Eigen-unsupported  3.4.90 (git rev a4098ac676528a83cfb73d4d26ce1b42ec05f47c)
Spline and spline fitting module

Detailed Description

This module provides a simple multi-dimensional spline class while offering most basic functionality to fit a spline to point sets.

#include <unsupported/Eigen/Splines>

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. 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...

◆ 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.
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.