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CGAL 4.8 - 3D Surface Mesh Generation

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ImplicitSurfaceTraits_3 Concept Reference
Concepts

## 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

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`.

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.

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`.

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`.

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`.

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.

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`.

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.

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`.

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`.

typedef unspecified_type ImplicitSurfaceTraits_3::FT

The numerical type.

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

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`.

typedef unspecified_type ImplicitSurfaceTraits_3::Point_3

The point type.

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