\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.6.1 - 3D Surface Mesh Generation
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ImplicitSurfaceTraits_3 Concept Reference

Definition

The concept ImplicitSurfaceTraits_3 describes the requirements of the traits class to be plugged as Traits in CGAL::Implicit_surface_3<Traits, Function>.

When make_surface_mesh is called with a surface of type CGAL::Implicit_surface_3<Traits,Function>, the surface mesher traits generator generates automatically a traits class that is a model of SurfaceMeshTraits_3. Actually, the concept ImplicitSurfaceTraits_3 provides the types, predicates and constructors that are passed to the generated model of SurfaceMeshTraits_3.

Has Models:
Any CGAL Kernel.
See Also
CGAL::Implicit_surface_3<Traits, Function>
CGAL::make_surface_mesh()

Types

typedef unspecified_type FT
 The numerical type. More...
 
typedef unspecified_type Point_3
 The point type. More...
 
typedef unspecified_type Line_3
 The line type.
 
typedef unspecified_type Ray_3
 The ray type.
 
typedef unspecified_type Segment_3
 The segment type.
 
typedef unspecified_type Vector_3
 The vector type.
 
typedef unspecified_type Sphere_3
 The sphere type.
 
typedef unspecified_type Compute_scalar_product_3
 A function object providing the operator. More...
 
typedef unspecified_type Compute_squared_distance_3
 A function object providing the operator. More...
 
typedef unspecified_type Compute_squared_radius_3
 A function object providing the operator. More...
 
typedef unspecified_type Construct_center_3
 A function object providing the operator. More...
 
typedef unspecified_type Construct_midpoint_3
 A function object providing the operator. More...
 
typedef unspecified_type Construct_point_on_3
 A function object providing the following operators: More...
 
typedef unspecified_type Construct_segment_3
 A function object providing the operator. More...
 
typedef unspecified_type Construct_scaled_vector_3
 A function object providing the operator. More...
 
typedef unspecified_type Construct_translated_point_3
 A function object providing the operator. More...
 
typedef unspecified_type Construct_vector_3
 A function object providing the operator. More...
 
typedef unspecified_type Has_on_bounded_side_3
 A function object providing the operator. More...
 

Operations

The following functions give access to the predicate and construction objects:

Compute_scalar_product_3 compute_scalar_product_3_object ()
 
Compute_squared_distance_3 compute_squared_distance_3_object ()
 
Compute_squared_radius_3 compute_squared_radius_3_object ()
 
Construct_center_3 construct_center_3_object ()
 
Construct_midpoint_3 construct_midpoint_3_object ()
 
Construct_point_on_3 construct_point_on_3_object ()
 
Construct_scaled_vector_3 construct_scaled_vector_3_object ()
 
Construct_segment_3 construct_segment_3_object ()
 
Construct_translated_point_3 construct_translated_point_3_object ()
 
Construct_vector_3 construct_vector_3_object ()
 
Has_on_bounded_side_3 has_on_bounded_side_3_object ()
 

Member Typedef Documentation

A function object providing the operator.

FT operator()(Vector_3 v, Vector_3 w) which returns the scalar (inner) product of the two vectors v and w.

A function object providing the operator.

FT operator()(Point_3, Point_3) which returns the squared distance between two points.

A function object providing the operator.

FT operator()(const Sphere_3& s) which returns the squared radius of s.

A function object providing the operator.

Point_3 operator()(const Sphere_3& s) which computes the center of the sphere s.

A function object providing the operator.

Point_3 operator()(const Point_3& p, const Point_3& q) which computes the midpoint of the segment pq.

A function object providing the following operators:

Point_3 operator()(const Line_3& l,int i) which returns an arbitrary point on l. It holds point(i) == point(j), iff i==j. Furthermore, is directed from point(i) to point(j), for all i \( <\) j.

Point_3 operator()(const Ray_3& r,int i) which returns a point on r. point(0) is the source, point(i), with \( i>0\), is different from the source.

Precondition
\( i \geq0\).

Point_3 operator()(const Segment_3& s,int i) which returns source or target of s: point(0) returns the source of s, point(1) returns the target of s. The parameter i is taken modulo 2, which gives easy access to the other end point.

A function object providing the operator.

Vector_3 operator()(const Vector_3 &v, const FT& scale) which returns the vector v scaled by a factor scale.

A function object providing the operator.

Segment_3 operator()(const Point_3 &p, const Point_3 &q) which returns a segment with source p and target q. It is directed from the source towards the target.

A function object providing the operator.

Point_3 operator()(const Point_3& p, const Vector_3& v) which returns the point obtained by translating p by the vector v.

A function object providing the operator.

Vector_3 operator()(const Point_3 &a, const Point_3 &b) which returns the vector b-a.

The numerical type.

It must be model of FieldWithSqrt and constructible from a double.

A function object providing the operator.

bool operator()(const Sphere_3&s, const Point_3&p) which returns true iff p lies on the bounded side of s.

The point type.

This point type must have a constructor Point_3(FT, FT, FT).