian (matrix of second partial derivatives) of coordinate coord at points u.

void invertPoints	(	const gsMatrix< T > &	points,
		gsMatrix< T > &	result,
		const T	accuracy = `1e-6`,
		const bool	useInitialPoint = `false`
	)		const

virtualinherited

Takes the physical points and computes the corresponding parameter values. If the point cannot be inverted (eg. is not part of the geometry) the corresponding parameter values will be undefined

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

virtualinherited

Evaluate the Laplacian at points u.

By default uses central finite differences with h=0.00001

Reimplemented in gsFunctionExpr< T >.

int newtonRaphson	(	const gsVector< T > &	value,
		gsVector< T > &	arg,
		bool	withSupport = `true`,
		const T	accuracy = `1e-6`,
		int	max_loop = `100`,
		T	damping_factor = `1`
	)		const

inherited

Newton-Raphson method to find a solution of the equation f(arg) = value with starting vector arg. If the point cannot be inverted the corresponding parameter values will be undefined

void recoverPoints	(	gsMatrix< T > &	xyz,
		gsMatrix< T > &	uv,
		index_t	k,
		const T	accuracy = `1e-6`
	)		const

inherited

Recovers a point on the (geometry) together with its parameters uv, assuming that the k-th coordinate of the point xyz is not known (and has a random value as input argument).

void setPiece ( unsigned const & i )

inline

The gsBasisFun points to the i-th spline function of m_spline after calling this setter.

index_t size ( ) const

inlinevirtualinherited

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 >.

Reimplemented in gsPiecewiseFunction< 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

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

Public Types

Public Member Functions

Private Member Functions

Member Function Documentation

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