CGAL::Monge_via_jet_fitting< DataKernel, LocalKernel, SvdTraits >::Monge_form Class Reference

#include <CGAL/Monge_via_jet_fitting.h>

Definition

The class Monge_form stores the Monge representation, i.e., the Monge coordinate system and the coefficients of the Monge form in this system.

The usual insert operator (operator<<) is overloaded for Monge_form, it gives the Monge coordinate system (the origin and an orthonormal basis) and the coefficients of the Monge form in this system.

See also

Monge_via_jet_fitting

Types
typedef DataKernel::FT	FT
typedef DataKernel::Point_3	Point_3
typedef DataKernel::Vector_3	Vector_3

Creation
	Monge_form ()
	default constructor. More...

Access Functions
Point_3	origin () const
	Point on the fitted surface where differential quantities are computed. More...

Monge Basis
Vector_3	maximal_principal_direction () const
Vector_3	minimal_principal_direction () const
Vector_3	normal_direction () const

Monge Coefficients
FT	principal_curvatures (size_t i) const
	\( i=0\) for the maximum and \( i=1\) for the minimum. More...
FT	third_order_coefficients (size_t i) const
	\( 0 \leq i \leq3\) More...
FT	fourth_order_coefficients (size_t i) const
	\( 0 \leq i \leq4\) More...

Operations
void	comply_wrt_given_normal (const Vector_3 &given_normal)
	change principal basis and Monge coefficients so that the given_normal and the Monge normal make an acute angle. More...

Member Typedef Documentation

template<typename DataKernel , typename LocalKernel , typename SvdTraits >

typedef DataKernel::FT CGAL::Monge_via_jet_fitting< DataKernel, LocalKernel, SvdTraits >::Monge_form::FT

template<typename DataKernel , typename LocalKernel , typename SvdTraits >

typedef DataKernel::Point_3 CGAL::Monge_via_jet_fitting< DataKernel, LocalKernel, SvdTraits >::Monge_form::Point_3

template<typename DataKernel , typename LocalKernel , typename SvdTraits >

typedef DataKernel::Vector_3 CGAL::Monge_via_jet_fitting< DataKernel, LocalKernel, SvdTraits >::Monge_form::Vector_3

Constructor & Destructor Documentation

template<typename DataKernel , typename LocalKernel , typename SvdTraits >

CGAL::Monge_via_jet_fitting< DataKernel, LocalKernel, SvdTraits >::Monge_form::Monge_form

(

)

default constructor.

Member Function Documentation

template<typename DataKernel , typename LocalKernel , typename SvdTraits >

void CGAL::Monge_via_jet_fitting< DataKernel, LocalKernel, SvdTraits >::Monge_form::comply_wrt_given_normal

(

const Vector_3 &

given_normal

)

change principal basis and Monge coefficients so that the given_normal and the Monge normal make an acute angle.

If given_normal.monge_normal \( < 0\) then change the orientation: if \( z=g(x,y)\) in the basis (d1,d2,n) then in the basis (d2,d1,-n) \( z=h(x,y)=-g(y,x)\).

template<typename DataKernel , typename LocalKernel , typename SvdTraits >

FT CGAL::Monge_via_jet_fitting< DataKernel, LocalKernel, SvdTraits >::Monge_form::fourth_order_coefficients

(

size_t

i

)

const

\( 0 \leq i \leq4\)

template<typename DataKernel , typename LocalKernel , typename SvdTraits >

Vector_3 CGAL::Monge_via_jet_fitting< DataKernel, LocalKernel, SvdTraits >::Monge_form::maximal_principal_direction

(

)

const

template<typename DataKernel , typename LocalKernel , typename SvdTraits >

Vector_3 CGAL::Monge_via_jet_fitting< DataKernel, LocalKernel, SvdTraits >::Monge_form::minimal_principal_direction

(

)

const

template<typename DataKernel , typename LocalKernel , typename SvdTraits >

Vector_3 CGAL::Monge_via_jet_fitting< DataKernel, LocalKernel, SvdTraits >::Monge_form::normal_direction

(

)

const

template<typename DataKernel , typename LocalKernel , typename SvdTraits >

Point_3 CGAL::Monge_via_jet_fitting< DataKernel, LocalKernel, SvdTraits >::Monge_form::origin

(

)

const

Point on the fitted surface where differential quantities are computed.

template<typename DataKernel , typename LocalKernel , typename SvdTraits >

FT CGAL::Monge_via_jet_fitting< DataKernel, LocalKernel, SvdTraits >::Monge_form::principal_curvatures

(

size_t

i

)

const

\( i=0\) for the maximum and \( i=1\) for the minimum.

template<typename DataKernel , typename LocalKernel , typename SvdTraits >

FT CGAL::Monge_via_jet_fitting< DataKernel, LocalKernel, SvdTraits >::Monge_form::third_order_coefficients

(

size_t

i

)

const

\( 0 \leq i \leq3\)