Classes | Functions
Splines_Module
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 $p$ is the degree and $m+1$ 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]ptsThe data points to which a spline should be fit.
[out]chord_lengthsThe 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]parametersThe input parameters. During interpolation one for each data point.
[in]degreeThe spline degree which is used during the interpolation.
[out]knotsThe 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]parametersThe parameters at which the interpolation B-Spline will intersect the given interpolation points. The parameters are assumed to be a non-decreasing sequence.
[in]degreeThe degree of the interpolating B-Spline. This must be greater than zero.
[in]derivativeIndicesThe indices corresponding to parameters at which there are derivative constraints. The indices are assumed to be a non-decreasing sequence.
[out]knotsThe 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.



gtsam
Author(s):
autogenerated on Tue Jul 4 2023 02:40:59