CGAL 4.12.1  3D Surface Mesh Generation

#include <CGAL/Implicit_surface_3.h>
The class Implicit_surface_3
implements a surface described as the zero level set of a function \( f : \mathbb{R}^3 \longrightarrow \mathbb{R}\).
For this type of surface, the library provides a partial specialization of the surface mesher traits generator: Surface_mesh_traits_generator_3<Implicit_surface_3<Traits, Function> >
, that provides a traits class, model of the concept SurfaceMeshTraits_3
, to be used by the surface mesher.
Traits  must be a geometric traits class that must be a model of ImplicitSurfaceTraits_3 . That concept defines all the types, predicates and constructors that the Traits has to provide to implement the surface mesh traits Surface_mesh_traits_generator_3<Implicit_surface_3<Traits, Function> > . 
Function  must be a of the concept ImplicitFunction . 
The number type Function::FT
has to match the type Traits::FT
.
Creation  
Implicit_surface_3 (Function f, Sphere_3 bounding_sphere, FT error_bound=FT(1e3))  
f is the object of type Function that represents the implicit surface. More...  
CGAL::Implicit_surface_3< Traits, Function >::Implicit_surface_3  (  Function  f, 
Sphere_3  bounding_sphere,  
FT  error_bound = FT(1e3) 

) 
f
is the object of type Function
that represents the implicit surface.
bounding_sphere
is a bounding sphere of the implicit surface. The evaluation of f
at the center c
of this sphere must be negative: \( f(c)<0\).
error_bound
is a relative error bound used to compute intersection points between the implicit surface and query segments. This bound is used in the default generated traits class. In this traits class, the intersection points between the surface and segments/rays/line are constructed by dichotomy. The dichotomy is stopped when the size of the intersected segment is less than the product of error_bound
by the radius of bounding_sphere
.