CGAL 4.12.1 - 3D Polyhedral Surface
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#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()
.