CGAL 5.3  2D and 3D Linear Geometry Kernel

#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.
Parameters
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
.
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.
Types  
typedef Point_3< K >  Point_2 
typedef Segment_3< K >  Segment_2 
typedef Triangle_3< K >  Triangle_2 
typedef Line_3< K >  Line_2 
Functors  
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 nondegenerate, 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  
typedef unspecified_type  Intersect_2 
A construction object. More...  
Creation  
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.  
typedef unspecified_type CGAL::Projection_traits_xy_3< K >::Intersect_2 
A construction object.
Provides the operator :
boost::optional< boost::variant<Point_2,Segment_2> > operator()(Segment_2 s1, Segment_2 s2);
which returns a 3D object whose projection on the xyplane 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
.
s1
and the projection of s2
are nondegenerate 2D
segments.