CGAL::Nef_polyhedron_3<Traits>::SHalfedge
Definition
A shalfedge is a great arc on a sphere map.
Figure
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.
Figure:
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
. 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
