Detailed Description

template<short_t d, class T>
class gismo::gsAlmostC1< d, T >

Constructs the D-Patch, from which the transformation matrix can be called.

Template Parameters

d	parametric dimension

Inheritance diagram for gsAlmostC1< d, T >:

Collaboration diagram for gsAlmostC1< d, T >:

Public Types
typedef memory::shared_ptr < gsAlmostC1 >	Ptr
	Shared pointer for gsAlmostC1.

typedef memory::unique_ptr < gsAlmostC1 >	uPtr
	Unique pointer for gsAlmostC1.

Public Member Functions
virtual void	compute ()
	Computes the construction.

virtual void	cornerInfo () const
	Returns information for all the corners in the topology. More...

virtual void	defaultOptions ()
	Sets the default options.

virtual gsGeometry< T > *	exportPatch (index_t patch, bool computeCoefs=true)
	Exports a single modified patch with index patch. More...

virtual gsMultiPatch< T >	exportToPatches (const gsMultiPatch< T > &patches)
	Exports the modified geometry to a gsMultiPatch object. More...

virtual const gsMultiPatch< T > &	getGeometry () const
	Returns the multipatch that is used for the D-Patch.

virtual void	globalBasis_into (gsMappedBasis< d, T > &mbasis) const
	Returns the basis that is used for the D-Patch. Could be THB refined.

virtual void	globalGeometry_into (const gsMultiPatch< T > &patches, gsMappedSpline< d, T > &mspline)
	Returns the multipatch that is used for the D-Patch.

	gsAlmostC1 ()
	Empty constructor.

	gsAlmostC1 (gsMultiPatch< T > const &mp)
	Default constructor. More...

virtual const gsMultiBasis< T > &	localBasis () const
	Returns the basis that is used for the D-Patch. Could be THB refined.

virtual void	localGeometry_into (gsMultiPatch< T > &localGeometry)
	Returns the modified geometry corresponding to the local basis.

virtual void	mapperInfo () const
	Returns for each basis function if it is free or eliminated. More...

virtual const gsSparseMatrix< T > &	matrix () const
	Returns the smoothing matrix. More...

virtual const void	matrix_into (gsSparseMatrix< T > &matrix) const
	Returns the smoothing matrix into matrix. More...

virtual void	sideInfo (patchSide side) const
	Returns information about a vertex. More...

virtual void	sideInfo () const
	Returns information for all the sides in the topology. More...

virtual void	vertexInfo (patchCorner corner) const
	Returns information about a vertex. More...

Protected Member Functions
void	_computeEVs ()
	Computes D-Patch smoothing. More...

virtual void	_computeMapper ()
	Calculates the mapper. More...

virtual void	_computeSmoothMatrix ()
	Calculates the smooth matrix.

void	_countDoFs ()
	Initializes the matrix, the basis and the mappers.

virtual void	_getLowestCorners (std::vector< patchCorner > &pcorners, index_t n=3) const
	From a list of patchCorners pcorners, get the lowest n corners. More...

virtual void	_getLowestIndices (std::vector< std::pair< index_t, index_t >> &indices, index_t n=3) const
	From a list of tuples (patch,index), get the lowest n tuples. More...

virtual const index_t	_getValence (patchCorner corner) const
	Gets the valence. More...

virtual void	_handleBoundary (patchSide side)
	Handles a boundary in the global matrix. More...

virtual void	_handleInterface (boundaryInterface iface)
	Handles an interface in the global matrix. More...

virtual void	_handleInterior ()
	Handles the interior in the global matrix. More...

void	_handleInteriorVertex (patchCorner pcorner, index_t valence)
	Handles a vertex in the global matrix. More...

virtual void	_handleRegularCorner (patchCorner pcorner)
	Handles a regular corner. More...

virtual void	_handleVertex (patchCorner pcorner)
	Handles a vertex in the global matrix. More...

virtual const index_t	_indexFromSides (index_t index1, const patchSide side1, index_t index2, const patchSide side2)
	Computes the index of a basis function using sides as reference. More...

virtual const index_t	_indexFromVert (const index_t index, const patchCorner corner, const patchSide side, const index_t offsets=0) const
	Computes the index of a basis function taking one corner and one side as reference. More...

void	_initBasis ()
	Initializes the basis.

virtual void	_initChecks ()
	Prepares the THB basis if needed. More...

virtual void	_initialize ()
	Initializes the class: -.

virtual void	_initMappers ()
	Initializes the matrix, the basis and the mappers.

virtual void	_initMatrix ()
	Initializes the matrix.

void	_initTHB ()
	Initializes the matrix, the basis and the mappers.

virtual const bool	_isInteriorVertex (patchCorner corner) const
	Determines whether the specified corner is interior vertex. More...

void	_makeTHB ()
	Prepares the THB basis if needed. More...

virtual void	_performChecks (bool basis)
	Performs checks on sides, vertices and bases.

gsMatrix< T >	_preCoefficients ()
	Computes the C1 coefficients for pre-multiplication to make the multipatch. More...

gsMatrix< T >	_preCoefficients (const gsMultiPatch< T > &patches)
	Computes the C1 coefficients for pre-multiplication to make the multipatch. More...

virtual void	_removeLowestCorners (std::vector< patchCorner > &pcorners, index_t n=3) const
	From a list of patchCorners pcorners, remove all but the lowest n corners. More...

virtual void	_removeLowestIndices (std::vector< std::pair< index_t, index_t >> &indices, index_t n=3) const
	From a list of tuples (patch,index), remove all but the lowest n tuples. More...

virtual void	_resetChecks (bool basis)
	Resets checks on sides, vertices and bases.

virtual const index_t	_sideIndex (index_t patch, boxSide bside) const
	Computes global index of the side. More...

virtual const index_t	_sideIndex (patchSide pside) const
	Computes global index of the side. More...

virtual const std::pair < index_t, bool >	_vertexData (const patchCorner corner) const
	Returns the valence and whether a corner is interior or boundary. More...

virtual const index_t	_vertIndex (index_t patch, boxCorner corner) const
	Computes global index of the corner. More...

virtual const index_t	_vertIndex (patchCorner pcorner) const
	Computes global index of the corner. More...

virtual void	_whichHandled ()
	Prints which DoFs have been handled and which have been eliminated.

gsMatrix< T >	freeCoefficients ()
	Computes the C1 coefficients for pre-multiplication to make the multipatch. More...

virtual std::vector< bool >	getSharpCorners (T tol=1e-2) const
	Checks if corners are sharp or not. More...

void	setCoefficients (const gsMatrix< T > &coefs, gsMultiPatch< T > &mp) const
	Set the coefficients of mp to coefs. More...

Private Member Functions
void	_handleRegularBoundaryVertexNonSmooth (patchCorner pcorner, index_t valence)
	Handles an interface in the global matrix. More...

Constructor & Destructor Documentation

gsAlmostC1 ( gsMultiPatch< T > const & mp )

Default constructor.

Parameters

mp	Multipatch of the geometry

Member Function Documentation

void _computeEVs ( )

protectedvirtual

Computes D-Patch smoothing.

Given a basis with THB refinement around the EVs, this function computes the D-Patch smoothing

Implements gsDPatchBase< d, T >.

void _computeMapper ( )

protectedvirtualinherited

Calculates the mapper.

NOT PARALLEL YET

void _getLowestCorners	(	std::vector< patchCorner > &	pcorners,
		index_t	n = `3`
	)		const

protectedvirtualinherited

From a list of patchCorners pcorners, get the lowest n corners.

Parameters

	pcorners	The pcorners
[in]	n	The number of corners

void _getLowestIndices	(	std::vector< std::pair< index_t, index_t >> &	indices,
		index_t	n = `3`
	)		const

protectedvirtualinherited

From a list of tuples (patch,index), get the lowest n tuples.

Parameters

	pcorners	The pcorners
[in]	n	The number of corners

virtual const index_t _getValence ( patchCorner corner ) const

inlineprotectedvirtualinherited

Gets the valence.

Parameters

[in] corner The corner

Returns: The valence.

void _handleBoundary ( patchSide side )

protectedvirtualinherited

Handles a boundary in the global matrix.

Handles all DoFs on the boundary with unit-weight, except the ones in the 0 and 1 rings around the vertices.

Parameters

[in] side The boundary side

void _handleInterface ( boundaryInterface iface )

protectedvirtualinherited

Handles an interface in the global matrix.

Gives all the DoFs that have offset 1 (orthogonal) from the interface weight 1.0 w.r.t itself. All the DoFs ON the interface (on both patches) will have weight 0.5 to the DoF with offset 1. This interface handling excludes the indices that are in the 0 and 1 ring around vertices.

Parameters

[in] iface The interface

void _handleInterior ( )

protectedvirtualinherited

Handles the interior in the global matrix.

Gives all left-over DoFs, which are in the interior, weight 1 w.r.t. itself

void _handleInteriorVertex	(	patchCorner	pcorner,
		index_t	valence
	)

protectedvirtual

Handles a vertex in the global matrix.

We use the following notation convention (per patch!): b00 is the basis function at the vertex b10 is the basis function next to the vertex along the first interface that connects to the vertex b20 is the basis function next to b10 along the first interface that connects to the vertex etc.

b01 is the basis function next to the vertex along the second interface that connects to the vertex b02 is the basis function next to b01 along the second interface that connects to the vertex etc.

b11 is the basis function with offset 1 from both interfaces and from the vertex itself b22 is the basis function with offset 2 from both interfaces and from the vertex itself etc.

There are different options. a) Boundary vertices i) Valence 1: b00, b10, b01 and b00 all get weight 1.0 w.r.t the same basis function in the local basis ii) Valence 2: This case contains an interface between two patches. We use index k to denote the row basis functions along the interface. So k=0 corresponds to the basis functions on the boundary and k=1 corresponds to the basis functions with offset 1 from the boundaries. Using this convention, the functions bk1 in the local basis, are coupled to bk1 in the global basis with weight 1. The functions bk0 in the local basis (on the considered patch) are coupled to bk1 in the global basis with weight 0.5. The functions bk0 in the local basis (on the other patch) are coupled to bk1 (on the considered patch) in the global basis with weight 0.5. iii)Valence 3: In this case, the matched vertices on all the adjacent patches are treated in one go! Note that all the basis functions corresponding to the vertex (b00) on all patches are matched! We couple the b00 functions of all patches (in the local basis) with weight 1/4 to the b00 of the adjacent patch with the lowest number in the global basis. Then, the b11 on the considered patch is coupled with weight 1 to itself and with weight 0.25 to the b00s of the other patches. Then, we will handle the vertices where an interface and a boundary meet (there are two of these). For the patch corners that are on an interface, we find the b11 and b10 vertices (orthogonal to the interface) and we give all b10s weight 0.5 w.r.t. the b11s in the global basis (on both patches). Lastly, we add weight 0.5 for the b10s along the boundaries (so only for two patches) to the (matched) b00 basis function (all b00s refer to the same dof in the global basis). b) Interior vertices (all valences): i) b11 gets weight 1.0 w.r.t the same basis function in the local basis ii) all associated b00s in the local basis get weight 1/valence w.r.t. b11 in the global basis iii)the b10 and b01 in the local basis get weight 1/2 w.r.t. b11 in the global basis

Parameters

[in] pcorner The patchcorner

Reimplemented from gsDPatchBase< d, T >.

void _handleRegularBoundaryVertexNonSmooth	(	patchCorner	pcorner,
		index_t	valence
	)

privatevirtual

Handles an interface in the global matrix.

Gives all the DoFs that have offset 1 (orthogonal) from the interface weight 1.0 w.r.t itself. All the DoFs ON the interface (on both patches) will have weight 0.5 to the DoF with offset 1. This interface handling excludes the indices that are in the 0 and 1 ring around vertices.

Parameters

[in] iface The interface Handles a boundary in the global matrix

Handles all DoFs on the boundary with unit-weight, except the ones in the 0 and 1 rings around the vertices.

Parameters

[in] side The boundary side Handles the interior in the global matrix

Gives all left-over DoFs, which are in the interior, weight 1 w.r.t. itself Handles a regular corner

Parameters

[in] pcorner The pcorner

Reimplemented from gsDPatchBase< d, T >.

void _handleRegularCorner ( patchCorner pcorner )

protectedvirtualinherited

Handles a regular corner.

Parameters

[in] pcorner The pcorner

void _handleVertex ( patchCorner pcorner )

protectedvirtualinherited

Handles a vertex in the global matrix.

We use the following notation convention (per patch!): b00 is the basis function at the vertex b10 is the basis function next to the vertex along the first interface that connects to the vertex b20 is the basis function next to b10 along the first interface that connects to the vertex etc.

b01 is the basis function next to the vertex along the second interface that connects to the vertex b02 is the basis function next to b01 along the second interface that connects to the vertex etc.

b11 is the basis function with offset 1 from both interfaces and from the vertex itself b22 is the basis function with offset 2 from both interfaces and from the vertex itself etc.

There are different options. a) Boundary vertices i) Valence 1: b00, b10, b01 and b00 all get weight 1.0 w.r.t the same basis function in the local basis ii) Valence 2: This case contains an interface between two patches. We use index k to denote the row basis functions along the interface. So k=0 corresponds to the basis functions on the boundary and k=1 corresponds to the basis functions with offset 1 from the boundaries. Using this convention, the functions bk1 in the local basis, are coupled to bk1 in the global basis with weight 1. The functions bk0 in the local basis (on the considered patch) are coupled to bk1 in the global basis with weight 0.5. The functions bk0 in the local basis (on the other patch) are coupled to bk1 (on the considered patch) in the global basis with weight 0.5. iii)Valence 3: In this case, the matched vertices on all the adjacent patches are treated in one go! Note that all the basis functions corresponding to the vertex (b00) on all patches are matched! We couple the b00 functions of all patches (in the local basis) with weight 1/4 to the b00 of the adjacent patch with the lowest number in the global basis. Then, the b11 on the considered patch is coupled with weight 1 to itself and with weight 0.25 to the b00s of the other patches. Then, we will handle the vertices where an interface and a boundary meet (there are two of these). For the patch corners that are on an interface, we find the b11 and b10 vertices (orthogonal to the interface) and we give all b10s weight 0.5 w.r.t. the b11s in the global basis (on both patches). Lastly, we add weight 0.5 for the b10s along the boundaries (so only for two patches) to the (matched) b00 basis function (all b00s refer to the same dof in the global basis). b) Interior vertices (all valences): i) b11 gets weight 1.0 w.r.t the same basis function in the local basis ii) all associated b00s in the local basis get weight 1/valence w.r.t. b11 in the global basis iii)the b10 and b01 in the local basis get weight 1/2 w.r.t. b11 in the global basis

Parameters

[in] pcorner The patchcorner

const index_t _indexFromSides	(	index_t	index1,
		const patchSide	side1,
		index_t	index2,
		const patchSide	side2
	)

protectedvirtualinherited

Computes the index of a basis function using sides as reference.

Parameters

[in]	index1	The index of the basis function parallel to the first side
[in]	side1	The first side
[in]	index2	The index of the basis function parallel to the second side
[in]	side2	The second side

Returns: Index that is index1 in direction of side1 and index2 in direction of side2

const index_t _indexFromVert	(	const index_t	index,
		const patchCorner	corner,
		const patchSide	side,
		const index_t	offsets = `0`
	)		const

protectedvirtualinherited

Computes the index of a basis function taking one corner and one side as reference.

Parameters

[in]	bases	(optional) Multibasis to evaluate the index on
[in]	index	Offset of the basis function parallel to the side side, measured from corner
[in]	corner	The corner to be measured from
[in]	side	The side which contains corner
[in]	offset	The offset from the side (orthogonal to the side)

Returns: Index of index places from corner along side, with offset offset and with offset levelOffset from the deepest level

void _initChecks ( )

protectedvirtualinherited

Prepares the THB basis if needed.

This function constructs THB refinements on the places where they are needed, i.e. around EVs. It also constructs the transfer matrix (m_tMatrix) forms the transformation between the original B-spline basis and the THB-Spline basis. Computes D-Patch smoothing

Given a basis with THB refinement around the EVs, this function computes the D-Patch smoothing Makes the Pi matrix

This matrix is used to transform the coefficients of the D-Patch smoothing matrix

Parameters

[in] valence The valence

Returns: Matrix for smoothing around an EV} Initializes the matrix, the basis and the mappers

virtual const bool _isInteriorVertex ( patchCorner corner ) const

inlineprotectedvirtualinherited

Determines whether the specified corner is interior vertex.

Parameters

[in] corner The corner

Returns: True if the specified corner is interior vertex, False otherwise.

void _makeTHB ( )

protectedvirtual

Prepares the THB basis if needed.

This function constructs THB refinements on the places where they are needed, i.e. around EVs. It also constructs the transfer matrix (m_tMatrix) forms the transformation between the original B-spline basis and the THB-Spline basis.

Change the coefficients

Handle the EVs

Implements gsDPatchBase< d, T >.

gsMatrix< T > _preCoefficients ( )

protectedvirtual

Computes the C1 coefficients for pre-multiplication to make the multipatch.

Takes the coefficients which are tagged as "free" in the modified DoFMapper (m_mapModified) and when a boundary vertex with valence=3 is present, this one is shifted.

Reimplemented from gsDPatchBase< d, T >.

gsMatrix<T> _preCoefficients ( const gsMultiPatch< T > & patches )

inlineprotectedvirtual

Computes the C1 coefficients for pre-multiplication to make the multipatch.

Takes the coefficients which are tagged as "free" in the modified DoFMapper (m_mapModified) and when a boundary vertex with valence=3 is present, this one is shifted.

Implements gsDPatchBase< d, T >.

void _removeLowestCorners	(	std::vector< patchCorner > &	pcorners,
		index_t	n = `3`
	)		const

protectedvirtualinherited

From a list of patchCorners pcorners, remove all but the lowest n corners.

Parameters

	pcorners	The pcorners
[in]	n	The number of corners

void _removeLowestIndices	(	std::vector< std::pair< index_t, index_t >> &	indices,
		index_t	n = `3`
	)		const

protectedvirtualinherited

From a list of tuples (patch,index), remove all but the lowest n tuples.

Parameters

	pcorners	The pcorners
[in]	n	The number of corners

virtual const index_t _sideIndex	(	index_t	patch,
		boxSide	bside
	)		const

inlineprotectedvirtualinherited

Computes global index of the side.

Parameters

[in]	patch	The patch number
[in]	bside	The boxSide

Returns: Returns a global index of the side

virtual const index_t _sideIndex ( patchSide pside ) const

inlineprotectedvirtualinherited

Computes global index of the side.

Parameters

[in] pside The patchSide

Returns: Returns a global index of the side

const std::pair< index_t, bool > _vertexData ( const patchCorner corner ) const

protectedvirtualinherited

Returns the valence and whether a corner is interior or boundary.

Parameters

[in] corner The patchCorner

Returns: A pair with .first giving the valence and .second being true if the vertex is interior and false if the vertex is on a boundary

virtual const index_t _vertIndex	(	index_t	patch,
		boxCorner	corner
	)		const

inlineprotectedvirtualinherited

Computes global index of the corner.

Parameters

[in]	patch	The patch number
[in]	corner	The boxCorner

Returns: Returns a global index of the corner

virtual const index_t _vertIndex ( patchCorner pcorner ) const

inlineprotectedvirtualinherited

Computes global index of the corner.

Parameters

[in] pcorner The patchCorner

Returns: Returns a global index of the side

void cornerInfo ( ) const

virtualinherited

Returns information for all the corners in the topology.

Returns for all the patches and for all corners (1 to 4) the valence and if it is an interior vertex or a boundary vertex.

gsGeometry< T > * exportPatch	(	index_t	patch,
		bool	computeCoefs = `true`
	)

virtualinherited

Exports a single modified patch with index patch.

The patch is obtained by transforming the coefficients of the D-Patch to the original basis, such that the original basis functions can be used to plot the geometry (and the patch structure will remain intact). To construct the geometry, the coefficients for the C1 basis are multiplied with the transpose of the transformation matrix. The C1 coefficients are obtained with _preCoefficients().

virtual gsMultiPatch<T> exportToPatches ( const gsMultiPatch< T > & patches )

inlinevirtualinherited

Exports the modified geometry to a gsMultiPatch object.

Returns: A multipatch with the geometry

gsMatrix< T > freeCoefficients ( )

protected

Computes the C1 coefficients for pre-multiplication to make the multipatch.

Takes the coefficients which are tagged as "free" in the modified DoFMapper (m_mapModified)

std::vector< bool > getSharpCorners ( T tol = 1e-2 ) const

protectedvirtualinherited

Checks if corners are sharp or not.

Parameters

[in] tol The tolerance

Returns: A vector with a boolean true if the corner is C0 (following in-class corner indexing convention)

void mapperInfo ( ) const

virtualinherited

Returns for each basis function if it is free or eliminated.

Returns for each basis function if it is free or eliminated and checks if the internal mapper is defined correctly

virtual const gsSparseMatrix<T>& matrix ( ) const

inlinevirtualinherited

Returns the smoothing matrix.

The number of columns of the matrix corresponds to the number of basis functions in the local basis; this is the sum of all the basis functions over all the patches. The number of rows of the matrix corresponds to the number of global basis functions, i.e. the number of basis functions corresponding to the D-Patch. Multiplying the basis with the local basis function values gives the values of the basis functions in the global basis.

Returns: A matrix result to transfer local to global coefficients

virtual const void matrix_into ( gsSparseMatrix< T > & matrix ) const

inlinevirtualinherited

Returns the smoothing matrix into matrix.

Parameters

matrix The matrix

void setCoefficients	(	const gsMatrix< T > &	coefs,
		gsMultiPatch< T > &	mp
	)		const

protected

Set the coefficients of mp to coefs.

Parameters

[in]	coefs	The coefs
	mp	The multipatch to update

void sideInfo ( patchSide side ) const

virtualinherited

Returns information about a vertex.

Parameters

[in] patch The patchSide

Returns: Prints the patch number, the side index, the valence and if the side is a boundary or an interface

void sideInfo ( ) const

virtualinherited

Returns information for all the sides in the topology.

Returns for all the patches and for all sides (1 to 4) if it is a boundary or an interface.

void vertexInfo ( patchCorner corner ) const

virtualinherited

Returns information about a vertex.

Parameters

[in] corner The patchCorner

Returns: Prints the patch number, the corner index, the valence and if the corner is an interior or a boundary vertex

Detailed Description

template<short_t d, class T> class gismo::gsAlmostC1< d, T >

Public Types

Public Member Functions

Protected Member Functions

Private Member Functions

Constructor & Destructor Documentation

Member Function Documentation

template<short_t d, class T>
class gismo::gsAlmostC1< d, T >