mfem::NURBSPatch Class Reference

A NURBS patch can be 1D, 2D, or 3D, and is defined as a tensor product of KnotVectors. More...

#include <nurbs.hpp>

Collaboration diagram for mfem::NURBSPatch:

Public Member Functions
	NURBSPatch (const NURBSPatch &orig)
	Copy constructor.
	NURBSPatch (std::istream &input)
	Constructor using data read from stream input.
	NURBSPatch (const KnotVector *kv0, const KnotVector *kv1, int dim)
	Constructor for a 2D patch. dim is the physical dimension plus 1.
	NURBSPatch (const KnotVector *kv0, const KnotVector *kv1, const KnotVector *kv2, int dim)
	Constructor for a 3D patch.
	NURBSPatch (const KnotVector *kv0, const KnotVector *kv1, int dim_, const real_t *control_points)
	NURBSPatch (const KnotVector *kv0, const KnotVector *kv1, const KnotVector *kv2, int dim_, const real_t *control_points)
	NURBSPatch (Array< const KnotVector * > &kv_, int dim_, const real_t *control_points)
	NURBSPatch (Array< const KnotVector * > &kv, int dim)
	Constructor for a patch of dimension equal to the size of kv.
NURBSPatch &	operator= (const NURBSPatch &)=delete
	Copy assignment not supported.
	~NURBSPatch ()
	Deletes data and KnotVectors.
void	Print (std::ostream &os) const
	Writes KnotVectors and data to the stream os.
void	DegreeElevate (int dir, int t)
	Increase the order in direction dir by t >= 0.
void	DegreeElevate (int t)
	Increase the order in all directions by t >= 0.
void	KnotInsert (int dir, const KnotVector &knot)
	Insert any new knots from knot in direction dir. If the order of knot is higher than the current order in direction dir, then the order is elevated in that direction to match.
void	KnotInsert (int dir, const Vector &knot)
	Insert knots from knot in direction dir. If a knot already exists, then it is still added, increasing its multiplicity.
void	KnotInsert (Array< Vector * > &knot)
	Call KnotInsert for each direction with the corresponding knot entry.
void	KnotInsert (Array< KnotVector * > &knot)
	Insert knots from knot determined by Difference, in each direction.
int	KnotRemove (int dir, real_t knot, int ntimes=1, real_t tol=1.0e-12)
	Remove knot with value knot from direction dir.
void	KnotRemove (int dir, Vector const &knot, real_t tol=1.0e-12)
	Remove all knots in knot once.
void	KnotRemove (Array< Vector * > &knot, real_t tol=1.0e-12)
	Remove all knots in knot once, for each direction.
void	UniformRefinement (int rf=2, int multiplicity=1)
	Refine with optional refinement factor rf. Uniform means refinement is done everywhere by the same factor, although nonuniform spacing functions may be used.
void	UniformRefinement (const Array< int > &rf, int multiplicity=1)
void	UniformRefinement (const std::vector< Array< int > > &rf, bool coarsened=false, int multiplicity=1)
	Flag coarsened indicates whether the patch is a single element.
void	Coarsen (int cf=2, real_t tol=1.0e-12)
	Coarsen with optional coarsening factor cf which divides the number of elements in each dimension. Nonuniform spacing functions may be used in each direction.
void	Coarsen (const Array< int > &cf, real_t tol=1.0e-12)
void	GetCoarseningFactors (Array< int > &f) const
	Calls KnotVector::GetCoarseningFactor for each direction.
void	SetKnotVectorsCoarse (bool c)
	Marks the KnotVector in each dimension as coarse.
void	FullyCoarsen (const Array2D< double > &cp, int ncp1D)
	Coarsen to a single element.
void	UpdateSpacingPartitions (const Array< KnotVector * > &pkv)
	Update piecewise spacing function partitions to match refined pkv.
int	GetNC () const
	Return the number of components stored in the NURBSPatch.
int	GetNKV () const
	Return the number of KnotVectors, which is the patch dimension.
KnotVector *	GetKV (int dir)
real_t &	operator() (int i, int l)
	1D access function. i is a B-NET index, and l is a variable index.
const real_t &	operator() (int i, int l) const
real_t &	operator() (int i, int j, int l)
	2D access function. i, j are B-NET indices, and l is a variable index.
const real_t &	operator() (int i, int j, int l) const
real_t &	operator() (int i, int j, int k, int l)
	3D access function. i, j, k are B-NET indices, and l is a variable index.
const real_t &	operator() (int i, int j, int k, int l) const
void	FlipDirection (int dir)
	Reverse data and knots in direction dir.
void	SwapDirections (int dir1, int dir2)
	Swap data and KnotVectors in directions dir1 and dir2.
void	Rotate (real_t angle, real_t normal[]=NULL)
	Rotate the NURBSPatch in 2D or 3D..
void	Rotate2D (real_t angle)
	Rotate the NURBSPatch, 2D case.
void	Rotate3D (real_t normal[], real_t angle)
	Rotate the NURBSPatch, 3D case.
int	MakeUniformDegree (int degree=-1)

Static Public Member Functions
static void	Get2DRotationMatrix (real_t angle, DenseMatrix &T)
	Compute the 2D rotation matrix T for angle angle.
static void	Get3DRotationMatrix (real_t n[], real_t angle, real_t r, DenseMatrix &T)
	Compute the 3D rotation matrix T for angle angle around axis n (a 3D vector, not necessarily normalized) and scalar factor r.

Protected Member Functions
int	SetLoopDirection (int dir)
	Flattens the B-NET in direction dir, producing a 1D net. Returns the number of variables per knot in flattened structure.
real_t &	slice (int i, int j)
	Access function for the effectively 1D flattened net, where i is a knot index, and j is an index of a variable per knot.
const real_t &	slice (int i, int j) const
	NURBSPatch (NURBSPatch *parent, int dir, int Order, int NCP)
	Copy constructor.
void	swap (NURBSPatch *np)
	Deletes own data, takes data from np, and deletes np.
void	init (int dim)

Protected Attributes
int	ni
	B-NET dimensions.
int	nj
int	nk
int	Dim
	Physical dimension plus 1.
real_t *	data
	Data with the layout (Dim x ni x nj x nk)
Array< KnotVector * >	kv
	KnotVectors in each direction.
int	nd
int	ls
int	sd

Friends
NURBSPatch *	Interpolate (NURBSPatch &p1, NURBSPatch &p2)
	Given two patches p1 and p2 of the same dimensions, create and return a new patch by merging their knots and data.
NURBSPatch *	Revolve3D (NURBSPatch &patch, real_t n[], real_t ang, int times)

Detailed Description

A NURBS patch can be 1D, 2D, or 3D, and is defined as a tensor product of KnotVectors.

Definition at line 225 of file nurbs.hpp.

Constructor & Destructor Documentation

NURBSPatch() [1/9]

mfem::NURBSPatch::NURBSPatch ( NURBSPatch * parent, int dir, int Order, int NCP )

protected

Copy constructor.

Definition at line 959 of file nurbs.cpp.

NURBSPatch() [2/9]

mfem::NURBSPatch::NURBSPatch

(

const NURBSPatch &

orig

)

Copy constructor.

Definition at line 873 of file nurbs.cpp.

NURBSPatch() [3/9]

mfem::NURBSPatch::NURBSPatch

(

std::istream &

input

)

Constructor using data read from stream input.

Definition at line 889 of file nurbs.cpp.

NURBSPatch() [4/9]

mfem::NURBSPatch::NURBSPatch	(	const KnotVector *	kv0,
		const KnotVector *	kv1,
		int	dim )

Constructor for a 2D patch. dim is the physical dimension plus 1.

Definition at line 931 of file nurbs.cpp.

NURBSPatch() [5/9]

mfem::NURBSPatch::NURBSPatch	(	const KnotVector *	kv0,
		const KnotVector *	kv1,
		const KnotVector *	kv2,
		int	dim )

Constructor for a 3D patch.

Definition at line 939 of file nurbs.cpp.

NURBSPatch() [6/9]

mfem::NURBSPatch::NURBSPatch	(	const KnotVector *	kv0,
		const KnotVector *	kv1,
		int	dim_,
		const real_t *	control_points )

Create a bivariate NURBS patch with given control points. See n-variate overload for additional notes.

Definition at line 5396 of file nurbs.cpp.

NURBSPatch() [7/9]

mfem::NURBSPatch::NURBSPatch	(	const KnotVector *	kv0,
		const KnotVector *	kv1,
		const KnotVector *	kv2,
		int	dim_,
		const real_t *	control_points )

Create a trivariate NURBS patch with given control points. See n-variate overload for additional notes.

Definition at line 5406 of file nurbs.cpp.

NURBSPatch() [8/9]

mfem::NURBSPatch::NURBSPatch	(	Array< const KnotVector * > &	kv_,
		int	dim_,
		const real_t *	control_points )

Create an n-variate NURBS patch with given control points of dimension dim_, where n is the length of the array of knot vectors and dim_ includes the weight. The array of control point coordinates stores each point's coordinates contiguously, and points are ordered in a standard ijk grid ordering.

Definition at line 5418 of file nurbs.cpp.

NURBSPatch() [9/9]

mfem::NURBSPatch::NURBSPatch	(	Array< const KnotVector * > &	kv,
		int	dim )

Constructor for a patch of dimension equal to the size of kv.

Definition at line 949 of file nurbs.cpp.

~NURBSPatch()

mfem::NURBSPatch::~NURBSPatch

(

)

Deletes data and KnotVectors.

Definition at line 1000 of file nurbs.cpp.

Member Function Documentation

Coarsen() [1/2]

void mfem::NURBSPatch::Coarsen	(	const Array< int > &	cf,
		real_t	tol = 1.0e-12 )

Definition at line 1196 of file nurbs.cpp.

Coarsen() [2/2]

void mfem::NURBSPatch::Coarsen	(	int	cf = 2,
		real_t	tol = 1.0e-12 )

Coarsen with optional coarsening factor cf which divides the number of elements in each dimension. Nonuniform spacing functions may be used in each direction.

Parameters

[in]	cf	Optional coarsening factor. If scalar, the factor is used for all dimensions. If an array, factors can be specified for each dimension.
[in]	tol	NURBS geometry deviation tolerance, cf. Algorithm A5.8 of "The NURBS Book", 2nd ed, Piegl and Tiller.

Definition at line 1218 of file nurbs.cpp.

DegreeElevate() [1/2]

void mfem::NURBSPatch::DegreeElevate	(	int	dir,
		int	t )

Increase the order in direction dir by t >= 0.

Definition at line 1611 of file nurbs.cpp.

DegreeElevate() [2/2]

void mfem::NURBSPatch::DegreeElevate

(

int

t

)

Increase the order in all directions by t >= 0.

Definition at line 1602 of file nurbs.cpp.

FlipDirection()

void mfem::NURBSPatch::FlipDirection

(

int

dir

)

Reverse data and knots in direction dir.

Definition at line 1867 of file nurbs.cpp.

FullyCoarsen()

void mfem::NURBSPatch::FullyCoarsen	(	const Array2D< double > &	cp,
		int	ncp1D )

Coarsen to a single element.

Definition at line 2161 of file nurbs.cpp.

Get2DRotationMatrix()

void mfem::NURBSPatch::Get2DRotationMatrix ( real_t angle, DenseMatrix & T )

static

Compute the 2D rotation matrix T for angle angle.

Definition at line 1921 of file nurbs.cpp.

Get3DRotationMatrix()

void mfem::NURBSPatch::Get3DRotationMatrix ( real_t n[], real_t angle, real_t r, DenseMatrix & T )

static

Compute the 3D rotation matrix T for angle angle around axis n (a 3D vector, not necessarily normalized) and scalar factor r.

Definition at line 1959 of file nurbs.cpp.

GetCoarseningFactors()

void mfem::NURBSPatch::GetCoarseningFactors

(

Array< int > &

f

)

const

Calls KnotVector::GetCoarseningFactor for each direction.

Definition at line 1225 of file nurbs.cpp.

GetKV()

KnotVector * mfem::NURBSPatch::GetKV ( int dir )

inline

Return a pointer to the KnotVector in direction dir.

Note

The returned object should NOT be deleted by the caller.

Definition at line 402 of file nurbs.hpp.

GetNC()

int mfem::NURBSPatch::GetNC ( ) const

inline

Return the number of components stored in the NURBSPatch.

Definition at line 395 of file nurbs.hpp.

GetNKV()

int mfem::NURBSPatch::GetNKV ( ) const

inline

Return the number of KnotVectors, which is the patch dimension.

Definition at line 398 of file nurbs.hpp.

init()

void mfem::NURBSPatch::init ( int dim )

protected

Sets dimensions and allocates data, based on KnotVectors. dim is the physical dimension plus 1.

Definition at line 811 of file nurbs.cpp.

KnotInsert() [1/4]

void mfem::NURBSPatch::KnotInsert

(

Array< KnotVector * > &

knot

)

Insert knots from knot determined by Difference, in each direction.

Definition at line 1234 of file nurbs.cpp.

KnotInsert() [2/4]

void mfem::NURBSPatch::KnotInsert

(

Array< Vector * > &

knot

)

Call KnotInsert for each direction with the corresponding knot entry.

Definition at line 1269 of file nurbs.cpp.

KnotInsert() [3/4]

void mfem::NURBSPatch::KnotInsert	(	int	dir,
		const KnotVector &	knot )

Insert any new knots from knot in direction dir. If the order of knot is higher than the current order in direction dir, then the order is elevated in that direction to match.

Definition at line 1243 of file nurbs.cpp.

KnotInsert() [4/4]

void mfem::NURBSPatch::KnotInsert	(	int	dir,
		const Vector &	knot )

Insert knots from knot in direction dir. If a knot already exists, then it is still added, increasing its multiplicity.

Definition at line 1296 of file nurbs.cpp.

KnotRemove() [1/3]

void mfem::NURBSPatch::KnotRemove	(	Array< Vector * > &	knot,
		real_t	tol = 1.0e-12 )

Remove all knots in knot once, for each direction.

Definition at line 1278 of file nurbs.cpp.

KnotRemove() [2/3]

int mfem::NURBSPatch::KnotRemove	(	int	dir,
		real_t	knot,
		int	ntimes = 1,
		real_t	tol = 1.0e-12 )

Remove knot with value knot from direction dir.

The optional input parameter ntimes specifies the number of times the knot should be removed, default 1. The knot is removed only if the new curve (in direction dir) deviates from the old curve by less than tol.

Returns

The number of times the knot was successfully removed.

Definition at line 1404 of file nurbs.cpp.

KnotRemove() [3/3]

void mfem::NURBSPatch::KnotRemove	(	int	dir,
		Vector const &	knot,
		real_t	tol = 1.0e-12 )

Remove all knots in knot once.

Definition at line 1286 of file nurbs.cpp.

MakeUniformDegree()

int mfem::NURBSPatch::MakeUniformDegree

(

int

degree = -1

)

Elevate KnotVectors in all directions to degree degree if given, otherwise to the maximum current degree among all directions.

Definition at line 2026 of file nurbs.cpp.

operator()() [1/6]

real_t & mfem::NURBSPatch::operator() ( int i, int j, int k, int l )

inline

3D access function. i, j, k are B-NET indices, and l is a variable index.

Definition at line 1264 of file nurbs.hpp.

operator()() [2/6]

const real_t & mfem::NURBSPatch::operator() ( int i, int j, int k, int l ) const

inline

Definition at line 1277 of file nurbs.hpp.

operator()() [3/6]

real_t & mfem::NURBSPatch::operator() ( int i, int j, int l )

inline

2D access function. i, j are B-NET indices, and l is a variable index.

Definition at line 1238 of file nurbs.hpp.

operator()() [4/6]

const real_t & mfem::NURBSPatch::operator() ( int i, int j, int l ) const

inline

Definition at line 1251 of file nurbs.hpp.

operator()() [5/6]

real_t & mfem::NURBSPatch::operator() ( int i, int l )

inline

1D access function. i is a B-NET index, and l is a variable index.

Definition at line 1212 of file nurbs.hpp.

operator()() [6/6]

const real_t & mfem::NURBSPatch::operator() ( int i, int l ) const

inline

Definition at line 1225 of file nurbs.hpp.

operator=()

NURBSPatch & mfem::NURBSPatch::operator= ( const NURBSPatch & )

delete

Copy assignment not supported.

Print()

void mfem::NURBSPatch::Print

(

std::ostream &

os

)

const

Writes KnotVectors and data to the stream os.

The output is formatted for writing a mesh to file. This function is called by NURBSExtension::Print.

Definition at line 1013 of file nurbs.cpp.

Rotate()

void mfem::NURBSPatch::Rotate	(	real_t	angle,
		real_t	normal[] = NULL )

Rotate the NURBSPatch in 2D or 3D..

A rotation of a 2D NURBS-patch requires an angle only. Rotating a 3D NURBS-patch requires a normal as well.

Definition at line 1904 of file nurbs.cpp.

Rotate2D()

void mfem::NURBSPatch::Rotate2D

(

real_t

angle

)

Rotate the NURBSPatch, 2D case.

Definition at line 1933 of file nurbs.cpp.

Rotate3D()

void mfem::NURBSPatch::Rotate3D	(	real_t	normal[],
		real_t	angle )

Rotate the NURBSPatch, 3D case.

Definition at line 2000 of file nurbs.cpp.

SetKnotVectorsCoarse()

void mfem::NURBSPatch::SetKnotVectorsCoarse

(

bool

c

)

Marks the KnotVector in each dimension as coarse.

Definition at line 2156 of file nurbs.cpp.

SetLoopDirection()

int mfem::NURBSPatch::SetLoopDirection ( int dir )

protected

Flattens the B-NET in direction dir, producing a 1D net. Returns the number of variables per knot in flattened structure.

Definition at line 1037 of file nurbs.cpp.

slice() [1/2]

real_t & mfem::NURBSPatch::slice ( int i, int j )

inlineprotected

Access function for the effectively 1D flattened net, where i is a knot index, and j is an index of a variable per knot.

Definition at line 1189 of file nurbs.hpp.

slice() [2/2]

const real_t & mfem::NURBSPatch::slice ( int i, int j ) const

inlineprotected

Definition at line 1200 of file nurbs.hpp.

swap()

void mfem::NURBSPatch::swap ( NURBSPatch * np )

protected

Deletes own data, takes data from np, and deletes np.

Definition at line 974 of file nurbs.cpp.

SwapDirections()

void mfem::NURBSPatch::SwapDirections	(	int	dir1,
		int	dir2 )

Swap data and KnotVectors in directions dir1 and dir2.

Note

Direction pairs (0,2) and (2,0) are not supported, resulting in an error being thrown.

Definition at line 1879 of file nurbs.cpp.

UniformRefinement() [1/3]

void mfem::NURBSPatch::UniformRefinement	(	const Array< int > &	rf,
		int	multiplicity = 1 )

Definition at line 1112 of file nurbs.cpp.

UniformRefinement() [2/3]

void mfem::NURBSPatch::UniformRefinement	(	const std::vector< Array< int > > &	rf,
		bool	coarsened = false,
		int	multiplicity = 1 )

Flag coarsened indicates whether the patch is a single element.

Definition at line 1128 of file nurbs.cpp.

UniformRefinement() [3/3]

void mfem::NURBSPatch::UniformRefinement	(	int	rf = 2,
		int	multiplicity = 1 )

Refine with optional refinement factor rf. Uniform means refinement is done everywhere by the same factor, although nonuniform spacing functions may be used.

Parameters

[in]	rf	Optional refinement factor. If scalar, the factor is used for all dimensions. If an array, factors can be specified for each dimension.
[in]	multiplicity	Optional multiplicity for new knots inserted.

Definition at line 1154 of file nurbs.cpp.

UpdateSpacingPartitions()

void mfem::NURBSPatch::UpdateSpacingPartitions

(

const Array< KnotVector * > &

pkv

)

Update piecewise spacing function partitions to match refined pkv.

Definition at line 1161 of file nurbs.cpp.

Friends And Related Symbol Documentation

Interpolate

NURBSPatch * Interpolate ( NURBSPatch & p1, NURBSPatch & p2 )

friend

Given two patches p1 and p2 of the same dimensions, create and return a new patch by merging their knots and data.

Note

The returned object should be deleted by the caller.

Definition at line 2049 of file nurbs.cpp.

Revolve3D

NURBSPatch * Revolve3D ( NURBSPatch & patch, real_t n[], real_t ang, int times )

friend

Create and return a new patch by revolving patch in 3D.

Note

The returned object should be deleted by the caller.

Definition at line 2096 of file nurbs.cpp.

Member Data Documentation

data

real_t* mfem::NURBSPatch::data

protected

Data with the layout (Dim x ni x nj x nk)

Definition at line 236 of file nurbs.hpp.

Dim

int mfem::NURBSPatch::Dim

protected

Physical dimension plus 1.

Definition at line 233 of file nurbs.hpp.

kv

Array<KnotVector *> mfem::NURBSPatch::kv

protected

KnotVectors in each direction.

Definition at line 239 of file nurbs.hpp.

ls

int mfem::NURBSPatch::ls

protected

Definition at line 253 of file nurbs.hpp.

nd

int mfem::NURBSPatch::nd

protected

Definition at line 252 of file nurbs.hpp.

ni

int mfem::NURBSPatch::ni

protected

B-NET dimensions.

Definition at line 230 of file nurbs.hpp.

nj

int mfem::NURBSPatch::nj

protected

Definition at line 230 of file nurbs.hpp.

nk

int mfem::NURBSPatch::nk

protected

Definition at line 230 of file nurbs.hpp.

sd

int mfem::NURBSPatch::sd

protected

Definition at line 254 of file nurbs.hpp.

---

The documentation for this class was generated from the following files:

• mesh/nurbs.hpp
• mesh/nurbs.cpp