\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - Spatial Sorting

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SpatialSortingTraits_3 Concept Reference
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## Definition

All 3D spatial sorting algorithms, including sorting on the sphere, provided in CGAL are parameterized by a traits class `Traits`, which defines the primitives (objects and predicates) that the sorting algorithms use. `SpatialSortingTraits_3` defines the complete set of primitives required in these functions and functors.

Has Models:

  Any CGAL kernel.

  `CGAL::Spatial_sort_traits_adapter_3<Base_traits,PointPropertyMap>`

## Types
typedef unspecified_type | Point_3
| The point type on which the sorting algorithms operate.
typedef unspecified_type | Compute_x_3
| Functor object type returning the \( x\) coordinate of a `Point_3`. More...
typedef unspecified_type | Compute_y_3
| Functor object type returning the \( y\) coordinate of a `Point_3`. More...
typedef unspecified_type | Compute_z_3
| Functor object type returning the \( z\) coordinate of a `Point_3`. More...
typedef unspecified_type | Less_x_3
| Binary predicate object type comparing `Point_3`s along the \( x\) coordinate. More...
typedef unspecified_type | Less_y_3
| Binary predicate object type comparing `Point_3`s along the \( y\) coordinate. More...
typedef unspecified_type | Less_z_3
| Binary predicate object type comparing `Point_3`s along the \( z\) coordinate. More...

## Creation
Only a copy constructor is required.
| SpatialSortingTraits_3 (const SpatialSortingTraits_3 &t)

## Operations
The following member functions to create instances of the above predicate object types must exist.
Compute_x_3 | compute_x_3_object ()
Compute_y_3 | compute_y_3_object ()
Compute_z_3 | compute_z_3_object ()
Less_x_3 | less_x_3_object ()
Less_y_3 | less_y_3_object ()
Less_z_3 | less_z_3_object ()

## Member Typedef Documentation

typedef unspecified_type SpatialSortingTraits_3::Compute_x_3

Functor object type returning the \( x\) coordinate of a `Point_3`.

Must provide `FT operator()(Point_3 p)` where `FT` can be used as argument of `CGAL::to_double`.

typedef unspecified_type SpatialSortingTraits_3::Compute_y_3

Functor object type returning the \( y\) coordinate of a `Point_3`.

Must provide `FT operator()(Point_3 p)` where `FT` can be used as argument of `CGAL::to_double`.

typedef unspecified_type SpatialSortingTraits_3::Compute_z_3

Functor object type returning the \( z\) coordinate of a `Point_3`.

Must provide `FT operator()(Point_3 p)` where `FT` can be used as argument of `CGAL::to_double`.

typedef unspecified_type SpatialSortingTraits_3::Less_x_3

Binary predicate object type comparing `Point_3`s along the \( x\) coordinate.

Must provide `bool operator()(Point_3 p, Point_3 q)` where `true` is returned iff \( p_x < q_x\), where \( p_x\) and \( q_x\) denote \( x\) coordinate of point \( p\) and \( q\), respectively.

typedef unspecified_type SpatialSortingTraits_3::Less_y_3

Binary predicate object type comparing `Point_3`s along the \( y\) coordinate.

Must provide `bool operator()(Point_3 p, Point_3 q)` where `true` is returned iff \( p_y < q_y\), where \( p_y\) and \( q_y\) denote \( y\) coordinate of point \( p\) and \( q\), respectively.

typedef unspecified_type SpatialSortingTraits_3::Less_z_3

Binary predicate object type comparing `Point_3`s along the \( z\) coordinate.

Must provide `bool operator()(Point_3 p, Point_3 q)` where `true` is returned iff \( p_z < q_z\), where \( p_z\) and \( q_z\) denote \( z\) coordinate of point \( p\) and \( q\), respectively.