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@ -48,7 +48,7 @@ structure.
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A Nef polyhedron `N` can be visualized in an open GL window. The
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output operator is defined in the file
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`CGAL/IO/Nef_-poly-hedron_2_-Win-dow_-stream.h`.
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`CGAL/IO/Nef_polyhedron_2_Window-stream.h`.
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### Implementation ###
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@ -147,7 +147,7 @@ p);
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/*!
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Returns a sphere circle
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in the oppostie direction of `c`.
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in the opposite direction of `c`.
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*/
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Sphere_circle opposite() ;
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@ -351,15 +351,14 @@ half-circle.
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bool is_long() ;
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/*!
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return true iff `s` is
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degenerate,
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i.e. source and target are the same.
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return true iff `s` is degenerate,
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i.e.\ source and target are the same.
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*/
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bool is_degenerate() ;
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/*!
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return true iff `s` is a
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perfect half-circle, i.e. `source().antipode == target()`.
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return true iff `s` is a perfect half-circle,
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i.e.\ `source().antipode == target()`.
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*/
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bool is_halfcircle() ;
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@ -434,32 +433,32 @@ SFace_cycle_iterator();
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/// @{
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/*!
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returns true if `sfc` represents a `SVertex_handle`.
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returns true if the iterator represents a `SVertex_handle`.
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*/
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bool is_svertex() const;
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/*!
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returns true if `sfc` represents a `SHalfedge_handle`.
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returns true if the iterator represents a `SHalfedge_handle`.
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*/
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bool is_shalfedge() const;
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/*!
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returns true if `sfc` represents a `SHalfloop_handle`.
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returns true if the iterator represents a `SHalfloop_handle`.
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*/
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bool is_shalfloop() const;
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/*!
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casts `sfc` to `SVertex_handle`.
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casts the iterator to `SVertex_handle`.
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*/
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operator SVertex_handle() const;
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/*!
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casts `sfc` to `SHalfedge_handle`.
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casts the iterator to `SHalfedge_handle`.
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*/
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operator SHalfedge_handle() const;
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/*!
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casts `sfc` to `SHalfloop_handle`.
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casts the iterator to `SHalfloop_handle`.
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*/
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operator SHalfloop_handle() const;
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@ -523,7 +522,7 @@ const handle to SFace.
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typedef Hidden_type SFace_const_handle;
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/*!
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const iterator over the entries to all sface cycles of a sface.
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const iterator over the entries to all `sface` cycles of a `sface`.
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*/
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typedef Hidden_type SFace_cycle_const_iterator;
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@ -533,12 +532,12 @@ typedef Hidden_type SFace_cycle_const_iterator;
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/// @{
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/*!
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the mark of `sf` .
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the mark of the `sface`.
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*/
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const Mark& mark() const;
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/*!
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iterator over the entries to all sface cycles of `sf` .
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iterator over the entries to all sface cycles of the `sface` .
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*/
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SFace_cycle_const_iterator sface_cycle_begin() const;
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@ -630,22 +629,22 @@ typedef Hidden_type SFace_const_handle;
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/// @{
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/*!
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the mark of `se` .
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the mark of the `sedge`.
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*/
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const Mark& mark() const;
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/*!
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the sphere circle of `se` .
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the sphere circle of the `sedge`.
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*/
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const Sphere_circle& circle() const;
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/*!
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the twin of `se` .
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the twin of the `sedge`.
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*/
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SHalfedge_const_handle twin() const;
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/*!
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the source svertex of `se` .
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the source svertex of the `sedge`.
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*/
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SVertex_const_handle source() const;
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@ -655,38 +654,38 @@ equals `twin()->source()`.
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SVertex_const_handle target() const;
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/*!
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the SHalfedge previous to `se` in a sface cycle.
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the SHalfedge previous to the `sedge` in a sface cycle.
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*/
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SHalfedge_const_handle sprev() const;
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/*!
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the next SHalfedge of `se` in a sface cycle.
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the next SHalfedge of the `sedge` in a sface cycle.
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*/
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SHalfedge_const_handle snext() const;
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/*!
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the edge before `se` in the cyclic ordered adjacency list of source().
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the edge before the `sedge` in the cyclic ordered adjacency list of `source()`.
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*/
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SHalfedge_const_handle cyclic_adj_pred() const;
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/*!
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the edge after `se` in the cyclic ordered adjacency list of source().
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the edge after the `sedge` in the cyclic ordered adjacency list of `source()`.
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*/
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SHalfedge_const_handle cyclic_adj_succ() const;
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/*!
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the incident sface of `se` .
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the incident `sface` of the `sedge`.
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*/
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SFace_const_handle incident_sface() const;
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/*!
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determines whether `se` is
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determines whether the `sedge` is
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in an outer sface cycle.
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*/
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bool in_outer_sface_cycle() const;
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/*!
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determines whether `se` is
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determines whether the `sedge` is
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in an inner sface cycle.
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*/
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bool in_inner_sface_cycle() const;
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@ -753,22 +752,22 @@ typedef Hidden_type SFace_const_handle;
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/// @{
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/*!
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the mark of `se` .
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the mark of the halfloop.
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*/
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const Mark& mark() const;
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/*!
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the sphere circle of `se` .
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the sphere circle of the halfloop.
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*/
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const Sphere_circle& circle() const;
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/*!
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the twin of `se` .
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the twin of the halfloop.
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*/
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SHalfloop_const_handle twin() const;
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/*!
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the incident sface of `se` .
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the incident sface of the halfloop.
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*/
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SFace_const_handle incident_sface() const;
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@ -782,7 +781,7 @@ SFace_const_handle incident_sface() const;
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Figure \ref figureNefS2SVertexIncidences illustrates the incidence of a svertex on a sphere map.
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The member function
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`out_sedge` returns the first outgoing shalfedge, and `incident_sface`
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`out_sedge()` returns the first outgoing shalfedge, and `incident_sface()`
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returns the incident sface.
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### Creation ###
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@ -834,32 +833,32 @@ typedef Hidden_type SFace_const_handle;
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/// @{
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/*!
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the mark of `e` .
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the mark of the `svertex`.
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*/
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const Mark& mark() const;
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/*!
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the sphere point of `e` .
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the sphere point of the `svertex`.
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*/
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const Sphere_point& point() const;
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/*!
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returns |true| if `e` has no adjacent sedges.
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returns |true| if the `svertex` has no adjacent sedges.
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*/
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bool is_isolated() const;
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/*!
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the twin of `e` .
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the twin of the `svertex`.
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*/
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SVertex_const_handle twin() const;
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/*!
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the first out sedge of `e` .
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the first out sedge of the `svertex`.
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*/
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SHalfedge_const_handle out_sedge() const;
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/*!
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the incident sface of `e` .
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the incident sface of the `svertex`.
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*/
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SFace_const_handle incident_sface() const;
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@ -58,7 +58,7 @@ We introduce geometric objects that are part of the spherical surface
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`Nef_polyhedron_S2::Sphere_circle`, `Nef_polyhedron_S2::Sphere_segment`, and `Nef_polyhedron_S2::Sphere_direction`.
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`Nef_polyhedron_S2::Sphere_point`s are points on \f$ S_2\f$, `Nef_polyhedron_S2::Sphere_circle`s are
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oriented great circles of \f$ S_2\f$, `Nef_polyhedron_S2::Sphere_segment`s are oriented
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parts of `Nef_polyhedron_S2::Sphere_circles` bounded by a pair of
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parts of `Nef_polyhedron_S2::Sphere_circle` bounded by a pair of
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`Nef_polyhedron_S2::Sphere_point`s, and `Nef_polyhedron_S2::Sphere_direction`s are directions that
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are part of great circles. (a direction is usually defined to be a
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vector without length, that floats around in its underlying space and
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@ -124,9 +124,9 @@ it is.
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The macro `CGAL_forall_sface_cycles_of` is equivalent to a for-loop
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on the range `[sf->sface_cycles_begin(), sf->sface_cycles_end())`. An
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`Nef_polyhedron_S2::SFace_cycle_const_iterator` either represents a `Nef_polyhedron_S2::SVertex_const_handle`,
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a `Nef_polyhedron_S2::SHalfede_const_handle` or a `Nef_polyhedron_S2::SHalfloop_const_handle`. In order
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a `Nef_polyhedron_S2::SHalfedge_const_handle` or a `Nef_polyhedron_S2::SHalfloop_const_handle`. In order
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to find out which handle type is represented, the functions
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`Nef_polyhedron_S2::is_svertex()`, `Nef_polyhedron_S2::is_shafledge()` and `Nef_polyhedron_S2::is_shalfloop()` are provided.
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`Nef_polyhedron_S2::is_svertex()`, `Nef_polyhedron_S2::is_shalfedge()` and `Nef_polyhedron_S2::is_shalfloop()` are provided.
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Afterwards the iterator can be casted to the proper handle type.
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\cgalexample{Nef_S2/nef_s2_exploration.cpp}
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@ -140,7 +140,7 @@ retrieved. `locate` returns an instance of type `Nef_polyhedron_S2::Object_handl
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is a container for any handle type. Here, it either a
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`Nef_polyhedron_S2::SVertex_const_handle`, a `Nef_polyhedron_S2::SHalfedge_const_handle`,
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a `Nef_polyhedron_S2::SHafloop_const_handle` or a `Nef_polyhedron_S2::SFace_const_handle`. The function
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`CGAL::assign` performs the cast operation and returns a boolean which
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`assign()` performs the cast operation and returns a Boolean which
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indicates whether the cast was successful or not.
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\cgalexample{Nef_S2/nef_s2_point_location.cpp}
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@ -3,7 +3,7 @@
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/// \ingroup PkgNefS2
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/*!
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\addtogroup PkgNefS2
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\todo check generated documentation
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\PkgDescriptionBegin{2D Boolean Operations on Nef Polygons Embedded on the Sphere,PkgNefS2Summary}
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\PkgPicture{Nef_S2-teaser-small.png}
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\PkgAuthors{Peter Hachenberger and Lutz Kettner}
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@ -40,7 +40,7 @@ into great arcs.
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The incidence structure of planar Nef polyhedra can be reused. The
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items are denoted as \em svertex, \em shalfedge and \em sface,
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analogous to their counterparts in `Nef_polyhedron_2`. Additionally,
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analogous to their counterparts in `CGAL::Nef_polyhedron_2`. Additionally,
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there is the <I>shalfloop</I> representing the great circles.
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*/
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