CGAL 5.5.2 - Weights
AnalyticWeightTraits_2 Concept Reference

Definition

A concept that describes the set of requirements of classes used in the computation of analytic weights in 2D.

Has Models:

Types

typedef unspecified_type FT
 A model of FieldNumberType.
 
typedef unspecified_type Comparison_result
 CGAL::Comparison_result or Uncertain<CGAL::Comparison_result>.
 
typedef unspecified_type Orientation
 CGAL::Orientation or Uncertain<CGAL::Orientation>.
 

Geometric Objects

typedef unspecified_type Point_2
 2D point type.
 
typedef unspecified_type Vector_2
 2D vector type.
 

Constructions

typedef unspecified_type Compute_area_2
 A construction object that must provide the function operator: More...
 
typedef unspecified_type Compute_squared_distance_2
 A construction object that must provide the function operator: More...
 
typedef unspecified_type Compute_squared_length_2
 A construction object that must provide the function operator: More...
 
typedef unspecified_type Compute_scalar_product_2
 A construction object that must provide the function operator: More...
 
typedef unspecified_type Compute_determinant_2
 A construction object that must provide the function operator: More...
 
typedef unspecified_type Construct_circumcenter_2
 A construction object that must provide the function operator: More...
 
typedef unspecified_type Construct_vector_2
 A construction object that must provide the function operator: More...
 
typedef unspecified_type Construct_midpoint_2
 A construction object that must provide the function operator: More...
 
typedef unspecified_type Construct_centroid_2
 A construction object that must provide the function operator: More...
 

Predicates

typedef unspecified_type Equal_2
 A predicate object that must provide the function operator: More...
 
typedef unspecified_type Collinear_2
 A predicate object that must provide the function operator: More...
 
typedef unspecified_type Less_xy_2
 A predicate object that must provide the function operator: More...
 
typedef unspecified_type Compare_x_2
 A predicate object that must provide the function operator: More...
 
typedef unspecified_type Compare_y_2
 A predicate object that must provide the function operator: More...
 
typedef unspecified_type Orientation_2
 A predicate object that must provide the function operator: More...
 

Member Typedef Documentation

◆ Collinear_2

A predicate object that must provide the function operator:

bool operator()(const Point_2& p, const Point_2& q, const Point_2& r)

that returns true if the points p, q, and r are collinear and false otherwise.

◆ Compare_x_2

A predicate object that must provide the function operator:

Comparison_result operator()(const Point_2& p, const Point_2& q)

that compares the Cartesian x-coordinates of the points p and q.

◆ Compare_y_2

A predicate object that must provide the function operator:

Comparison_result operator()(const Point_2& p, const Point_2& q)

that compares the Cartesian y-coordinates of the points p and q.

◆ Compute_area_2

A construction object that must provide the function operator:

FT operator()(const Point_2& p, const Point_2& q, const Point_2& r)

that returns the signed area of the triangle defined by the points p, q, and r.

◆ Compute_determinant_2

A construction object that must provide the function operator:

FT operator()(const Vector_2& v, const Vector_2& w)

that returns the determinant of the vectors v and w.

◆ Compute_scalar_product_2

A construction object that must provide the function operator:

FT operator()(const Vector_2& v, const Vector_2& w)

that returns the scalar product of the vectors v and w.

◆ Compute_squared_distance_2

A construction object that must provide the function operator:

FT operator()(const Point_2& p, const Point_2& q)

that returns the squared Euclidean distance between the points p and q.

◆ Compute_squared_length_2

A construction object that must provide the function operator:

FT operator()(const Vector_2& v)

that returns the squared length of the vector v.

◆ Construct_centroid_2

A construction object that must provide the function operator:

Point_2 operator()(const Point_2& p, const Point_2& q, const Point_2& r)

that returns the centroid of the points p, q, and r.

◆ Construct_circumcenter_2

A construction object that must provide the function operator:

Point_2 operator()(const Point_2& p, const Point_2& q, const Point_2& r)

that returns the center of the circle passing through the points p, q, and r.

Precondition
The points p, q, and r are not collinear.

◆ Construct_midpoint_2

A construction object that must provide the function operator:

Point_2 operator()(const Point_2& p, const Point_2& q)

that returns the midpoint between the points p and q.

◆ Construct_vector_2

A construction object that must provide the function operator:

Vector_2 operator()(const Point_2& p, const Point_2& q)

that returns the vector through the points p and q.

◆ Equal_2

A predicate object that must provide the function operator:

bool operator()(const Point_2& p, const Point_2& q)

that returns true if p = q and false otherwise.

◆ Less_xy_2

A predicate object that must provide the function operator:

bool operator()(const Point_2& p, const Point_2& q)

that returns true iff the x-coordinate of p is smaller than the x-coordinate of q or if they are the same and the y-coordinate of p is smaller than the y-coordinate of q.

◆ Orientation_2

A predicate object that must provide the function operator:

Orientation operator()(const Point_2& p, const Point_2& q, const Point_2& r)

that returns CGAL::LEFT_TURN if r lies to the left of the oriented line l defined by p and q, returns CGAL::RIGHT_TURN if r lies to the right of l, and returns CGAL::COLLINEAR if r lies on l.