CGAL::Implicit_surface_3<Traits, Function>

Definition

The class Implicit_surface_3<Traits, Function> implements a surface described as the zero level set of a function $$f : ³ .

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.

The parameter Traits is a traits class that has to be implemented with a model of ImplicitSurfaceTraits_3. Actually, this traits class implements the oracle needed by the surface mesher: the types, predicates and constructors provided in Traits are passed by the surface mesher traits generator to the generated the traits class used by the surface mesher.

The template parameter Function stands for a model of the concept ImplicitFunction. The number type Function::FT has to match the type Traits::FT.

#include <CGAL/Implicit_surface_3.h>

Creation

Implicit_surface_3<Traits, Function> surface ( Function f, Sphere_3 bounding_sphere, FT error_bound = FT(1e-3));

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.

See Also