\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.13.2 - 2D Polygon Partitioning
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IsYMonotoneTraits_2 Concept Reference
2D Polygon Partitioning Reference » Concepts

Definition

Requirements of a traits class to be used with the function is_y_monotone_2() that tests whether a sequence of 2D points defines a \( y\)-monotone polygon or not.

Has Models:

CGAL::Partition_traits_2<R>

CGAL::Kernel_traits_2

See also
CGAL::Is_y_monotone_2<Traits>
CGAL::y_monotone_partition_2()
CGAL::y_monotone_partition_is_valid_2()

Types

The following two types are required:

typedef unspecified_type Point_2
 The point type of the polygon vertices.
 
typedef unspecified_type Less_yx_2
 Predicate object type that compares Point_2s lexicographically. More...
 

Creation

Only a copy constructor is required.

 IsYMonotoneTraits_2 (IsYMonotoneTraits_2 tr)
 

Operations

The following function that creates an instance of the above predicate object type must exist:

Less_yx_2 less_yx_2_object ()
 

Member Typedef Documentation

◆ Less_yx_2

typedef unspecified_type IsYMonotoneTraits_2::Less_yx_2

Predicate object type that compares Point_2s lexicographically.

Must provide bool operator()(Point_2 p, Point_2 q) where true is returned 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 \( x\) and \( y\) coordinate of point \( p\) resp.