gsGeometrySlice< T > Class Template Reference

Detailed Description

template<class T>
class gismo::gsGeometrySlice< T >

gsGeometrySlice is a class representing an iso parametric slice of a geometry object. It stores a pointer to the geometry object, which is only valid as long as this object is alive. Methods for printing to paraview are available in gsWriteToParaview.h

Inheritance diagram for gsGeometrySlice< T >:

Collaboration diagram for gsGeometrySlice< T >:

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

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.
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	deriv_into (const gsMatrix< T > &u, gsMatrix< T > &result) const
	Gives back the derivative of this slice at points u in result.
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
	Gives back the domain dimension of this slice Note that this is one less than the domain dimension of the underlying geometry.
gsMatrix< T >	eval (const gsMatrix< T > &u) const
	Evaluate the function,. More...
void	eval_into (const gsMatrix< T > &u, gsMatrix< T > &result) const
	Gives back the values of this slice at points u in result.
std::vector< gsMatrix< T > >	evalAllDers (const gsMatrix< T > &u, int n, bool sameElement=false) const
	Evaluate all derivatives upto order n,. More...
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. More...
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.
	gsGeometrySlice (const gsGeometrySlice *geoSlice)
	Copyconstructor for new gsGeometrySlice(*this)
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.
virtual 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
index_t	size () const
	size More...
gsMatrix< T >	support () const
	Gives back the parameterRange of this slice in a Matrix.
short_t	targetDim () const
	Gives back the target dimension of this slice Note that this is the same as the target dimension of the underlying geometry.
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	deriv2_into (const gsMatrix< T > &u, gsMatrix< T > &result) const
	Evaluate second derivatives of the function at points u into result. More...
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
void	getFullParMatrix (const gsMatrix< T > &u, gsMatrix< T > &fullU) const
	This function takes a point matrix u and adds the row of the fixed direction filled with the value for it.

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.

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

virtualinherited

Evaluate second derivatives of the function at points u into result.

Let n be the dimension of the source space ( n = domainDim() ).
Let m be the dimension of the image/target space ( m = targetDim() ).
Let N denote the number of evaluation points.

Parameters

[in]	u	gsMatrix of size n x N, where each column of u represents one evaluation point.
[out]	result	gsMatrix of size (S*m) x N, where S=n*(n+1)/2. Each column in result corresponds to one point (i.e., one column in u) and contains the following values (for n=3, m=3): \( (\partial_{xx} f^{(1)}, \partial_{yy} f^{(1)}, \partial_{zz} f^{(1)}, \partial_{xy} f^{(1)}, \partial_{xz} f^{(1)}, \partial_{yz} f^{(1)}, \partial_{xx} f^{(2)},\ldots,\partial_{yz} f^{(3)} )^T\)

Warning

By default uses central finite differences with h=0.00001! One must override this function in derived classes to get proper results.

Reimplemented from gsFunctionSet< T >.

Reimplemented in gsGeometry< T >, gsFunctionExpr< T >, gsConstantFunction< T >, gsPreCICEFunction< T >, gsAffineFunction< T >, gsMappedSingleSpline< d, T >, gsGeometryTransform< T >, and gsFuncCoordinate< 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

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

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).

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 >.