Added docs to the spline module.

This commit is contained in:
Hauke Heibel
2011-12-04 18:44:01 +01:00
parent 9bd902ed9c
commit a8a2bf3b5a
4 changed files with 198 additions and 66 deletions

View File

@@ -33,6 +33,25 @@
namespace Eigen
{
/**
* \brief Computes knot averages.
* \ingroup Splines_Module
*
* The knots are computes as
* \f{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
* \f}
* where \f$p\f$ is the degree and \f$m+1\f$ the number knots
* of the desired interpolating spline.
*
* \param[in] parameters The input parameters. During interpolation one for each data point.
* \param[in] degree The spline degree which is used during the interpolation.
* \param[out] knots The output knot vector.
*
* \sa Les Piegl and Wayne Tiller, The NURBS book (2nd ed.), 1997, 9.2.1 Global Curve Interpolation to Point Data
**/
template <typename KnotVectorType>
void KnotAveraging(const KnotVectorType& parameters, DenseIndex degree, KnotVectorType& knots)
{
@@ -47,6 +66,15 @@ namespace Eigen
knots.segment(knots.size()-degree-1,degree+1) = KnotVectorType::Ones(degree+1);
}
/**
* \brief Computes chord length parameters which are required for spline interpolation.
* \ingroup Splines_Module
*
* \param[in] pts The data points to which a spline should be fit.
* \param[out] chord_lengths The resulting chord lenggth vector.
*
* \sa Les Piegl and Wayne Tiller, The NURBS book (2nd ed.), 1997, 9.2.1 Global Curve Interpolation to Point Data
**/
template <typename PointArrayType, typename KnotVectorType>
void ChordLengths(const PointArrayType& pts, KnotVectorType& chord_lengths)
{
@@ -67,9 +95,16 @@ namespace Eigen
chord_lengths(n-1) = Scalar(1);
}
/**
* \brief Spline fitting methods.
* \ingroup Splines_Module
**/
template <typename SplineType>
struct SplineFitting
{
/**
* \brief Fits an interpolating Spline to the given data points.
**/
template <typename PointArrayType>
static SplineType Interpolate(const PointArrayType& pts, DenseIndex degree);
};