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

CGAL 4.8 - Geometric Object Generators

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RandomPolygonTraits_2 Concept Reference
Concepts

## Definition

The concept `RandomPolygonTraits_2` describes the requirements for the traits class used by the function `random_polygon_2()`.

Has Models:
  CGAL kernels.

Operations

The following two member functions returning instances of the above predicate object types are required.

## Types
typedef unspecified_type | FT
| The coordinate type of the points of the polygon.
typedef unspecified_type | Point_2
| The point type of the polygon.
typedef unspecified_type | Orientation_2
| Predicate object type that determines the orientation of three points. More...
typedef unspecified_type | Less_xy_2
| Binary predicate object type comparing `Point_2`s lexicographically. More...

## Operations
Less_xy_2 | less_xy_2_object ()
Orienation_2 | orientation_2_object ()

## Member Typedef Documentation

typedef unspecified_type RandomPolygonTraits_2::Less_xy_2

Binary predicate object type comparing `Point_2`s lexicographically.

It must provide `bool operator()(Point_2 p, Point_2 q)` that returns `true` iff \( p <_{xy} q\). We have \( p<_{xy}q\), iff \( p_x < q_x\) or \( p_x = q_x\) and \( p_y < q_y\), where \( p_x\) and \( p_y\) denote the \( x\) and \( y\) coordinates of point \( p\), resp.

typedef unspecified_type RandomPolygonTraits_2::Orientation_2

Predicate object type that determines the orientation of three points.

It must provide `Orientation operator()(Point_2 p, Point_2 q, Point_2 r)` that returns `LEFT_TURN`, if \( r\) lies to the left of the oriented line \( l\) defined by \( p\) and \( q\), returns `RIGHT_TURN` if \( r\) lies to the right of \( l\), and returns `COLLINEAR` if \( r\) lies on \( l\).