CGAL::Nef_polyhedron_3<Traits>::SHalfedge
Definition
A shalfedge is a great arc on a sphere map.
Figure 25.10
depicts the relationship between a shalfedge and its incident
shalfedges, svertices, and sfaces on a sphere map. A shalfedge is
an oriented sedge between two svertices. It is always paired with a
shalfedge pointing in
the opposite direction. The twin() member function returns
this shalfedge of opposite orientation.
The snext() member function points
to the successor shalfedge around this sface while the sprev() member
function points to the preceding shalfedge. An
successive assignments of the form se = se->snext() cycles
counterclockwise around the sface (or hole).
Similarly, the successive
assignments of the form se = se->snext()->twin() cycle
clockwise around the svertex and traverse all halfedges incident to
this svertex. The assignment se = se->cyclic_adj_succ() can be
used as a shortcut.
The role of shalfedges in a facet is illustrated in
Figure 25.10.
The facet() member function returns the facet in which
the shalfedge is part of one of the facet cycles. The successive assignment of
the form se = se->next() cycles counterclockwise around the facet (or a
hole of the facet).
A const circulators is provided for each of the three circular orders.
The circulators are bidirectional and assignable to SHalfedge_const_handle.
#include <CGAL/Nef_polyhedron_3.h>
Types
The following types are the same as in Nef_polyhedron_3<Traits>.
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Nef_polyhedron_3<Traits>::SHalfedge::Mark
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type of mark.
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Nef_polyhedron_3<Traits>::SHalfedge::Sphere_circle
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sphere circle type stored in SHalfedge.
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Nef_polyhedron_3<Traits>::SHalfedge::Halffacet_const_handle
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const handle to Halffacet.
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Nef_polyhedron_3<Traits>::SHalfedge::SVertex_const_handle
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const handle to SVertex.
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Nef_polyhedron_3<Traits>::SHalfedge::SHalfedge_const_handle
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const handle to SHalfedge.
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Nef_polyhedron_3<Traits>::SHalfedge::SFace_const_handle
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const handle to SFace.
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Creation
There is no need for a user to create a SHalfedge explicitly. The
class Nef_polyhedron_3<Traits> manages the needed shalfedges internally.
Operations
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Mark
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se.mark ()
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the mark of se .
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Sphere_circle
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se.circle ()
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the sphere circle of se .
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SHalfedge_const_handle
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se.twin ()
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the twin of se .
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SVertex_const_handle
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se.source ()
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the source svertex of se .
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SVertex_const_handle
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se.target ()
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equals twin()->source().
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SHalfedge_const_handle
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se.prev ()
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the SHalfedge previous to se in a facet cycle.
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SHalfedge_const_handle
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se.next ()
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the next SHalfedge of se in a facet cycle.
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SHalfedge_const_handle
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se.sprev ()
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the SHalfedge previous to se in a sface cycle.
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SHalfedge_const_handle
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se.snext ()
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the next SHalfedge of se in a sface cycle.
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SHalfedge_const_handle
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se.cyclic_adj_pred ()
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the edge before se in the cyclic ordered adjacency list of source().
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SHalfedge_const_handle
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se.cyclic_adj_succ ()
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the edge after se in the cyclic ordered adjacency list of source().
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Halffacet_const_handle
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se.facet ()
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the facet that corresponds to se in the 3D incidence structure.
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SFace_const_handle
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se.incident_sface ()
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the incident
sface of se .
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bool
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se.in_outer_sface_cycle ()
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determines whether se is
in an outer sface cycle.
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bool
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se.in_inner_sface_cycle ()
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determines whether se is
in an inner sface cycle.
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bool
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se.in_outer_facet_cycle ()
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determines whether se is
in an outer facet cycle.
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bool
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se.in_inner_facet_cycle ()
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determines whether se is
in an inner facet cycle.
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See Also
CGAL::Nef_polyhedron_3<Traits>::Halfedge
CGAL::Nef_polyhedron_3<Traits>::Halffacet
CGAL::Nef_polyhedron_3<Traits>::SFace
CGAL::Nef_polyhedron_S2<Traits>::Sphere_circle
