mirror of https://github.com/CGAL/cgal
367 lines
10 KiB
C++
367 lines
10 KiB
C++
/// \file intersections.h
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/*!
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\def CGAL_INTERSECTION_VERSION
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\ingroup intersection_grp
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The macro `CGAL_INTERSECTION_VERSION` can be used to configure
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which version of the \ref intersection_grp function should be used and
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enables the corresponding APIs in other \cgal packages. It should be
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defined before any \cgal header is included.
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- `CGAL_INTERSECTION_VERSION == 1` \ref intersection_grp uses `Object`
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- `CGAL_INTERSECTION_VERSION == 2` \ref intersection_grp uses `boost::optional< boost::variant< T... > >`
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*/
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#define CGAL_INTERSECTION_VERSION
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namespace CGAL {
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/*!
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\addtogroup do_intersect_grp
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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_grp
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\ingroup do_intersect
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\sa `do_intersect_circular_grp`
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\sa `do_intersect_spherical_grp`
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\sa `intersection_grp`
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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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- `Line_3<Kernel>` and `Iso_cuboid_3<Kernel>`
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- `Ray_3<Kernel>` and `Iso_cuboid_3<Kernel>`
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- `Segment_3<Kernel>` and `Iso_cuboid_3<Kernel>`
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- `Iso_cuboid_3<Kernel>` and `Iso_cuboid_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 intersection_grp
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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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\cgalHeading{Notes on Backward Compatibility}
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The \ref intersection_grp function used to return an `Object`, but starting with
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\cgal 4.2 the
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return type is determined by a metafunction defined by the kernel. To
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preserve backward compatibility `Object` can be
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constructed from the new return types implicitly, but switching to the
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new style is recommended. To enable the old style without any overhead,
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the macro \link CGAL_INTERSECTION_VERSION `CGAL_INTERSECTION_VERSION` \endlink must be defined to
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`1` before any \cgal header is included.
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\sa \ref upgrading_object
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\sa \ref do_intersect_grp
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\sa CGAL_INTERSECTION_VERSION
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*/
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/*!
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\addtogroup intersection_linear_grp
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\ingroup intersection
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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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Here, `Intersect_23` means either `Intersect_2` or `Intersect_3`,
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depending on the arguments.
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The following tables give the possible values for `Type1` and `Type2`.
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\cgalHeading{2D Intersections}
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The return type can be obtained through `CGAL::cpp11::result_of<Kernel::Intersect_2(A, B)>::%type`.
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It is equivalent to `boost::optional< boost::variant< T... > >`, the last column in the table providing the template parameter pack.
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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: `T...` </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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</DIV>
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\cgalHeading{3D Intersections}
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The return type can be obtained through `CGAL::cpp11::result_of<Kernel::Intersect_3(A, B)>::%type`.
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It is equivalent to `boost::optional< boost::variant< T... > >`, the last column in the table providing the template parameter pack.
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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: `T...` </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{Examples}
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The following examples demonstrate the most common use of
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`intersection()` functions with the 2D and 3D Linear %Kernel.
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In the first two examples we intersect a segment and a line.
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The result type can be obtained with `CGAL::cpp11::result_of`. It looks simpler
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if you use a C++ compiler which supports `auto`,
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but you must anyways know that the result type is a `boost::optional<boost::variant<..> >`, in order to unpack the point or segment.
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<A HREF="http://www.boost.org/libs/optional/">`boost::optional`</A> comes in
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as there might be no intersection. <A HREF="http://www.boost.org/libs/variant/">`boost::variant`</A> comes in
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as, if there is an intersection, it is either a point or a segment.
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As explained in the boost manual pages for <A HREF="http://www.boost.org/libs/variant/">`boost::variant`</A>, there are two ways to access the variants. The first examples uses `boost::get`.
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\cgalExample{Kernel_23/intersection_get.cpp}
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The second example uses `boost::apply_visitor`.
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\cgalExample{Kernel_23/intersection_visitor.cpp}
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A third example shows the use of the intersection function as a
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plain function call and with `Dispatch_output_iterator`, combined with
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a standard library algorithm.
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\cgalExample{Kernel_23/intersections.cpp}
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*/
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template <typename Kernel>
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cpp11::result_of<Kernel::Intersect_23(Type1, Type2)>::type
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intersection(Type1<Kernel> obj1, Type2<Kernel> obj2);
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/*!
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returns the intersection of 3 planes, which can be a
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point, a line, a plane, or empty.
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*/
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template <typename Kernel>
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boost::optional< boost::variant< Point_3, Line_3, Plane_3 > >
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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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