Monge_via_jet_fitting< DataKernel, LocalKernel, SvdTraits>::Monge

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

Definition

The class Monge_via_jet_fitting< DataKernel, LocalKernel, SvdTraits>::Monge_form stores the Monge representation, i.e., the Monge coordinate system and the coefficients of the Monge form in this system.

#include <CGAL/Monge_via_jet_fitting.h>

Types

typedef typename DataKernel::FT	FT;
typedef typename DataKernel::Point_3
	Point_3;
typedef typename DataKernel::Vector_3
	Vector_3;

Creation

Monge_via_jet_fitting< DataKernel, LocalKernel, SvdTraits>::Monge_form monge_form;
	default constructor.

Access Functions

Point_3

monge_form.origin ()

Point on the fitted surface where differential quantities are computed.

The Monge basis is given by:

Vector_3	monge_form.maximal_principal_direction ()
Vector_3	monge_form.minimal_principal_direction ()
Vector_3	monge_form.normal_direction ()

The Monge coefficients are given by:

FT	monge_form.principal_curvatures ( size_t i)
		i=0 for the maximum and i=1 for the minimum.
FT	monge_form.third_order_coefficients ( size_t i)
		0 i 3
FT	monge_form.fourth_order_coefficients ( size_t i)
		0 i 4

Operations

void	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).