CGAL::Monge_via_jet_fitting<DataKernel, LocalKernel, SvdTraits>


The class Monge_via_jet_fitting<DataKernel, LocalKernel, SvdTraits> is designed to perform the estimation of the local differential quantities at a given point. The point range is given by a pair of input iterators, and it is assumed that the point where the calculation is carried out is the point that the begin iterator refers to. The results are stored in an instance of the nested class Monge_form, the particular information returned depending on the degrees specified for the polynomial fitting and for the Monge form.

The default for the template LocalKernel is Cartesian<double> and the default for SvdTraits is Lapack_svd.

#include <CGAL/Monge_via_jet_fitting.h>


The class Monge_via_jet_fitting<DataKernel, LocalKernel, SvdTraits> has three template parameters. Parameter DataKernel provides the geometric classes and tools corresponding to the input points, and also members of the Monge_form class. Parameter LocalKernel provides the geometric classes and tools required by local computations. Parameter SvdTraits features the linear algebra algorithm required by the fitting method.


typedef DataKernel Data_kernel;
typedef LocalKernel Local_kernel;
typedef typename Local_kernel::FT FT;
typedef typename Local_kernel::Vector_3

Monge_via_jet_fitting<DataKernel, LocalKernel, SvdTraits>::Monge_form
see the section below.


Monge_via_jet_fitting<DataKernel, LocalKernel, SvdTraits> monge_fitting;
default constructor


template <class InputIterator>
Monge_form monge_fitting ( InputIterator begin , InputIterator end , size_t d , size_t d' )
This operator performs all the computations. The N input points are given by the InputIterator parameters which value-type are Data_kernel::Point_3, d is the degree of the fitted polynomial, d' is the degree of the expected Monge coefficients.
Precondition: N greater or equal Nd:=(d+1)(d+2)/2, 1 d' min(d,4) .

FT monge_fitting.condition_number () condition number of the linear fitting system.
std::pair<FT, Vector_3> monge_fitting.pca_basis ( size_t i)
pca eigenvalues and eigenvectors, the pca_basis has always 3 such pairs. Precondition : i ranges from 0 to 2.

See Also

Lapack_svd, Monge_form