\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.10 - 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_2s 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_2s 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 \( l\).