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 All models of the CGAL concept Kernel See alsoCGAL::Implicit_surface_3<Traits, Function> CGAL::make_surface_mesh() Types typedef unspecified_type FT The numerical type. typedef unspecified_type Point_3 The point type. 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. typedef unspecified_type Compute_squared_distance_3 A function object providing the operator. typedef unspecified_type Compute_squared_radius_3 A function object providing the operator. typedef unspecified_type Construct_center_3 A function object providing the operator. typedef unspecified_type Construct_midpoint_3 A function object providing the operator. typedef unspecified_type Construct_point_on_3 A function object providing the following operators: typedef unspecified_type Construct_segment_3 A function object providing the operator. typedef unspecified_type Construct_scaled_vector_3 A function object providing the operator. typedef unspecified_type Construct_translated_point_3 A function object providing the operator. typedef unspecified_type Construct_vector_3 A function object providing the operator. typedef unspecified_type Has_on_bounded_side_3 A function object providing the operator. 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 Compute_scalar_product_3 typedef unspecified_type ImplicitSurfaceTraits_3::Compute_scalar_product_3 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. Compute_squared_distance_3 typedef unspecified_type ImplicitSurfaceTraits_3::Compute_squared_distance_3 A function object providing the operator. FT operator()(Point_3, Point_3) which returns the squared distance between two points. Compute_squared_radius_3 typedef unspecified_type ImplicitSurfaceTraits_3::Compute_squared_radius_3 A function object providing the operator. FT operator()(const Sphere_3& s) which returns the squared radius of s. Construct_center_3 typedef unspecified_type ImplicitSurfaceTraits_3::Construct_center_3 A function object providing the operator. Point_3 operator()(const Sphere_3& s) which computes the center of the sphere s. Construct_midpoint_3 typedef unspecified_type ImplicitSurfaceTraits_3::Construct_midpoint_3 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. Construct_point_on_3 typedef unspecified_type ImplicitSurfaceTraits_3::Construct_point_on_3 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. Construct_scaled_vector_3 typedef unspecified_type ImplicitSurfaceTraits_3::Construct_scaled_vector_3 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. Construct_segment_3 typedef unspecified_type ImplicitSurfaceTraits_3::Construct_segment_3 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. Construct_translated_point_3 typedef unspecified_type ImplicitSurfaceTraits_3::Construct_translated_point_3 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. Construct_vector_3 typedef unspecified_type ImplicitSurfaceTraits_3::Construct_vector_3 A function object providing the operator. Vector_3 operator()(const Point_3 &a, const Point_3 &b) which returns the vector b-a. FT typedef unspecified_type ImplicitSurfaceTraits_3::FT The numerical type. It must be model of FieldWithSqrt and constructible from a double. Has_on_bounded_side_3 typedef unspecified_type ImplicitSurfaceTraits_3::Has_on_bounded_side_3 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. Point_3 typedef unspecified_type ImplicitSurfaceTraits_3::Point_3 The point type. This point type must have a constructor Point_3(FT, FT, FT). ImplicitSurfaceTraits_3 Generated by 1.17.0

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

All models of the CGAL concept Kernel

See also

CGAL::Implicit_surface_3<Traits, Function>

CGAL::make_surface_mesh()

Types
typedef unspecified_type	FT
	The numerical type.
typedef unspecified_type	Point_3
	The point type.
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.
typedef unspecified_type	Compute_squared_distance_3
	A function object providing the operator.
typedef unspecified_type	Compute_squared_radius_3
	A function object providing the operator.
typedef unspecified_type	Construct_center_3
	A function object providing the operator.
typedef unspecified_type	Construct_midpoint_3
	A function object providing the operator.
typedef unspecified_type	Construct_point_on_3
	A function object providing the following operators:
typedef unspecified_type	Construct_segment_3
	A function object providing the operator.
typedef unspecified_type	Construct_scaled_vector_3
	A function object providing the operator.
typedef unspecified_type	Construct_translated_point_3
	A function object providing the operator.
typedef unspecified_type	Construct_vector_3
	A function object providing the operator.
typedef unspecified_type	Has_on_bounded_side_3
	A function object providing the operator.

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

Compute_scalar_product_3

typedef unspecified_type ImplicitSurfaceTraits_3::Compute_scalar_product_3

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.

Compute_squared_distance_3

typedef unspecified_type ImplicitSurfaceTraits_3::Compute_squared_distance_3

A function object providing the operator.

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

Compute_squared_radius_3

typedef unspecified_type ImplicitSurfaceTraits_3::Compute_squared_radius_3

A function object providing the operator.

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

Construct_center_3

typedef unspecified_type ImplicitSurfaceTraits_3::Construct_center_3

A function object providing the operator.

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

Construct_midpoint_3

typedef unspecified_type ImplicitSurfaceTraits_3::Construct_midpoint_3

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.

Construct_point_on_3

typedef unspecified_type ImplicitSurfaceTraits_3::Construct_point_on_3

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.

Construct_scaled_vector_3

typedef unspecified_type ImplicitSurfaceTraits_3::Construct_scaled_vector_3

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.

Construct_segment_3

typedef unspecified_type ImplicitSurfaceTraits_3::Construct_segment_3

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.

Construct_translated_point_3

typedef unspecified_type ImplicitSurfaceTraits_3::Construct_translated_point_3

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.

Construct_vector_3

typedef unspecified_type ImplicitSurfaceTraits_3::Construct_vector_3

A function object providing the operator.

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

FT

typedef unspecified_type ImplicitSurfaceTraits_3::FT

The numerical type.

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

Has_on_bounded_side_3

typedef unspecified_type ImplicitSurfaceTraits_3::Has_on_bounded_side_3

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.

Point_3

typedef unspecified_type ImplicitSurfaceTraits_3::Point_3

The point type.

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