Eigen-unsupported  3.3.7 Eigen::Spline< _Scalar, _Dim, _Degree > Class Template Reference

## Detailed Description

### template<typename _Scalar, int _Dim, int _Degree> class Eigen::Spline< _Scalar, _Dim, _Degree >

A class representing multi-dimensional spline curves.

The class represents B-splines with non-uniform knot vectors. Each control point of the B-spline is associated with a basis function Template Parameters
 _Scalar The underlying data type (typically float or double) _Dim The curve dimension (e.g. 2 or 3) _Degree Per default set to Dynamic; could be set to the actual desired degree for optimization purposes (would result in stack allocation of several temporary variables).

## Public Types

enum  { Dimension }

enum  { Degree }

typedef SplineTraits< Spline >::BasisDerivativeType BasisDerivativeType
The data type used to store the values of the basis function derivatives.

typedef SplineTraits< Spline >::BasisVectorType BasisVectorType
The data type used to store non-zero basis functions.

typedef SplineTraits< Spline >::ControlPointVectorType ControlPointVectorType
The data type representing the spline's control points.

typedef SplineTraits< Spline >::KnotVectorType KnotVectorType
The data type used to store knot vectors.

typedef SplineTraits< Spline >::ParameterVectorType ParameterVectorType
The data type used to store parameter vectors.

typedef SplineTraits< Spline >::PointType PointType
The point type the spline is representing.

typedef _Scalar Scalar

## Public Member Functions

SplineTraits< Spline >::BasisDerivativeType basisFunctionDerivatives (Scalar u, DenseIndex order) const
Computes the non-zero spline basis function derivatives up to given order. More...

template<int DerivativeOrder>
SplineTraits< Spline, DerivativeOrder >::BasisDerivativeType basisFunctionDerivatives (Scalar u, DenseIndex order=DerivativeOrder) const
Computes the non-zero spline basis function derivatives up to given order. More...

SplineTraits< Spline >::BasisVectorType basisFunctions (Scalar u) const
Computes the non-zero basis functions at the given site. More...

const ControlPointVectorTypectrls () const
Returns the ctrls of the underlying spline.

DenseIndex degree () const
Returns the spline degree.

SplineTraits< Spline >::DerivativeType derivatives (Scalar u, DenseIndex order) const
Evaluation of spline derivatives of up-to given order. More...

template<int DerivativeOrder>
SplineTraits< Spline, DerivativeOrder >::DerivativeType derivatives (Scalar u, DenseIndex order=DerivativeOrder) const
Evaluation of spline derivatives of up-to given order. More...

const KnotVectorTypeknots () const
Returns the knots of the underlying spline.

PointType operator() (Scalar u) const
Returns the spline value at a given site . More...

DenseIndex span (Scalar u) const
Returns the span within the knot vector in which u is falling. More...

Spline ()
Creates a (constant) zero spline. For Splines with dynamic degree, the resulting degree will be 0.

template<typename OtherVectorType , typename OtherArrayType >
Spline (const OtherVectorType &knots, const OtherArrayType &ctrls)
Creates a spline from a knot vector and control points. More...

template<int OtherDegree>
Spline (const Spline< Scalar, Dimension, OtherDegree > &spline)
Copy constructor for splines. More...

## Static Public Member Functions

static BasisDerivativeType BasisFunctionDerivatives (const Scalar u, const DenseIndex order, const DenseIndex degree, const KnotVectorType &knots)
Computes the non-zero spline basis function derivatives up to given order. More...

static BasisVectorType BasisFunctions (Scalar u, DenseIndex degree, const KnotVectorType &knots)
Returns the spline's non-zero basis functions. More...

static DenseIndex Span (typename SplineTraits< Spline >::Scalar u, DenseIndex degree, const typename SplineTraits< Spline >::KnotVectorType &knots)
Computes the span within the provided knot vector in which u is falling.

## ◆ Scalar

template<typename _Scalar, int _Dim, int _Degree>
 typedef _Scalar Eigen::Spline< _Scalar, _Dim, _Degree >::Scalar

The spline curve's scalar type.

## ◆ anonymous enum

template<typename _Scalar, int _Dim, int _Degree>
 anonymous enum
Enumerator
Dimension

The spline curve's dimension.

## ◆ anonymous enum

template<typename _Scalar, int _Dim, int _Degree>
 anonymous enum
Enumerator
Degree

The spline curve's degree.

## ◆ Spline() [1/2]

template<typename _Scalar, int _Dim, int _Degree>
template<typename OtherVectorType , typename OtherArrayType >
 Eigen::Spline< _Scalar, _Dim, _Degree >::Spline ( const OtherVectorType & knots, const OtherArrayType & ctrls )
inline

Creates a spline from a knot vector and control points.

Parameters
 knots The spline's knot vector. ctrls The spline's control point vector.

## ◆ Spline() [2/2]

template<typename _Scalar, int _Dim, int _Degree>
template<int OtherDegree>
 Eigen::Spline< _Scalar, _Dim, _Degree >::Spline ( const Spline< Scalar, Dimension, OtherDegree > & spline )
inline

Copy constructor for splines.

Parameters
 spline The input spline.

## ◆ basisFunctionDerivatives() [1/2]

template<typename _Scalar , int _Dim, int _Degree>
 SplineTraits< Spline< _Scalar, _Dim, _Degree >, DerivativeOrder >::BasisDerivativeType Eigen::Spline< _Scalar, _Dim, _Degree >::basisFunctionDerivatives ( Scalar u, DenseIndex order ) const

Computes the non-zero spline basis function derivatives up to given order.

The function computes with i ranging from 0 up to the specified order.

Parameters
 u Parameter at which the non-zero basis function derivatives are computed. order The order up to which the basis function derivatives are computes.

## ◆ basisFunctionDerivatives() [2/2]

template<typename _Scalar, int _Dim, int _Degree>
template<int DerivativeOrder>
 SplineTraits::BasisDerivativeType Eigen::Spline< _Scalar, _Dim, _Degree >::basisFunctionDerivatives ( Scalar u, DenseIndex order = DerivativeOrder ) const

Computes the non-zero spline basis function derivatives up to given order.

The function computes with i ranging from 0 up to the specified order.

Parameters
 u Parameter at which the non-zero basis function derivatives are computed. order The order up to which the basis function derivatives are computes. Using the template version of this function is more efficieent since temporary objects are allocated on the stack whenever this is possible.

## ◆ BasisFunctionDerivatives()

template<typename _Scalar, int _Dim, int _Degree>
 SplineTraits< Spline< _Scalar, _Dim, _Degree > >::BasisDerivativeType Eigen::Spline< _Scalar, _Dim, _Degree >::BasisFunctionDerivatives ( const Scalar u, const DenseIndex order, const DenseIndex degree, const KnotVectorType & knots )
static

Computes the non-zero spline basis function derivatives up to given order.

The function computes with i ranging from 0 up to the specified order.

Parameters
 u Parameter at which the non-zero basis function derivatives are computed. order The order up to which the basis function derivatives are computes. degree The degree of the underlying spline knots The underlying spline's knot vector.

## ◆ basisFunctions()

template<typename _Scalar , int _Dim, int _Degree>
 SplineTraits< Spline< _Scalar, _Dim, _Degree > >::BasisVectorType Eigen::Spline< _Scalar, _Dim, _Degree >::basisFunctions ( Scalar u ) const

Computes the non-zero basis functions at the given site.

Splines have local support and a point from their image is defined by exactly control points where is the spline degree.

This function computes the non-zero basis function values for a given parameter value . It returns Parameters
 u Parameter at which the non-zero basis functions are computed.

## ◆ BasisFunctions()

template<typename _Scalar, int _Dim, int _Degree>
 Spline< _Scalar, _Dim, _Degree >::BasisVectorType Eigen::Spline< _Scalar, _Dim, _Degree >::BasisFunctions ( Scalar u, DenseIndex degree, const KnotVectorType & knots )
static

Returns the spline's non-zero basis functions.

The function computes and returns Parameters
 u The site at which the basis functions are computed. degree The degree of the underlying spline. knots The underlying spline's knot vector.

## ◆ derivatives() [1/2]

template<typename _Scalar , int _Dim, int _Degree>
 SplineTraits< Spline< _Scalar, _Dim, _Degree >, DerivativeOrder >::DerivativeType Eigen::Spline< _Scalar, _Dim, _Degree >::derivatives ( Scalar u, DenseIndex order ) const

Evaluation of spline derivatives of up-to given order.

The function returns for i ranging between 0 and order.

Parameters
 u Parameter at which the spline derivative is evaluated. order The order up to which the derivatives are computed.

## ◆ derivatives() [2/2]

template<typename _Scalar, int _Dim, int _Degree>
template<int DerivativeOrder>
 SplineTraits::DerivativeType Eigen::Spline< _Scalar, _Dim, _Degree >::derivatives ( Scalar u, DenseIndex order = DerivativeOrder ) const

Evaluation of spline derivatives of up-to given order.

The function returns for i ranging between 0 and order.

Parameters
 u Parameter at which the spline derivative is evaluated. order The order up to which the derivatives are computed. Using the template version of this function is more efficieent since temporary objects are allocated on the stack whenever this is possible.

## ◆ operator()()

template<typename _Scalar , int _Dim, int _Degree>
 Spline< _Scalar, _Dim, _Degree >::PointType Eigen::Spline< _Scalar, _Dim, _Degree >::operator() ( Scalar u ) const

Returns the spline value at a given site .

The function returns Parameters
 u Parameter at which the spline is evaluated.
Returns
The spline value at the given location .

## ◆ span()

template<typename _Scalar , int _Dim, int _Degree>
 DenseIndex Eigen::Spline< _Scalar, _Dim, _Degree >::span ( Scalar u ) const

Returns the span within the knot vector in which u is falling.

Parameters
 u The site for which the span is determined.

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