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CGAL 6.1 - 3D Polyhedral Surface
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CGAL 6.1 - 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.
Types | |
| typedef unspecified_type | Vertex |
| type of incident vertices. | |
| typedef unspecified_type | Facet |
| type of incident facets. | |
| typedef unspecified_type | Vertex_handle |
| handle to vertex. | |
| typedef unspecified_type | Halfedge_handle |
| handle to halfedge. | |
| typedef unspecified_type | Facet_handle |
| handle to facet. | |
| typedef unspecified_type | Halfedge_around_vertex_circulator |
| circulator of halfedges around a vertex. | |
| typedef unspecified_type | Halfedge_around_facet_circulator |
| circulator of halfedges around a facet. | |
| typedef unspecified_type | Vertex_const_handle |
| typedef unspecified_type | Halfedge_const_handle |
| typedef unspecified_type | Facet_const_handle |
| typedef unspecified_type | Halfedge_around_vertex_const_circulator |
| typedef unspecified_type | Halfedge_around_facet_const_circulator |
| typedef unspecified_type | Supports_halfedge_prev |
\( \equiv\) CGAL::Tag_true or CGAL::Tag_false. | |
| typedef unspecified_type | Supports_halfedge_vertex |
\( \equiv\) CGAL::Tag_true or CGAL::Tag_false. | |
| typedef unspecified_type | Supports_halfedge_face |
\( \equiv\) CGAL::Tag_true or CGAL::Tag_false. | |
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). | |
| Halfedge_handle | prev_on_vertex () |
| Halfedge_const_handle | prev_on_vertex () const |
| the previous halfedge around the vertex (counterclockwise). | |
| 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. | |
| 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().
1.9.6