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.

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

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.
FT	third_order_coefficients (size_t i) const
	\( 0 \leq i \leq3\)
FT	fourth_order_coefficients (size_t i) const
	\( 0 \leq i \leq4\)

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 Function Documentation

comply_wrt_given_normal()

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