CGAL 5.1.3 - Optimal Transportation Curve Reconstruction
OptimalTransportationReconstructionTraits_2 Concept Reference

## Definition

The concept OptimalTransportationReconstructionTraits_2 describes the requirements for the traits class of CGAL::Optimal_transportation_reconstruction_2.

Refines:
DelaunayTriangulationTraits_2
Has Models:

Any model of the Kernel concept

CGAL::Exact_predicates_inexact_constructions_kernel (recommended)

CGAL::Optimal_transportation_reconstruction_2

## Types

typedef unspecified_type FT
A coordinate type. More...

typedef unspecified_type Vector_2
The vector type.

typedef unspecified_type Construct_point_2
A function object to construct a Point_2. More...

typedef unspecified_type Construct_vector_2
A function object to construct a Vector_2. More...

typedef unspecified_type Construct_line_2
A function object to construct a Line_2. More...

typedef unspecified_type Construct_translated_point_2
Must provides: Point_2 operator()(Point_2 p, Vector_2 v) that computes the point p + v.

typedef unspecified_type Construct_scaled_vector_2
Must provides: Vector_2 operator()(Vector_2 v, FT c) that computes the vector c * v.

typedef unspecified_type Construct_sum_of_vectors_2
Must provides: Vector_2 operator()(Vector_2 v1, Vector_2 v2) that computes the vector v1 + v2.

typedef unspecified_type Construct_projected_point_2
Must provides: Point_2 operator()(Line_2 l, Point_2 p) that computes the projection of the point p on the line l.

typedef unspecified_type Has_on_2
Must provides: bool operator()(Line_2 l, Point_2 p) that returns true iff p lies on l.

typedef unspecified_type Compute_scalar_product_2
Must provides: FT operator()(Vector_2 v1, Vector_2 v2) that computes the scalar product between v1 and v2.

typedef unspecified_type Compute_squared_length_2
Must provides: FT operator()(Vector_2 v) that computes the squared length of v.

typedef unspecified_type Compute_squared_distance_2
Must provides: FT operator()(Point p1, Point p2) that computes the squared distance between p1 and p2.

## Creation

OptimalTransportationReconstructionTraits_2 ()
Default constructor.

OptimalTransportationReconstructionTraits_2 (const OptimalTransportationReconstructionTraits_2 &)
Copy constructor.

OptimalTransportationReconstructionTraits_2operator= (const OptimalTransportationReconstructionTraits_2 &)
Assignment operator.

Construct_point_2 construct_point_2_object ()

Construct_vector_2 construct_vector_2_object ()

Construct_line_2 construct_line_2_object ()

Construct_translated_point_2 construct_translated_point_2_object ()

Construct_scaled_vector_2 construct_scaled_vector_2_object ()

Construct_sum_of_vectors_2 construct_sum_of_vectors_2_object ()

Construct_projected_point_2 construct_projected_point_2_object ()

Has_on_2 has_on_2_object ()

Compute_scalar_product_2 compute_scalar_product_2_object ()

Compute_squared_length_2 compute_squared_length_2_object ()

Compute_squared_distance_2 compute_squared_distance_2_object ()

## ◆ Construct_line_2

A function object to construct a Line_2.

Must provides: Line_2 operator()(Point p, Vector v), which constructs a 2D line from a point and a vector.

## ◆ Construct_point_2

A function object to construct a Point_2.

Must provides: Point_2 operator()(FT x, FT y), which constructs a 2D point from its coordinates.

## ◆ Construct_vector_2

A function object to construct a Vector_2.

Must provides: Vector_2 operator()(FT x, FT y), which constructs a 2D vector from its coordinates, and Vector_2 operator()(Point p0, Point p1), which constructs a 2D vector from 2 points.

## ◆ FT

A coordinate type.

The type must provide a copy constructor, assignment, comparison operators, negation, multiplication, division and allow the declaration and initialization with a small integer and double constant (cf. requirements for number types). An obvious choice would be coordinate type of the point class.