Splines_Module

Classes
struct	Eigen::SplineFitting< SplineType >
	Spline fitting methods. More...
struct	Eigen::SplineTraits< Spline< _Scalar, _Dim, _Degree >, Dynamic >
	Compile-time attributes of the Spline class for Dynamic degree. More...
struct	Eigen::SplineTraits< Spline< _Scalar, _Dim, _Degree >, _DerivativeOrder >
	Compile-time attributes of the Spline class for fixed degree. More...
class	Eigen::Spline< _Scalar, _Dim, _Degree >
	A class representing multi-dimensional spline curves. More...

Functions
template<typename KnotVectorType >
void	Eigen::KnotAveraging (const KnotVectorType &parameters, DenseIndex degree, KnotVectorType &knots)
	Computes knot averages. More...
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...

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 lenggth vector.

See also

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

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