Collaboration diagram for Splines_Module:

Classes
class	Eigen::Spline< _Scalar, _Dim, _Degree >
	A class representing multi-dimensional spline curves. More...

struct	Eigen::SplineFitting< SplineType >
	Spline fitting methods. More...

struct	Eigen::SplineTraits< Spline< _Scalar, _Dim, _Degree >, _DerivativeOrder >
	Compile-time attributes of the Spline class for fixed degree. More...

struct	Eigen::SplineTraits< Spline< _Scalar, _Dim, _Degree >, Dynamic >
	Compile-time attributes of the Spline class for Dynamic degree. More...

Functions
template<typename PointArrayType , typename KnotVectorType >
void	Eigen::ChordLengths (const PointArrayType &pts, KnotVectorType &chord_lengths)
	Computes chord length parameters which are required for spline interpolation. More...

template<typename KnotVectorType >
void	Eigen::KnotAveraging (const KnotVectorType &parameters, DenseIndex degree, KnotVectorType &knots)
	Computes knot averages.The knots are computed as $\begin{align} u_0 & = \hdots = u_p = 0 \\ u_{m-p} & = \hdots = u_{m} = 1 \\ u_{j+p} & = \frac{1}{p}\sum_{i=j}^{j+p-1}\bar{u}_i \quad\quad j=1,\hdots,n-p \end{align}$ where is the degree and the number knots of the desired interpolating spline. More...

template<typename KnotVectorType , typename ParameterVectorType , typename IndexArray >
void	Eigen::KnotAveragingWithDerivatives (const ParameterVectorType &parameters, const unsigned int degree, const IndexArray &derivativeIndices, KnotVectorType &knots)
	Computes knot averages when derivative constraints are present. Note that this is a technical interpretation of the referenced article since the algorithm contained therein is incorrect as written. More...

Detailed Description

Function Documentation

◆ ChordLengths()

template<typename PointArrayType , typename KnotVectorType >

void Eigen::ChordLengths	(	const PointArrayType &	pts,
		KnotVectorType &	chord_lengths
	)

Computes chord length parameters which are required for spline interpolation.

Parameters

[in]	pts	The data points to which a spline should be fit.
[out]	chord_lengths	The resulting chord length vector.

See also: Les Piegl and Wayne Tiller, The NURBS book (2nd ed.), 1997, 9.2.1 Global Curve Interpolation to Point Data

Definition at line 189 of file SplineFitting.h.

◆ KnotAveraging()

template<typename KnotVectorType >

void Eigen::KnotAveraging	(	const KnotVectorType &	parameters,
		DenseIndex	degree,
		KnotVectorType &	knots
	)

Computes knot averages.The knots are computed as

$\begin{align*} u_0 & = \hdots = u_p = 0 \\ u_{m-p} & = \hdots = u_{m} = 1 \\ u_{j+p} & = \frac{1}{p}\sum_{i=j}^{j+p-1}\bar{u}_i \quad\quad j=1,\hdots,n-p \end{align*}$

where $p$ is the degree and $m+1$ the number knots of the desired interpolating spline.

Parameters

[in]	parameters	The input parameters. During interpolation one for each data point.
[in]	degree	The spline degree which is used during the interpolation.
[out]	knots	The output knot vector.

See also: Les Piegl and Wayne Tiller, The NURBS book (2nd ed.), 1997, 9.2.1 Global Curve Interpolation to Point Data

Definition at line 45 of file SplineFitting.h.

◆ KnotAveragingWithDerivatives()

template<typename KnotVectorType , typename ParameterVectorType , typename IndexArray >

void Eigen::KnotAveragingWithDerivatives	(	const ParameterVectorType &	parameters,
		const unsigned int	degree,
		const IndexArray &	derivativeIndices,
		KnotVectorType &	knots
	)

Computes knot averages when derivative constraints are present. Note that this is a technical interpretation of the referenced article since the algorithm contained therein is incorrect as written.

Parameters

[in]	parameters	The parameters at which the interpolation B-Spline will intersect the given interpolation points. The parameters are assumed to be a non-decreasing sequence.
[in]	degree	The degree of the interpolating B-Spline. This must be greater than zero.
[in]	derivativeIndices	The indices corresponding to parameters at which there are derivative constraints. The indices are assumed to be a non-decreasing sequence.
[out]	knots	The calculated knot vector. These will be returned as a non-decreasing sequence

See also: Les A. Piegl, Khairan Rajab, Volha Smarodzinana. 2008. Curve interpolation with directional constraints for engineering design. Engineering with Computers

Definition at line 78 of file SplineFitting.h.

Classes

Functions

Detailed Description

Function Documentation

◆ ChordLengths()

◆ KnotAveraging()

◆ KnotAveragingWithDerivatives()