 CGAL 4.12 - Estimation of Local Differential Properties of Point-Sampled Surfaces
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.

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...

## ◆ 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) $$z=h(x,y)=-g(y,x)$$.