CGAL 5.4  2D Boolean Operations on Nef Polygons Embedded on the Sphere

#include <CGAL/Nef_polyhedron_S2.h>
A shalfedge is a great arc on a sphere map.
The figure below depicts the relationship between a shalfedge and its incident shalfedges, svertices, and sfaces on a sphere map. A shalfedge is an oriented sedge between two svertices. It is always paired with a shalfedge pointing in the opposite direction. The twin()
member function returns this shalfedge of opposite orientation.
snext()
member function points to the successor shalfedge around this sface while the sprev()
member function points to the preceding shalfedge. An successive assignments of the form se = se>snext()
cycles counterclockwise around the sface (or hole).
Similarly, the successive assignments of the form se = se>snext()>twin()
cycle clockwise around the svertex and traverse all halfedges incident to this svertex. The assignment se = se>cyclic_adj_succ()
can be used as a shortcut.
A const circulator is provided for each of the two circular orders. The circulators are bidirectional and assignable to SHalfedge_const_handle
.
Creation
There is no need for a user to create a SHalfedge
explicitly. The class Nef_polyhedron_S2<Traits>
manages the needed shalfedges internally.
Types  
The following types are the same as in  
typedef unspecified_type  Mark 
type of mark.  
typedef unspecified_type  Sphere_circle 
sphere circle type stored in SHalfedge.  
typedef unspecified_type  SVertex_const_handle 
const handle to SVertex.  
typedef unspecified_type  SHalfedge_const_handle 
const handle to SHalfedge.  
typedef unspecified_type  SFace_const_handle 
const handle to SFace.  
Operations  
const Mark &  mark () const 
the mark of the sedge .  
const Sphere_circle &  circle () const 
the sphere circle of the sedge .  
SHalfedge_const_handle  twin () const 
the twin of the sedge .  
SVertex_const_handle  source () const 
the source svertex of the sedge .  
SVertex_const_handle  target () const 
equals twin()>source() .  
SHalfedge_const_handle  sprev () const 
the SHalfedge previous to the sedge in a sface cycle.  
SHalfedge_const_handle  snext () const 
the next SHalfedge of the sedge in a sface cycle.  
SHalfedge_const_handle  cyclic_adj_pred () const 
the edge before the sedge in the cyclic ordered adjacency list of source() .  
SHalfedge_const_handle  cyclic_adj_succ () const 
the edge after the sedge in the cyclic ordered adjacency list of source() .  
SFace_const_handle  incident_sface () const 
the incident sface of the sedge .  
bool  in_outer_sface_cycle () const 
determines whether the sedge is in an outer sface cycle.  
bool  in_inner_sface_cycle () const 
determines whether the sedge is in an inner sface cycle.  