A class representing multi-dimensional spline curves. More...

#include <Spline.h>

Public Types
enum	{ Dimension = Dim_ }

enum	{ Degree = Degree_ }

typedef Scalar_	Scalar

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

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

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

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

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

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

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

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...

const KnotVectorType &	knots () const
	Returns the knots of the underlying spline. More...

const ControlPointVectorType &	ctrls () const
	Returns the ctrls of the underlying spline. More...

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

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...

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

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...

DenseIndex	degree () const
	Returns the spline degree. More...

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

Static Public Member Functions
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. More...

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

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 Private Member Functions
template<typename DerivativeType >
static void	BasisFunctionDerivativesImpl (const typename Spline< Scalar_, Dim_, Degree_ >::Scalar u, const DenseIndex order, const DenseIndex p, const typename Spline< Scalar_, Dim_, Degree_ >::KnotVectorType &U, DerivativeType &N_)

Private Attributes
KnotVectorType	m_knots

ControlPointVectorType	m_ctrls

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

\begin{align*} C(u) & = \sum_{i=0}^{n}N_{i,p}(u)P_i \end{align*}

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).

Member Typedef Documentation

◆ BasisDerivativeType

template<typename Scalar_ , int Dim_, int Degree_>

typedef SplineTraits<Spline>::BasisDerivativeType Eigen::Spline< Scalar_, Dim_, Degree_ >::BasisDerivativeType

The data type used to store the values of the basis function derivatives.

◆ BasisVectorType

template<typename Scalar_ , int Dim_, int Degree_>

typedef SplineTraits<Spline>::BasisVectorType Eigen::Spline< Scalar_, Dim_, Degree_ >::BasisVectorType

The data type used to store non-zero basis functions.

◆ ControlPointVectorType

template<typename Scalar_ , int Dim_, int Degree_>

typedef SplineTraits<Spline>::ControlPointVectorType Eigen::Spline< Scalar_, Dim_, Degree_ >::ControlPointVectorType

The data type representing the spline's control points.

◆ KnotVectorType

template<typename Scalar_ , int Dim_, int Degree_>

typedef SplineTraits<Spline>::KnotVectorType Eigen::Spline< Scalar_, Dim_, Degree_ >::KnotVectorType

The data type used to store knot vectors.

◆ ParameterVectorType

template<typename Scalar_ , int Dim_, int Degree_>

typedef SplineTraits<Spline>::ParameterVectorType Eigen::Spline< Scalar_, Dim_, Degree_ >::ParameterVectorType

The data type used to store parameter vectors.

◆ PointType

template<typename Scalar_ , int Dim_, int Degree_>

typedef SplineTraits<Spline>::PointType Eigen::Spline< Scalar_, Dim_, Degree_ >::PointType

The point type the spline is representing.

◆ Scalar

template<typename Scalar_ , int Dim_, int Degree_>

typedef Scalar_ Eigen::Spline< Scalar_, Dim_, Degree_ >::Scalar

The spline curve's scalar type.

Member Enumeration Documentation

◆ anonymous enum

template<typename Scalar_ , int Dim_, int Degree_>

anonymous enum

Enumerator
Dimension	The spline curve's dimension.

40 { Dimension = Dim_ };

Eigen::Spline::Dimension

@ Dimension

Definition: Spline.h:40

◆ anonymous enum

template<typename Scalar_ , int Dim_, int Degree_>

anonymous enum

Enumerator
Degree	The spline curve's degree.

41 { Degree = Degree_ };

Eigen::Spline::Degree

@ Degree

Definition: Spline.h:41

Constructor & Destructor Documentation

◆ Spline() [1/3]

template<typename Scalar_ , int Dim_, int Degree_>

Eigen::Spline< Scalar_, Dim_, Degree_ >::Spline ( )

inline

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

       : m_knots(1, (Degree == Dynamic ? 2 : 2 * Degree + 2)),
         m_ctrls(ControlPointVectorType::Zero(Dimension, (Degree == Dynamic ? 1 : Degree + 1))) {
     // in theory this code can go to the initializer list but it will get pretty
     // much unreadable ...
     enum { MinDegree = (Degree == Dynamic ? 0 : Degree) };
     m_knots.template segment<MinDegree + 1>(0) = Array<Scalar, 1, MinDegree + 1>::Zero();
     m_knots.template segment<MinDegree + 1>(MinDegree + 1) = Array<Scalar, 1, MinDegree + 1>::Ones();
   }

References Eigen::Spline< Scalar_, Dim_, Degree_ >::Degree, Eigen::Dynamic, Eigen::Spline< Scalar_, Dim_, Degree_ >::m_knots, and oomph::PseudoSolidHelper::Zero.

◆ Spline() [2/3]

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.

81 : m_knots(knots), m_ctrls(ctrls) {}

Eigen::Spline::ctrls

const ControlPointVectorType & ctrls() const

Returns the ctrls of the underlying spline.

Definition: Spline.h:98

Eigen::Spline::knots

const KnotVectorType & knots() const

Returns the knots of the underlying spline.

Definition: Spline.h:93

◆ Spline() [3/3]

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.

88 : m_knots(spline.knots()), m_ctrls(spline.ctrls()) {}

Member Function Documentation

◆ 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

\begin{align*} \frac{d^i}{du^i} N_{i,p}(u), \hdots, \frac{d^i}{du^i} N_{i+p+1,p}(u) \end{align*}

with i ranging from 0 up to the specified order.

Parameters

u	Parameter \(u \in [0;1]\) 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.

                                                                         {
   typename SplineTraits<Spline>::BasisDerivativeType der;
   BasisFunctionDerivativesImpl(u, order, degree, knots, der);
   return der;
 }

References constants::degree.

◆ 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

\begin{align*} \frac{d^i}{du^i} N_{i,p}(u), \hdots, \frac{d^i}{du^i} N_{i+p+1,p}(u) \end{align*}

with i ranging from 0 up to the specified order.

Parameters

u	Parameter \(u \in [0;1]\) at which the non-zero basis function derivatives are computed.
order	The order up to which the basis function derivatives are computes.

                                                                                          {
   typename SplineTraits<Spline<Scalar_, Dim_, Degree_> >::BasisDerivativeType der;
   BasisFunctionDerivativesImpl(u, order, degree(), knots(), der);
   return der;
 }

References constants::degree.

◆ basisFunctionDerivatives() [2/2]

template<typename Scalar_ , int Dim_, int Degree_>

template<int DerivativeOrder>

SplineTraits<Spline, DerivativeOrder>::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

\begin{align*} \frac{d^i}{du^i} N_{i,p}(u), \hdots, \frac{d^i}{du^i} N_{i+p+1,p}(u) \end{align*}

with i ranging from 0 up to the specified order.

Parameters

u	Parameter \(u \in [0;1]\) 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.

◆ BasisFunctionDerivativesImpl()

template<typename Scalar_ , int Dim_, int Degree_>

template<typename DerivativeType >

void Eigen::Spline< Scalar_, Dim_, Degree_ >::BasisFunctionDerivativesImpl	(	const typename Spline< Scalar_, Dim_, Degree_ >::Scalar	u,
		const DenseIndex	order,
		const DenseIndex	p,
		const typename Spline< Scalar_, Dim_, Degree_ >::KnotVectorType &	U,
		DerivativeType &	N_
	)

staticprivate

                                                                                         {
   typedef Spline<Scalar_, Dim_, Degree_> SplineType;
   enum { Order = SplineTraits<SplineType>::OrderAtCompileTime };
  
   const DenseIndex span = SplineType::Span(u, p, U);
  
   const DenseIndex n = (std::min)(p, order);
  
   N_.resize(n + 1, p + 1);
  
   BasisVectorType left = BasisVectorType::Zero(p + 1);
   BasisVectorType right = BasisVectorType::Zero(p + 1);
  
   Matrix<Scalar, Order, Order> ndu(p + 1, p + 1);
  
   Scalar saved, temp;  // FIXME These were double instead of Scalar. Was there a reason for that?
  
   ndu(0, 0) = 1.0;
  
   DenseIndex j;
   for (j = 1; j <= p; ++j) {
     left[j] = u - U[span + 1 - j];
     right[j] = U[span + j] - u;
     saved = 0.0;
  
     for (DenseIndex r = 0; r < j; ++r) {
       /* Lower triangle */
       ndu(j, r) = right[r + 1] + left[j - r];
       temp = ndu(r, j - 1) / ndu(j, r);
       /* Upper triangle */
       ndu(r, j) = static_cast<Scalar>(saved + right[r + 1] * temp);
       saved = left[j - r] * temp;
     }
  
     ndu(j, j) = static_cast<Scalar>(saved);
   }
  
   for (j = p; j >= 0; --j) N_(0, j) = ndu(j, p);
  
   // Compute the derivatives
   DerivativeType a(n + 1, p + 1);
   DenseIndex r = 0;
   for (; r <= p; ++r) {
     DenseIndex s1, s2;
     s1 = 0;
     s2 = 1;  // alternate rows in array a
     a(0, 0) = 1.0;
  
     // Compute the k-th derivative
     for (DenseIndex k = 1; k <= static_cast<DenseIndex>(n); ++k) {
       Scalar d = 0.0;
       DenseIndex rk, pk, j1, j2;
       rk = r - k;
       pk = p - k;
  
       if (r >= k) {
         a(s2, 0) = a(s1, 0) / ndu(pk + 1, rk);
         d = a(s2, 0) * ndu(rk, pk);
       }
  
       if (rk >= -1)
         j1 = 1;
       else
         j1 = -rk;
  
       if (r - 1 <= pk)
         j2 = k - 1;
       else
         j2 = p - r;
  
       for (j = j1; j <= j2; ++j) {
         a(s2, j) = (a(s1, j) - a(s1, j - 1)) / ndu(pk + 1, rk + j);
         d += a(s2, j) * ndu(rk + j, pk);
       }
  
       if (r <= pk) {
         a(s2, k) = -a(s1, k - 1) / ndu(pk + 1, r);
         d += a(s2, k) * ndu(r, pk);
       }
  
       N_(k, r) = static_cast<Scalar>(d);
       j = s1;
       s1 = s2;
       s2 = j;  // Switch rows
     }
   }
  
   /* Multiply through by the correct factors */
   /* (Eq. [2.9])                             */
   r = p;
   for (DenseIndex k = 1; k <= static_cast<DenseIndex>(n); ++k) {
     for (j = p; j >= 0; --j) N_(k, j) *= r;
     r *= p - k;
   }
 }

References a, j, k, min, n, p, UniformPSDSelfTest::r, RachelsAdvectionDiffusion::U, and oomph::PseudoSolidHelper::Zero.

◆ 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 \(p+1\) control points \(P_i\) where \(p\) is the spline degree.

This function computes the \(p+1\) non-zero basis function values for a given parameter value \(u\). It returns

\begin{align*} N_{i,p}(u), \hdots, N_{i+p+1,p}(u) \end{align*}

Parameters

u	Parameter \(u \in [0;1]\) at which the non-zero basis functions are computed.

                     {
   return Spline::BasisFunctions(u, degree(), knots());
 }

References Eigen::Spline< Scalar_, Dim_, Degree_ >::BasisFunctions(), and constants::degree.

◆ 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

\begin{align*} N_{i,p}(u), \hdots, N_{i+p+1,p}(u) \end{align*}

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.

                                                                         {
   const DenseIndex p = degree;
   const DenseIndex i = Spline::Span(u, degree, knots);
  
   const KnotVectorType& U = knots;
  
   BasisVectorType left(p + 1);
   left(0) = Scalar(0);
   BasisVectorType right(p + 1);
   right(0) = Scalar(0);
  
   VectorBlock<BasisVectorType, Degree>(left, 1, p) =
       u - VectorBlock<const KnotVectorType, Degree>(U, i + 1 - p, p).reverse();
   VectorBlock<BasisVectorType, Degree>(right, 1, p) = VectorBlock<const KnotVectorType, Degree>(U, i + 1, p) - u;
  
   BasisVectorType N(1, p + 1);
   N(0) = Scalar(1);
   for (DenseIndex j = 1; j <= p; ++j) {
     Scalar saved = Scalar(0);
     for (DenseIndex r = 0; r < j; r++) {
       const Scalar tmp = N(r) / (right(r + 1) + left(j - r));
       N[r] = saved + right(r + 1) * tmp;
       saved = left(j - r) * tmp;
     }
     N(j) = saved;
   }
   return N;
 }

References constants::degree, i, j, N, p, UniformPSDSelfTest::r, Eigen::Spline< Scalar_, Dim_, Degree_ >::Span(), tmp, and RachelsAdvectionDiffusion::U.

Referenced by Eigen::Spline< Scalar_, Dim_, Degree_ >::basisFunctions().

◆ ctrls()

template<typename Scalar_ , int Dim_, int Degree_>

const ControlPointVectorType& Eigen::Spline< Scalar_, Dim_, Degree_ >::ctrls ( ) const

inline

Returns the ctrls of the underlying spline.

98 { return m_ctrls; }

References Eigen::Spline< Scalar_, Dim_, Degree_ >::m_ctrls.

◆ degree()

template<typename Scalar_ , int Dim_, int Degree_>

DenseIndex Eigen::Spline< Scalar_, Dim_, Degree_ >::degree

Returns the spline degree.

                                                         {
   if (Degree_ == Dynamic)
     return m_knots.size() - m_ctrls.cols() - 1;
   else
     return Degree_;
 }

References Eigen::Dynamic.

◆ 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

\begin{align*} \frac{d^i}{du^i}C(u) & = \sum_{i=0}^{n} \frac{d^i}{du^i} N_{i,p}(u)P_i \end{align*}

for i ranging between 0 and order.

Parameters

u	Parameter \(u \in [0;1]\) at which the spline derivative is evaluated.
order	The order up to which the derivatives are computed.

                                       {
   typename SplineTraits<Spline>::DerivativeType res;
   derivativesImpl(*this, u, order, res);
   return res;
 }

References Eigen::derivativesImpl(), and res.

Referenced by check_global_interpolation_with_derivatives2d().

◆ derivatives() [2/2]

template<typename Scalar_ , int Dim_, int Degree_>

template<int DerivativeOrder>

SplineTraits<Spline, DerivativeOrder>::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

\begin{align*} \frac{d^i}{du^i}C(u) & = \sum_{i=0}^{n} \frac{d^i}{du^i} N_{i,p}(u)P_i \end{align*}

for i ranging between 0 and order.

Parameters

u	Parameter \(u \in [0;1]\) 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.

◆ knots()

template<typename Scalar_ , int Dim_, int Degree_>

const KnotVectorType& Eigen::Spline< Scalar_, Dim_, Degree_ >::knots ( ) const

inline

Returns the knots of the underlying spline.

93 { return m_knots; }

References Eigen::Spline< Scalar_, Dim_, Degree_ >::m_knots.

Referenced by eval_spline3d_onbrks().

◆ 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 \(u\).

The function returns

\begin{align*} C(u) & = \sum_{i=0}^{n}N_{i,p}P_i \end{align*}

Parameters

u	Parameter \(u \in [0;1]\) at which the spline is evaluated.

Returns: The spline value at the given location \(u\).

                                                                                                           {
   enum { Order = SplineTraits<Spline>::OrderAtCompileTime };
  
   const DenseIndex span = this->span(u);
   const DenseIndex p = degree();
   const BasisVectorType basis_funcs = basisFunctions(u);
  
   const Replicate<BasisVectorType, Dimension, 1> ctrl_weights(basis_funcs);
   const Block<const ControlPointVectorType, Dimension, Order> ctrl_pts(ctrls(), 0, span - p, Dimension, p + 1);
   return (ctrl_weights * ctrl_pts).rowwise().sum();
 }

References constants::degree, and p.

◆ 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.

                                                               {
   return Spline::Span(u, degree(), knots());
 }

References constants::degree, and Eigen::Spline< Scalar_, Dim_, Degree_ >::Span().

◆ Span()

template<typename Scalar_ , int Dim_, int Degree_>

DenseIndex Eigen::Spline< Scalar_, Dim_, Degree_ >::Span	(	typename SplineTraits< Spline< Scalar_, Dim_, Degree_ > >::Scalar	u,
		DenseIndex	degree,
		const typename SplineTraits< Spline< Scalar_, Dim_, Degree_ > >::KnotVectorType &	knots
	)

static

Computes the span within the provided knot vector in which u is falling.

                                                                                        {
   // Piegl & Tiller, "The NURBS Book", A2.1 (p. 68)
   if (u <= knots(0)) return degree;
   const Scalar* pos = std::upper_bound(knots.data() + degree - 1, knots.data() + knots.size() - degree - 1, u);
   return static_cast<DenseIndex>(std::distance(knots.data(), pos) - 1);
 }

References constants::degree.

Referenced by Eigen::Spline< Scalar_, Dim_, Degree_ >::BasisFunctions(), and Eigen::Spline< Scalar_, Dim_, Degree_ >::span().

Member Data Documentation

◆ m_ctrls

template<typename Scalar_ , int Dim_, int Degree_>

ControlPointVectorType Eigen::Spline< Scalar_, Dim_, Degree_ >::m_ctrls

private

Control points.

Referenced by Eigen::Spline< Scalar_, Dim_, Degree_ >::ctrls().

◆ m_knots

template<typename Scalar_ , int Dim_, int Degree_>

KnotVectorType Eigen::Spline< Scalar_, Dim_, Degree_ >::m_knots

private

Knot vector.

Referenced by Eigen::Spline< Scalar_, Dim_, Degree_ >::knots(), and Eigen::Spline< Scalar_, Dim_, Degree_ >::Spline().

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

Spline.h

Public Types

Public Member Functions

Static Public Member Functions

Static Private Member Functions

Private Attributes

Detailed Description

template<typename Scalar_, int Dim_, int Degree_> class Eigen::Spline< Scalar_, Dim_, Degree_ >

Member Typedef Documentation

◆ BasisDerivativeType

◆ BasisVectorType

◆ ControlPointVectorType

◆ KnotVectorType

◆ ParameterVectorType

◆ PointType

◆ Scalar

Member Enumeration Documentation

◆ anonymous enum

◆ anonymous enum

Constructor & Destructor Documentation

◆ Spline() [1/3]

◆ Spline() [2/3]

◆ Spline() [3/3]

Member Function Documentation

◆ BasisFunctionDerivatives()

◆ basisFunctionDerivatives() [1/2]

◆ basisFunctionDerivatives() [2/2]

◆ BasisFunctionDerivativesImpl()

◆ basisFunctions()

◆ BasisFunctions()

◆ ctrls()

◆ degree()

◆ derivatives() [1/2]

◆ derivatives() [2/2]

◆ knots()

◆ operator()()

◆ span()

◆ Span()

Member Data Documentation

◆ m_ctrls

◆ m_knots

template<typename Scalar_, int Dim_, int Degree_>
class Eigen::Spline< Scalar_, Dim_, Degree_ >