mirror of https://github.com/CGAL/cgal
576 lines
16 KiB
C++
576 lines
16 KiB
C++
namespace CGAL {
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/*!
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\addtogroup do_intersect
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\brief
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\details Depending on which \cgal kernel is used, different overloads of this global
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function are available.
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*/
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/*!
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\addtogroup do_intersect_linear do_intersect (2D/3D Linear Kernel)
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\ingroup do_intersect
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\code
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#include <CGAL/intersections.h>
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\endcode
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\sa \ref do_intersect_circular
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\sa \ref do_intersect_spherical
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\sa `intersection`
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\details See Chapter \ref chapterkernel23 "2D and 3D Geometry Kernel" for details on a linear kernel instantiation.
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*/
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/// @{
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/*!
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checks whether `obj1` and `obj2` intersect. Two objects `obj1` and
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`obj2` intersect if there is a point `p` that is part of both `obj1`
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and `obj2`. The intersection region of those two objects is defined
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as the set of all points `p` that are part of both `obj1` and `obj2`.
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Note that for objects like triangles and polygons that enclose a
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bounded region, this region is part of the object.
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The types `Type1` and `Type2` can be any of the following:
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- `Point_2<Kernel>`
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- `Line_2<Kernel>`
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- `Ray_2<Kernel>`
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- `Segment_2<Kernel>`
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- `Triangle_2<Kernel>`
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- `Iso_rectangle_2<Kernel>`
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Also, `Type1` and `Type2` can be both of type
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- `Line_2<Kernel>`
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- `Circle_2<Kernel>`
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In three-dimensional space, the types `Type1` and
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`Type2` can be any of the following:
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- `Plane_3<Kernel>`
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- `Line_3<Kernel>`
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- `Ray_3<Kernel>`
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- `Segment_3<Kernel>`
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- `Triangle_3<Kernel>`.
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- `Bbox_3`.
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Also, `Type1` and `Type2` can be respectively of types
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- `Triangle_3<Kernel>` and `Tetrahedron_3<Kernel>`
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- `Plane_3<Kernel>` and `Sphere_3<Kernel>` (or the contrary)
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- `Sphere_3<Kernel>` and `Sphere_3<Kernel>`.
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*/
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bool do_intersect(Type1<Kernel> obj1, Type2<Kernel> obj2);
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/// @}
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/*!
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\addtogroup do_intersect_circular do_intersect (2D Circular Kernel)
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\ingroup do_intersect
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\code
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#include <CGAL/Circular_kernel_intersections.h>
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\endcode
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\sa \ref do_intersect_linear
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\sa \ref do_intersect_spherical
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\sa \link intersection `CGAL::intersection()` \endlink
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\details See Chapter \ref Chapter_2D_Circular_Geometry_Kernel "2D Circular Geometry Kernel" for details on a circular kernel instantiation.
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When using a circular kernel, in addition to the function overloads documented \ref do_intersect_linear "here",
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the following function overloads are also available.
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*/
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/// @{
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/*!
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checks whether `obj1` and `obj2` intersect. Two objects `obj1` and
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`obj2` intersect if there is a point `p` that is part of both `obj1`
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and `obj2`. The intersection region of those two objects is defined
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as the set of all points `p` that are part of both `obj1` and `obj2`.
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Note that for objects like triangles and polygons that enclose a
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bounded region, this region is part of the object.
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`Type1` and `Type2` can be any of
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the following:
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- `Line_2<CircularKernel>`
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- `Circle_2<CircularKernel>`
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- `Line_arc_2<CircularKernel>`
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- `Circular_arc_2<CircularKernel>`
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An example illustrating this is presented in
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Chapter \ref Chapter_2D_Circular_Geometry_Kernel "2D Circular Geometry Kernel".
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*/
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bool do_intersect(Type1<CircularKernel> obj1, Type2<CircularKernel> obj2);
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/// @}
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/*!
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\addtogroup do_intersect_spherical do_intersect (3D Spherical Kernel)
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\ingroup do_intersect
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\code
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#include <CGAL/Spherical_kernel_intersections.h>
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\endcode
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\sa \ref do_intersect_linear
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\sa \ref do_intersect_circular
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\sa \link intersection `CGAL::intersection()` \endlink
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\details See Chapter \ref Chapter_3D_Spherical_Geometry_Kernel "3D Spherical Geometry Kernel" for details on a spherical kernel instantiation.
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When using a circular kernel, in addition to the function overloads documented \ref do_intersect_linear "here",
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the following function overloads are also available.
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*/
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/// @{
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/*!
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checks whether `obj1` and `obj2` intersect. Two objects `obj1` and
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`obj2` intersect if there is a point `p` that is part of both `obj1`
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and `obj2`. The intersection region of those two objects is defined
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as the set of all points `p` that are part of both `obj1` and `obj2`.
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Note that for objects like triangles and polygons that enclose a
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bounded region, this region is part of the object.
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`Type1` and `Type2` can be any of
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the following:
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- `Line_3<SphericalKernel>`
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- `Circle_3<SphericalKernel>`
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- `Plane_3<SphericalKernel>`
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- `Sphere_3<SphericalKernel>`
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- `Line_arc_3<SphericalKernel>`
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- `Circular_arc_3<SphericalKernel>`
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An example illustrating this is presented in
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Chapter \ref Chapter_3D_Spherical_Geometry_Kernel "3D Spherical Geometry Kernel".
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*/
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bool do_intersect(Type1<SphericalKernel> obj1, Type2<SphericalKernel> obj2);
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/*!
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checks whether `obj1`, `obj2` and `obj3` intersect.
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`Type1`, `Type2` and `Type3` can be:
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- `Sphere_3<SphericalKernel>`
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- `Plane_3<SphericalKernel>`
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*/
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bool do_intersect(Type1<SphericalKernel> obj1, Type2<SphericalKernel> obj2, Type3<SphericalKernel> obj3);
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/// @}
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/*!
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\addtogroup intersection
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\brief
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\details Depending on which \cgal kernel is used, different overloads of this global
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function are available.
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*/
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/*!
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\addtogroup intersection_linear intersection (2D/3D Linear Kernel)
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\ingroup intersection
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\code
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#include <CGAL/intersections.h>
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\endcode
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\sa intersection_circular
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\sa intersection_spherical
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\sa \link do_intersect `CGAL::do_intersect()` \endlink
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\sa `CGAL::Object`
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\details See Chapter \ref chapterkernel23 "2D and 3D Geometry Kernel" for details on a linear kernel instantiation.
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*/
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/// @{
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/*!
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Two objects `obj1` and `obj2` intersect if there is a point `p` that
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is part of both `obj1` and `obj2`. The intersection region of those
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two objects is defined as the set of all points `p` that are part of
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both `obj1` and `obj2`. Note that for objects like triangles and
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polygons that enclose a bounded region, this region is considered part
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of the object. If a segment lies completely inside a triangle, then
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those two objects intersect and the intersection region is the
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complete segment.
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The possible value for types `Type1` and `Type2` and the
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possible return values wrapped in `Object` are the
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following:
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<DIV ALIGN="CENTER">
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<TABLE CELLPADDING=3 BORDER="1">
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<TR> <TH> Type1 </TH>
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<TH> Type2 </TH>
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<TH> Return Type: Object<Type> </TH>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Iso_rectangle_2 </TD>
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<TD VALIGN="CENTER" > Iso_rectangle_2 </TD>
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<TD>Iso_rectangle_2</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Iso_rectangle_2 </TD>
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<TD VALIGN="CENTER" > Line_2 </TD>
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<TD>Point_2, or Segment_2</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Iso_rectangle_2 </TD>
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<TD VALIGN="CENTER" > Ray_2 </TD>
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<TD>Point_2, or Segment_2</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Iso_rectangle_2 </TD>
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<TD VALIGN="CENTER" > Segment_2 </TD>
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<TD>Point_2, or Segment_2</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Iso_rectangle_2 </TD>
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<TD VALIGN="CENTER" > Triangle_2 </TD>
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<TD>Point_2, or Segment_2, or Triangle_2, or std::vector<Point_2></TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Line_2 </TD>
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<TD VALIGN="CENTER" > Line_2 </TD>
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<TD>Point_2, or Line_2</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Line_2 </TD>
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<TD VALIGN="CENTER" > Ray_2 </TD>
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<TD>Point_2, or Ray_2</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Line_2 </TD>
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<TD VALIGN="CENTER" > Segment_2 </TD>
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<TD>Point_2, or Segment_2</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Line_2 </TD>
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<TD VALIGN="CENTER" > Triangle_2 </TD>
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<TD>Point_2, or Segment_2</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Ray_2 </TD>
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<TD VALIGN="CENTER" > Ray_2 </TD>
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<TD>Point_2, or Segment_2, or Ray_2</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Ray_2 </TD>
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<TD VALIGN="CENTER" > Segment_2 </TD>
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<TD>Point_2, or Segment_2</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Ray_2 </TD>
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<TD VALIGN="CENTER" > Triangle_2 </TD>
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<TD>Point_2, or Segment_2</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Segment_2 </TD>
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<TD VALIGN="CENTER" > Segment_2 </TD>
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<TD>Point_2, or Segment_2</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Segment_2 </TD>
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<TD VALIGN="CENTER" > Triangle_2 </TD>
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<TD>Point_2, or Segment_2</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Triangle_2 </TD>
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<TD VALIGN="CENTER" > Triangle_2 </TD>
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<TD>Point_2, or Segment_2, or Triangle_2, or std::vector<Point_2></TD>
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</TR>
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</TABLE>
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<TABLE CELLPADDING=3 BORDER="1">
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<TR> <TH> Type1 </TH>
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<TH> Type2 </TH>
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<TH> Return Type: Object<Type> </TH>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Line_3 </TD>
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<TD VALIGN="CENTER" > Line_3 </TD>
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<TD>Point_3, or Line_3</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Line_3 </TD>
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<TD VALIGN="CENTER" > Plane_3 </TD>
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<TD>Point_3, or Line_3</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Line_3 </TD>
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<TD VALIGN="CENTER" > Ray_3 </TD>
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<TD>Point_3, or Ray_3</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Line_3 </TD>
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<TD VALIGN="CENTER" > Segment_3 </TD>
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<TD>Point_3, or Segment_3</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Line_3 </TD>
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<TD VALIGN="CENTER" > Triangle_3 </TD>
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<TD>Point_3, or Segment_3</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Plane_3 </TD>
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<TD VALIGN="CENTER" > Plane_3 </TD>
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<TD>Line_3, or Plane_3</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Plane_3 </TD>
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<TD VALIGN="CENTER" > Ray_3 </TD>
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<TD>Point_3, or Ray_3</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Plane_3 </TD>
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<TD VALIGN="CENTER" > Segment_3 </TD>
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<TD>Point_3, or Segment_3</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Plane_3 </TD>
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<TD VALIGN="CENTER" > Sphere_3 </TD>
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<TD>Point_3, or Circle_3</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Plane_3 </TD>
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<TD VALIGN="CENTER" > Triangle_3 </TD>
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<TD>Point_3, or Segment_3, or Triangle_3</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Ray_3 </TD>
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<TD VALIGN="CENTER" > Ray_3 </TD>
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<TD>Point_3, or Ray_3, or Segment_3</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Ray_3 </TD>
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<TD VALIGN="CENTER" > Segment_3 </TD>
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<TD>Point_3, or Segment_3</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Ray_3 </TD>
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<TD VALIGN="CENTER" > Triangle_3 </TD>
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p <TD>Point_3, or Segment_3</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Segment_3 </TD>
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<TD VALIGN="CENTER" > Segment_3 </TD>
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<TD>Point_3, or Segment_3</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Segment_3 </TD>
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<TD VALIGN="CENTER" > Triangle_3 </TD>
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<TD>Point_3, or Segment_3</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Sphere_3 </TD>
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<TD VALIGN="CENTER" > Sphere_3 </TD>
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<TD>Point_3, or Circle_3, or Sphere_3</TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Triangle_3 </TD>
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<TD VALIGN="CENTER" > Triangle_3 </TD>
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<TD>Point_3, or Segment_3, or Triangle_3, or std::vector < Point_3 ></TD>
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</TR>
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</TABLE>
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</DIV>
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\cgalHeading{Example}
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The following example demonstrates the most common use of
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`intersection` routines with the 2D and 3D Linear %Kernel.
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\code
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#include <CGAL/intersections.h>
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void foo(CGAL::Segment_2<Kernel> seg, CGAL::Line_2<Kernel> line)
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{
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CGAL::Object result = CGAL::intersection(seg, line);
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if (const CGAL::Point_2<Kernel> *ipoint = CGAL::object_cast<CGAL::Point_2<Kernel> >(&result)) {
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// handle the point intersection case with *ipoint.
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} else
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if (const CGAL::Segment_2<Kernel> *iseg = CGAL::object_cast<CGAL::Segment_2<Kernel> >(&result)) {
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// handle the segment intersection case with *iseg.
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} else {
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// handle the no intersection case.
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}
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}
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\endcode
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*/
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Object intersection(Type1<Kernel> obj1, Type2<Kernel> obj2);
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/*!
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returns the intersection of 3 planes, which can be either a
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point, a line, a plane, or empty.
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*/
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Object intersection(const Plane_3<Kernel>& pl1,
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const Plane_3<Kernel>& pl2,
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const Plane_3<Kernel>& pl3);
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/// @}
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/*!
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\addtogroup intersection_circular intersection (2D Circular Kernel)
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\ingroup intersection
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\code
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#include <CGAL/Circular_kernel_intersections.h>
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\endcode
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\sa intersection_linear
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\sa intersection_spherical
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\sa \link do_intersect `CGAL::do_intersect()` \endlink
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\sa `CGAL::Object`
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\details See Chapter \ref Chapter_2D_Circular_Geometry_Kernel "2D Circular Geometry Kernel" for details on a circular kernel instantiation.
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When using a circular kernel, in addition to the function overloads documented \ref intersection_linear "here",
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the following function overloads are also available.
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Since both the number of intersections, if any, and their type,
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depend on the arguments, the function returns an output
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iterator on `Object`'s, as presented below.
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*/
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/// @{
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/*!
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Copies in the output iterator the intersection elements between the
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two objects. `intersections` iterates on
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elements of type `CGAL::Object`, in lexicographic order,
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where `Type1` and `Type2` can both be either
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- `Line_2<CircularKernel>` or
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- `Line_arc_2<CircularKernel>` or
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- `Circle_2<CircularKernel>` or
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- `Circular_arc_2<CircularKernel>`
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\details Depending on the types `Type1` and `Type2`, these elements can be assigned to
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- `std::pair<Circular_arc_point_2<CircularKernel>, unsigned>`,
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where the unsigned integer is the multiplicity of the corresponding
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intersection point between `obj1` and `obj2`,
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- `Circular_arc_2<CircularKernel>` in case of an overlap of
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two circular arcs,
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- `Line_arc_2<CircularKernel>` in case of an overlap of two
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line segments or
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- `Line_2<CircularKernel>` or
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`Circle_2<CircularKernel>` in case of two equal input lines or circles.
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*/
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template < typename Type1, typename Type2, typename OutputIterator >
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OutputIterator
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intersection(const Type1 &obj1, const Type2 &obj2,
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OutputIterator intersections);
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/// @}
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/*!
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\addtogroup intersection_spherical intersection (3D Spherical Kernel)
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\ingroup intersection
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\code
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#include <CGAL/Spherical_kernel_intersections.h>
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\endcode
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\sa intersection_linear
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\sa intersection_circular
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\sa \link do_intersect `CGAL::do_intersect()` \endlink
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\sa `CGAL::Object`
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\details See Chapter \ref Chapter_3D_Spherical_Geometry_Kernel "3D Spherical Geometry Kernel" for details on a spherical kernel instantiation.
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When using a spherical kernel, in addition to the function overloads documented \ref intersection_linear "here",
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the following function overloads are also available.
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Since both the number of intersections, if any, and their type,
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depend on the arguments, the functions return an output
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iterator on `Object`'s, as presented below.
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*/
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/// @{
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/*!
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Copies in the output iterator the intersection elements between the
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two objects. `intersections` iterates on
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elements of type `CGAL::Object`, in lexicographic order,
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when this ordering is defined on the computed objects,
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where `SphericalType1` and `SphericalType2` can both be either:
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- `Sphere_3<SphericalKernel>`,
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- `Plane_3<SphericalKernel>`,
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- `Line_3<SphericalKernel>`,
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- `Circle_3<SphericalKernel>`,
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- `Line_arc_3<SphericalKernel>` or
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- `Circular_arc_3<SphericalKernel>`,
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and depending on the types `SphericalType1` and `SphericalType2`, the computed
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`CGAL::Object`s can be assigned to
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- `std::pair<Circular_arc_point_3<SphericalKernel>, unsigned>`,
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where the unsigned integer is the multiplicity of the corresponding
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intersection point between `obj1` and `obj2`,
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- `SphericalType1`, when `SphericalType1` and `SphericalType2` are equal,
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and if the two objets `obj1` and `obj2` are equal,
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- `Line_3<SphericalKernel>` or
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`Circle_3<SphericalKernel>` when `SphericalType1` and `SphericalType2`
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are two-dimensional objets intersecting along a curve (2 planes, or 2
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spheres, or one plane and one sphere),
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- `Circular_arc_3<SphericalKernel>` in case of an overlap of
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two circular arcs or
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- `Line_arc_3<SphericalKernel>` in case of an overlap of two
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line segments.
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*/
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template < typename SphericalType1, typename SphericalType1, typename OutputIterator >
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OutputIterator
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intersection(const SphericalType1 &obj1, const SphericalType2 &obj2,
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OutputIterator intersections);
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|
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/*!
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Copies in the output iterator the intersection elements between the
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three objects. `intersections` iterates on
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|
elements of type `CGAL::Object`, in lexicographic order
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when this ordering is defined on the computed objects
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where `Type1`, `Type2` and `Type3`
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can be either
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- `Sphere_3<SphericalKernel>` or
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- `Plane_3<SphericalKernel>`
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and depending of these types, the computed `CGAL::Object`s can be
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assigned to
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- `std::pair<Circular_arc_point_3<SphericalKernel>, unsigned>`,
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where the unsigned integer is the multiplicity of the corresponding
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intersection point,
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- `Circle_3<SphericalKernel>` or
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- `Type1`, when `Type1`, `Type2` and
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`Type3` are equal, and if the three objets `obj1` and `obj2`
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and `obj3` are equal.
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*/
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template < typename Type1, typename Type2, typename OutputIterator >
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OutputIterator
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intersection(const Type1 &obj1, const Type2 &obj2, const Type3 &obj3,
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OutputIterator intersections);
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/// @}
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}
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