CGAL 6.1 - 3D Isosurfacing

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IsosurfacingTraits_3 Concept Reference
Reference Manual » Concepts

## Definition

Refines
  `DefaultConstructible`
  `Assignable`

The concept `IsosurfacingTraits_3` describes the set of requirements to be fulfilled by the traits class of a model of `IsosurfacingDomain_3`.

Has models
  All models of the concept `Kernel`

## Types
typedef unspecified_type | FT
| The scalar type.
typedef unspecified_type | Point_3
| The 3D point type.
typedef unspecified_type | Vector_3
| The 3D vector type.
typedef unspecified_type | IsoCuboid_3
| The 3D cuboid type.
typedef unspecified_type | Compute_x_3
| A construction object that must provide the function operators:
typedef unspecified_type | Compute_y_3
| A construction object that must provide the function operators:
typedef unspecified_type | Compute_z_3
| A construction object that must provide the function operators:
typedef unspecified_type | Construct_point_3
| A construction object that must provide the function operator:
typedef unspecified_type | Construct_vector_3
| A construction object that must provide the function operator:
typedef unspecified_type | Construct_iso_cuboid_3
| A construction object that must provide the function operator:
typedef unspecified_type | Construct_vertex_3
| A construction object that must provide the function operator:

## Operations
The following functions give access to the predicate and construction objects:
Compute_x_3 | compute_x_3_object ()
Compute_y_3 | compute_y_3_object ()
Compute_z_3 | compute_z_3_object ()
Construct_point_3 | construct_point_3_object ()
Construct_vector_3 | construct_vector_3_object ()
Construct_iso_cuboid_3 | construct_iso_cuboid_3_object ()
Construct_vertex_3 | construct_vertex_3_object ()

## Member Typedef Documentation

## ◆ Compute_x_3

typedef unspecified_type IsosurfacingTraits_3::Compute_x_3

A construction object that must provide the function operators:

`FT operator()(Point_3 p)`

and

`FT operator()(Vector_3 p)`

which return the \( x\)-coordinate of the point and the vector, respectively.

## ◆ Compute_y_3

typedef unspecified_type IsosurfacingTraits_3::Compute_y_3

A construction object that must provide the function operators:

`FT operator()(Point_3 p)`

and

`FT operator()(Vector_3 p)`

which return the \( y\)-coordinate of the point and the vector, respectively.

## ◆ Compute_z_3

typedef unspecified_type IsosurfacingTraits_3::Compute_z_3

A construction object that must provide the function operators:

`FT operator()(Point_3 p)`

and

`FT operator()(Vector_3 p)`

which return the \( z\)-coordinate of the point and the vector, respectively.

## ◆ Construct_iso_cuboid_3

typedef unspecified_type IsosurfacingTraits_3::Construct_iso_cuboid_3

A construction object that must provide the function operator:

`IsoCuboid_3 operator()(Point_3 p, Point_3 q)`

which constructs an iso-oriented cuboid with diagonal opposite vertices `p` and `q` such that `p` is the lexicographically smallest point in the cuboid.

## ◆ Construct_point_3

typedef unspecified_type IsosurfacingTraits_3::Construct_point_3

A construction object that must provide the function operator:

`Point_3 operator()(FT x, FT y, FT z)`

which constructs a 3D point from its three coordinates.

## ◆ Construct_vector_3

typedef unspecified_type IsosurfacingTraits_3::Construct_vector_3

A construction object that must provide the function operator:

`Vector_3 operator()(FT x, FT y, FT z)`

which constructs a 3D vector from its three coordinates.

## ◆ Construct_vertex_3

typedef unspecified_type IsosurfacingTraits_3::Construct_vertex_3

A construction object that must provide the function operator:

`Point_3 operator()(IsoCuboid_3 c, int i)`

which returns the i-th vertex of an iso-cuboid `c`. See `Kernel::ConstructVertex_3` for the order of vertices.

## ◆ FT

typedef unspecified_type IsosurfacingTraits_3::FT

The scalar type.

Must be a model of `FieldNumberType`.

## ◆ IsoCuboid_3

typedef unspecified_type IsosurfacingTraits_3::IsoCuboid_3

The 3D cuboid type.

Must be a model of `Kernel::IsoCuboid_3`

## ◆ Point_3

typedef unspecified_type IsosurfacingTraits_3::Point_3

The 3D point type.

Must be a model of `Kernel::Point_3`.

## ◆ Vector_3

typedef unspecified_type IsosurfacingTraits_3::Vector_3

The 3D vector type.

Must be a model of `Kernel::Vector_3`.