The concept HalfedgeDSHalfedge defines the requirements for the local Halfedge type in the HalfedgeDS concept. It is also required in the Halfedge_wrapper<Refs,Traits> member class template of an items class, see the HalfedgeDSItems concept.
A halfedge is an oriented edge between two vertices. It is always paired with a halfedge pointing in the opposite direction. The opposite() member function returns this halfedge of opposite orientation. The next() member function points to the successor halfedge along the face - or if the halfedge is a border halfedge - along the open region. A halfedge optionally stores a reference to the previous halfedge along the face, a reference to an incident vertex, and a reference to an incident face. Type tags indicate whether the related member functions are supported. Figure depicts the relationship between a halfedge and its incident halfedges, vertices, and faces.
For the protection of the integrity of the data structure classes such as CGAL::Polyhedron_3 are allowed to redefine the modifying member functions to be private. In order to make them accessible for the halfedge data structure they must be derived from a base class Base where the modifying member functions are still public. Even more protection is provided for the set_opposite() member function. The base class Base_base provides access to it. (The protection could be bypassed also by an user, but not by accident.)
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instantiated HalfedgeDS ( Refs).
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base class that allows modifications.
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base class to access set_opposite().
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model of HalfedgeDSVertex.
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model of HalfedgeDSFace.
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handle to vertex.
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handle to halfedge.
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handle to face.
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CGAL::Tag_true or
CGAL::Tag_false.
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default constructor.
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the opposite halfedge. | ||
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sets opposite halfedge to . | ||
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| the next halfedge around the face. | |
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sets next halfedge to . | ||
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is true if h is a border halfedge. |
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| the previous halfedge around the face. | |
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sets prev halfedge to . |
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| the incident vertex of h. | |
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sets incident vertex to . |
CGAL::HalfedgeDS_halfedge_base<Refs>
CGAL::HalfedgeDS_halfedge_min_base<Refs>
HalfedgeDS<Traits,Items,Alloc>
HalfedgeDSItems
HalfedgeDSVertex
HalfedgeDSFace