CGAL 5.3  Estimation of Local Differential Properties of PointSampled Surfaces

#include <CGAL/Monge_via_jet_fitting.h>
The class Monge_via_jet_fitting
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.
If CGAL_EIGEN3_ENABLED
is defined, LocalKernel
and SvdTraits
template parameters have defaults, Simple_cartesian<double>
and Eigen_svd
respectively.
DataKernel  provides the geometric classes and tools corresponding to the input points, and also members of the Monge_form class. 
LocalKernel  provides the geometric classes and tools required by local computations. 
SvdTraits  features the linear algebra algorithm required by the fitting method. The scalar type, SvdTraits::FT , must be the same as that of the LocalKernel concept : LocalKernel::FT . 
Eigen_svd
Monge_form
Classes  
class  Monge_form 
The class Monge_form stores the Monge representation, i.e., the Monge coordinate system and the coefficients of the Monge form in this system. More...  
Types  
typedef DataKernel  Data_kernel 
typedef LocalKernel  Local_kernel 
typedef Local_kernel::FT  FT 
typedef Local_kernel::Vector_3  Vector_3 
typedef unspecified_type  Monge_form 
see the page Monge_via_jet_fitting::Monge_form .  
Creation  
Monge_via_jet_fitting ()  
default constructor  
Operations  
template<class InputIterator >  
Monge_form  operator() (InputIterator begin, InputIterator end, size_t d, size_t d') 
This operator performs all the computations. More...  
FT  condition_number () 
condition number of the linear fitting system.  
std::pair< FT, Vector_3 >  pca_basis (size_t i) 
pca eigenvalues and eigenvectors, the pca_basis has always 3 such pairs. More...  
Monge_form CGAL::Monge_via_jet_fitting< DataKernel, LocalKernel, SvdTraits >::operator()  (  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 valuetype are Data_kernel::Point_3
, d
is the degree of the fitted polynomial, d'
is the degree of the expected Monge coefficients.
std::pair<FT, Vector_3> CGAL::Monge_via_jet_fitting< DataKernel, LocalKernel, SvdTraits >::pca_basis  (  size_t  i  ) 
pca eigenvalues and eigenvectors, the pca_basis has always 3 such pairs.