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CGAL 6.0 - Estimation of Local Differential Properties of Point-Sampled Surfaces
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#include <CGAL/Monge_via_jet_fitting.h>
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. | |
| 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) \( z=h(x,y)=-g(y,x)\).