NuTo::Nurbs< TDimParameter > Class Template Reference

Class for NURBS curves, with IGA specific functions. NURBS specific algorithms taken from Piegl, Tiller 'The NURBS book' 1996. More...

#include <Nurbs.h>

Public Types
enum	mParametrization { chord, centripetal }

Public Member Functions
	Nurbs (const std::array< std::vector< double >, TDimParameter > &knots, const std::vector< std::vector< NodeSimple * >> &controlPoints, const std::vector< std::vector< double >> &weights, const std::array< int, TDimParameter > &degree)
	Constructors. More...
int	GetDimension () const
	Getter. More...
int	GetNumControlPointsElement (int dir) const
	get the number of control points for each IGA element (one parametric span) in a specific direction More...
int	GetNumControlPointsElement () const
	get the number of control points for each IGA element (one parametric span) More...
std::array< Eigen::Vector2d, TDimParameter >	GetKnotVectorElement (std::array< int, TDimParameter > knotIDs) const
	get the knots to given knot ids More...
Eigen::VectorXd	GetControlPointsElement (const std::array< int, TDimParameter > &knotID, int instance=0) const
Eigen::VectorXd	Evaluate (const Eigen::Matrix< double, TDimParameter, 1 > &parameter, int derivativeOrder=0) const
	Evaluation. More...
const std::array< int, TDimParameter >	FindSpan (const Eigen::Matrix< double, TDimParameter, 1 > &parameter) const
	calculates the knot span to given parameters More...
Eigen::MatrixXd	BasisFunctionsAndDerivativesRational (int der, const Eigen::Matrix< double, TDimParameter, 1 > &parameter) const
template<>
Eigen::VectorXd	GetControlPointsElement (const std::array< int, 1 > &knotID, int instance) const
template<>
Eigen::VectorXd	GetControlPointsElement (const std::array< int, 2 > &knotID, int instance) const
template<>
Eigen::MatrixXd	BasisFunctionsAndDerivativesRational (int der, const Eigen::Matrix< double, 1, 1 > &parameter) const
template<>
Eigen::MatrixXd	BasisFunctionsAndDerivativesRational (int der, const Eigen::Matrix< double, 2, 1 > &parameter) const

Static Public Member Functions
static int	FindSpan (double parameter, int degree, const std::vector< double > &knots)
	Basis Functions. More...
static Eigen::MatrixXd	BasisFunctionsAndDerivatives (int derivativeOrder, double parameter, int spanIdx, int degree, const std::vector< double > &knots)
	calculates the basisfunctions and derivatives, see Piegl/Tiller 'NURBS Book' 2nd ed., Page 72 More...
static Eigen::VectorXd	BasisFunctionsAndDerivativesRational (int derivativeOrder, double parameter, int spanIdx, int degree, const std::vector< double > &knots, const std::vector< double > &weights)
	calculates the basisfunctions and derivatives, see Piegl/Tiller 'NURBS Book' 2nd ed., Page 72 More...

Detailed Description

template<int TDimParameter>
class NuTo::Nurbs< TDimParameter >

Class for NURBS curves, with IGA specific functions. NURBS specific algorithms taken from Piegl, Tiller 'The NURBS book' 1996.

Author

Peter Otto, BAM

Date

September, 2017

Template Parameters

TDimParameter

dimension of the parametric space: curve is 1D and surface is 2D

Member Enumeration Documentation

template<int TDimParameter>

enum NuTo::Nurbs::mParametrization

Enumerator
chord
centripetal

Constructor & Destructor Documentation

template<int TDimParameter>

NuTo::Nurbs< TDimParameter >::Nurbs ( const std::array< std::vector< double >, TDimParameter > &  knots, const std::vector< std::vector< NodeSimple * >> &  controlPoints, const std::vector< std::vector< double >> &  weights, const std::array< int, TDimParameter > &  degree  )

inline

Constructors.

constructor

Parameters

degree	degree of the polynomial
knots	knot vector
controlPoints	control points

Member Function Documentation

template<int TDimParameter>

static Eigen::MatrixXd NuTo::Nurbs< TDimParameter >::BasisFunctionsAndDerivatives ( int  derivativeOrder, double  parameter, int  spanIdx, int  degree, const std::vector< double > &  knots  )

inlinestatic

calculates the basisfunctions and derivatives, see Piegl/Tiller 'NURBS Book' 2nd ed., Page 72

Parameters

derivativeOrder	up to order derivativeOrder
parameter	parameter at which the functions are calculated
spanIdx	spanIdx to the parameter
degree	degree of the given NURBS curve
knots	knot vector

Returns

Eigen::MatrixXd matrix containing the shape functions up to derivative der, the row index represents the derivative order

template<int TDimParameter>

static Eigen::VectorXd NuTo::Nurbs< TDimParameter >::BasisFunctionsAndDerivativesRational ( int  derivativeOrder, double  parameter, int  spanIdx, int  degree, const std::vector< double > &  knots, const std::vector< double > &  weights  )

inlinestatic

calculates the basisfunctions and derivatives, see Piegl/Tiller 'NURBS Book' 2nd ed., Page 72

Parameters

derivativeOrder	up to order derivativeOrder
parameter	parameter at which the functions are calculated
spanIdx	spanIdx to the parameter
degree	degree of the given NURBS curve
knots	knot vector
weights	weights vector

Returns

Eigen::VectorXd vector containing the shape functions (no derivatives)

template<int TDimParameter>

Eigen::MatrixXd NuTo::Nurbs< TDimParameter >::BasisFunctionsAndDerivativesRational	(	int	der,
		const Eigen::Matrix< double, TDimParameter, 1 > &	parameter
	)		const

template<>

Eigen::MatrixXd NuTo::Nurbs< 1 >::BasisFunctionsAndDerivativesRational ( int  der, const Eigen::Matrix< double, 1, 1 > &  parameter  ) const

inline

template<>

Eigen::MatrixXd NuTo::Nurbs< 2 >::BasisFunctionsAndDerivativesRational ( int  der, const Eigen::Matrix< double, 2, 1 > &  parameter  ) const

inline

template<int TDimParameter>

Eigen::VectorXd NuTo::Nurbs< TDimParameter >::Evaluate ( const Eigen::Matrix< double, TDimParameter, 1 > &  parameter, int  derivativeOrder = 0  ) const

inline

Evaluation.

template<int TDimParameter>

static int NuTo::Nurbs< TDimParameter >::FindSpan ( double  parameter, int  degree, const std::vector< double > &  knots  )

inlinestatic

Basis Functions.

template<int TDimParameter>

const std::array<int, TDimParameter> NuTo::Nurbs< TDimParameter >::FindSpan ( const Eigen::Matrix< double, TDimParameter, 1 > &  parameter ) const

inline

calculates the knot span to given parameters

Parameters

parameter

parameter(s) at which the functions are calculated

Returns

std::array knot span(s) to given parameter(s)

template<int TDimParameter>

Eigen::VectorXd NuTo::Nurbs< TDimParameter >::GetControlPointsElement	(	const std::array< int, TDimParameter > &	knotID,
		int	instance = 0
	)		const

template<>

Eigen::VectorXd NuTo::Nurbs< 1 >::GetControlPointsElement ( const std::array< int, 1 > &  knotID, int  instance  ) const

inline

template<>

Eigen::VectorXd NuTo::Nurbs< 2 >::GetControlPointsElement ( const std::array< int, 2 > &  knotID, int  instance  ) const

inline

template<int TDimParameter>

int NuTo::Nurbs< TDimParameter >::GetDimension ( ) const

inline

Getter.

get the dimension of the curve = dimension of each control point

Returns

dimension of the curve

template<int TDimParameter>

std::array<Eigen::Vector2d, TDimParameter> NuTo::Nurbs< TDimParameter >::GetKnotVectorElement ( std::array< int, TDimParameter >  knotIDs ) const

inline

get the knots to given knot ids

Returns

knots

template<int TDimParameter>

int NuTo::Nurbs< TDimParameter >::GetNumControlPointsElement ( int  dir ) const

inline

get the number of control points for each IGA element (one parametric span) in a specific direction

Returns

degree + 1

template<int TDimParameter>

int NuTo::Nurbs< TDimParameter >::GetNumControlPointsElement ( ) const

inline

get the number of control points for each IGA element (one parametric span)

Returns

product of the number of control points in each direction

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

• nuto/mechanics/iga/Nurbs.h