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CGAL 6.1.3 - 3D Polyhedral Surface
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CGAL 6.1.3 - 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.
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.
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().
1.17.0