\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.11.3 - Optimal Transportation Curve Reconstruction
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OptimalTransportationReconstructionTraits_2 Concept Reference

Definition

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.
 

Access to Predicate and Constructors Objects

Construct_point_2 construct_point_2_object ()
 
Construct_vector_2 construct_vector_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 ()
 

Member Typedef Documentation

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.

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.

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.

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.