CGAL 5.5  3D Polyhedral Surface

#include <CGAL/Polyhedron_3.h>
A halfedge is an oriented edge between two vertices.
It is always paired with a halfedge pointing in the opposite direction. The Halfedge::opposite()
member function returns this halfedge of opposite orientation. If a halfedge is incident to a facet the Halfedge::next()
member function points to the successor halfedge around this facet. For border edges the Halfedge::next()
member function points to the successor halfedge along the hole. For more than two border edges at a vertex, the next halfedge along a hole is not uniquely defined, but a consistent assignment of the next halfedge will be maintained in the data structure. An invariant is that successive assignments of the form h = h>next()
cycle counterclockwise around the facet (or hole) and traverse all halfedges incident to this facet (or hole). A similar invariant is that successive assignments of the form h = h>next()>opposite()
cycle clockwise around the vertex and traverse all halfedges incident to this vertex. Two circulators are provided for these circular orders.
Vertex
, Halfedge
, and Facet
of the polyhedral surface. Member functions with shaded background are mandatory. The others are optionally supported.The incidences encoded in Halfedge::opposite()
and Halfedge::next()
are available for each instantiation of polyhedral surfaces. The other incidences are optionally available as indicated with type tags. The Halfedge::prev()
member function points to the preceding halfedge around the same facet. It is always available, though it might perform a search around the facet using the Halfedge::next()
member function to find the previous halfedge if the underlying halfedge data structure does not provide an efficient Halfedge::prev()
member function for halfedges. Handles to the incident vertex and facet are optionally stored.
The circulators are assignable to the Halfedge_handle
. The circulators are bidirectional if the halfedge provided to the polyhedron with the Items
template argument provides a member function Halfedge::prev()
, otherwise they are of the forward category.
CGAL::Polyhedron_3::Vertex
CGAL::Polyhedron_3::Facet
CGAL::Polyhedron_3<Traits>
Implementation
The member functions Halfedge::prev()
and Halfedge::prev_on_vertex()
work in constant time if Supports_halfedge_prev
\( \equiv\) CGAL::Tag_true
. Otherwise both methods search for the previous halfedge around the incident facet.
Creation  
Halfedge ()  
default constructor.  
Operations  
Halfedge_handle  opposite () 
Halfedge_const_handle  opposite () const 
the opposite halfedge.  
Halfedge_handle  next () 
Halfedge_const_handle  next () const 
the next halfedge around the facet.  
Halfedge_handle  prev () 
Halfedge_const_handle  prev () const 
the previous halfedge around the facet.  
Halfedge_handle  next_on_vertex () 
Halfedge_const_handle  next_on_vertex () const 
the next halfedge around the vertex (clockwise). More...  
Halfedge_handle  prev_on_vertex () 
Halfedge_const_handle  prev_on_vertex () const 
the previous halfedge around the vertex (counterclockwise). More...  
bool  is_border () const 
is true if h is a border halfedge.  
bool  is_border_edge () const 
is true if this or the opposite halfedge is a border halfedge.  
Halfedge_around_vertex_circulator  vertex_begin () 
Halfedge_around_vertex_const_circulator  vertex_begin () const 
circulator of halfedges around the vertex (clockwise), the vertex of the halfedges being *this .  
Halfedge_around_facet_circulator  facet_begin () 
Halfedge_around_facet_const_circulator  facet_begin () const 
circulator of halfedges around the facet (counterclockwise).  
std::size_t  vertex_degree () const 
the degree of the incident vertex, i.e., number of edges emanating from this vertex.  
bool  is_bivalent () const 
returns true if the incident vertex has exactly two incident edges.  
bool  is_trivalent () const 
returns true if the incident vertex has exactly three incident edges.  
std::size_t  facet_degree () const 
the degree of the incident facet, i.e., number of edges on the boundary of this facet.  
bool  is_triangle () const 
returns true if the incident facet is a triangle.  
bool  is_quad () const 
returns true if the incident facet is a quadrilateral.  
Operations available if Supports_halfedge_vertex is CGAL::Tag_true  
Vertex_handle  vertex () 
Vertex_const_handle  vertex () const 
the incident vertex of the halfedge.  
Operations available if Supports_halfedge_facet is CGAL::Tag_true  
Facet_handle  facet () 
Facet_const_handle  facet () const 
the incident facet of the halfedge. More...  
Facet_const_handle CGAL::Polyhedron_3< Traits >::Halfedge::facet  (  )  const 
the incident facet of the halfedge.
If the hafedge is a border halfedge the result is default construction of the handle.
Halfedge_const_handle CGAL::Polyhedron_3< Traits >::Halfedge::next_on_vertex  (  )  const 
the next halfedge around the vertex (clockwise).
Is equal to h.next()>opposite()
.
Halfedge_const_handle CGAL::Polyhedron_3< Traits >::Halfedge::prev_on_vertex  (  )  const 
the previous halfedge around the vertex (counterclockwise).
Is equal to h.opposite()>prev()
.