\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.10 - 2D and 3D Linear Geometry Kernel
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CGAL::Projection_traits_xy_3< K > Class Template Reference

#include <CGAL/Projection_traits_xy_3.h>


The class Projection_traits_xy_3 is an adapter to apply 2D algorithms to the projections of 3D data on the xy-plane.

CGAL provides also predefined geometric traits classes Projection_traits_yz_3<K> and Projection_traits_xz_3<K> to deal with projections on the zx- and the zy-plane, respectively.


The template parameter K has to be instantiated by a model of the Kernel concept. Projection_traits_xy_3 uses types and predicates defined in K.

Is Model Of:

The class is a model of several 2D triangulation traits class concepts, except that it does not provide the type and constructors required to build the dual Voronoi diagram.









typedef Point_3< K > Point_2
typedef Segment_3< K > Segment_2
typedef Triangle_3< K > Triangle_2
typedef Line_3< K > Line_2


The functors provided by this class are those listed in the concepts, except that it does not provide the type and constructors required to build the dual Voronoi diagram.

The functors operate on the 2D projection of their arguments. They come with preconditions that projections of the arguments are non-degenerate, eg. a line segment does not project on a single point, two points do not project on the same point, etc. In the following, we specify the choice of the z-coordinate in case a new point is constructed.

typedef unspecified_type Intersect_2
 A construction object. More...


 Projection_traits_xy_3 ()
 default constructor.
 Projection_traits_xy_3 (Projection_traits_xy_3 tr)
 Copy constructor.
Projection_traits_xy_3 operator= (Projection_traits_xy_3 tr)
 Assignment operator.

Member Typedef Documentation

template<typename K >
typedef unspecified_type CGAL::Projection_traits_xy_3< K >::Intersect_2

A construction object.

Provides the operator :

Object_2 operator()(Segment_2 s1, Segment_2 s2); which returns a 3D object whose projection on the xy-plane is the intersection of the projections of s1 and s2. If non empty, the returned object is either a segment or a point. Its embedding in 3D is computed as the interpolation between s1 and s2, meaning that any point p of the returned object is the midpoint of segment p1p2 where p1 and p2 are the two points of s1 and s2 respectively, both projecting on p.

The projection of s1 and the projection of s2 are non-degenerate 2D segments.