Revision 1d7da5b79fddc413a3218c0e0b546fa69f15de54 authored by Laurent Rineau on 06 March 2015, 08:18:03 UTC, committed by Laurent Rineau on 06 March 2015, 08:18:03 UTC
1 parent 39a43e3
intersections.h
/// \file intersections.h
/*!
\def CGAL_INTERSECTION_VERSION
\ingroup intersection_grp
The macro `CGAL_INTERSECTION_VERSION` can be used to configure
which version of the \ref intersection_grp function should be used and
enables the corresponding APIs in other \cgal packages. It should be
defined before any \cgal header is included.
- `CGAL_INTERSECTION_VERSION == 1` \ref intersection_grp uses `Object`
- `CGAL_INTERSECTION_VERSION == 2` \ref intersection_grp uses `boost::optional< boost::variant< T... > >`
*/
#define CGAL_INTERSECTION_VERSION
namespace CGAL {
/*!
\addtogroup do_intersect_grp
\brief
\details Depending on which \cgal kernel is used, different overloads of this global
function are available.
*/
/*!
\addtogroup do_intersect_linear_grp
\ingroup do_intersect
\sa `do_intersect_circular_grp`
\sa `do_intersect_spherical_grp`
\sa `intersection_grp`
\details See Chapter \ref chapterkernel23 "2D and 3D Geometry Kernel" for details on a linear kernel instantiation.
*/
/// @{
/*!
checks whether `obj1` and `obj2` intersect. Two objects `obj1` and
`obj2` intersect if there is a point `p` that is part of both `obj1`
and `obj2`. The intersection region of those two objects is defined
as the set of all points `p` that are part of both `obj1` and `obj2`.
Note that for objects like triangles and polygons that enclose a
bounded region, this region is part of the object.
The types `Type1` and `Type2` can be any of the following:
- `Point_2<Kernel>`
- `Line_2<Kernel>`
- `Ray_2<Kernel>`
- `Segment_2<Kernel>`
- `Triangle_2<Kernel>`
- `Iso_rectangle_2<Kernel>`
Also, `Type1` and `Type2` can be both of type
- `Line_2<Kernel>`
- `Circle_2<Kernel>`
In three-dimensional space, the types `Type1` and
`Type2` can be any of the following:
- `Plane_3<Kernel>`
- `Line_3<Kernel>`
- `Ray_3<Kernel>`
- `Segment_3<Kernel>`
- `Triangle_3<Kernel>`.
- `Bbox_3`.
Also, `Type1` and `Type2` can be respectively of types
- `Triangle_3<Kernel>` and `Tetrahedron_3<Kernel>`
- `Plane_3<Kernel>` and `Sphere_3<Kernel>` (or the contrary)
- `Sphere_3<Kernel>` and `Sphere_3<Kernel>`.
*/
bool do_intersect(Type1<Kernel> obj1, Type2<Kernel> obj2);
/// @}
/*!
\addtogroup intersection_grp
\brief
\details Depending on which \cgal kernel is used, different overloads of this global
function are available.
\cgalHeading{Notes on Backward Compatibility}
The \ref intersection_grp function used to return an `Object`, but starting with
\cgal 4.2 the
return type is determined by a metafunction defined by the kernel. To
preserve backward compatibility `Object` can be
constructed from the new return types implicitly, but switching to the
new style is recommended. To enable the old style without any overhead,
the macro \link CGAL_INTERSECTION_VERSION `CGAL_INTERSECTION_VERSION` \endlink must be defined to
`1` before any \cgal header is included.
\sa \ref upgrading_object
\sa \ref do_intersect_grp
\sa CGAL_INTERSECTION_VERSION
*/
/*!
\addtogroup intersection_linear_grp
\ingroup intersection
*/
/// @{
/*!
Two objects `obj1` and `obj2` intersect if there is a point `p` that
is part of both `obj1` and `obj2`. The intersection region of those
two objects is defined as the set of all points `p` that are part of
both `obj1` and `obj2`. Note that for objects like triangles and
polygons that enclose a bounded region, this region is considered part
of the object. If a segment lies completely inside a triangle, then
those two objects intersect and the intersection region is the
complete segment.
Here, `Intersect_23` means either `Intersect_2` or `Intersect_3`,
depending on the arguments.
The following tables give the possible values for `Type1` and `Type2`.
\cgalHeading{2D intersections}
The return type can be obtained through `cpp11::result_of<Kernel::Intersect_2(A, B)>::%type`.
It is equivalent to `boost::optional< boost::variant< T... > >`, the last column in the table providing the template parameter pack.
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1">
<TR> <TH> Type1 </TH>
<TH> Type2 </TH>
<TH> Return Type: `T...` </TH>
</TR>
<TR>
<TD VALIGN="CENTER" > Iso_rectangle_2 </TD>
<TD VALIGN="CENTER" > Iso_rectangle_2 </TD>
<TD>Iso_rectangle_2</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Iso_rectangle_2 </TD>
<TD VALIGN="CENTER" > Line_2 </TD>
<TD>Point_2, or Segment_2</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Iso_rectangle_2 </TD>
<TD VALIGN="CENTER" > Ray_2 </TD>
<TD>Point_2, or Segment_2</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Iso_rectangle_2 </TD>
<TD VALIGN="CENTER" > Segment_2 </TD>
<TD>Point_2, or Segment_2</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Iso_rectangle_2 </TD>
<TD VALIGN="CENTER" > Triangle_2 </TD>
<TD>Point_2, or Segment_2, or Triangle_2, or std::vector<Point_2></TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Line_2 </TD>
<TD VALIGN="CENTER" > Line_2 </TD>
<TD>Point_2, or Line_2</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Line_2 </TD>
<TD VALIGN="CENTER" > Ray_2 </TD>
<TD>Point_2, or Ray_2</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Line_2 </TD>
<TD VALIGN="CENTER" > Segment_2 </TD>
<TD>Point_2, or Segment_2</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Line_2 </TD>
<TD VALIGN="CENTER" > Triangle_2 </TD>
<TD>Point_2, or Segment_2</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Ray_2 </TD>
<TD VALIGN="CENTER" > Ray_2 </TD>
<TD>Point_2, or Segment_2, or Ray_2</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Ray_2 </TD>
<TD VALIGN="CENTER" > Segment_2 </TD>
<TD>Point_2, or Segment_2</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Ray_2 </TD>
<TD VALIGN="CENTER" > Triangle_2 </TD>
<TD>Point_2, or Segment_2</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Segment_2 </TD>
<TD VALIGN="CENTER" > Segment_2 </TD>
<TD>Point_2, or Segment_2</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Segment_2 </TD>
<TD VALIGN="CENTER" > Triangle_2 </TD>
<TD>Point_2, or Segment_2</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Triangle_2 </TD>
<TD VALIGN="CENTER" > Triangle_2 </TD>
<TD>Point_2, or Segment_2, or Triangle_2, or std::vector<Point_2></TD>
</TR>
</TABLE>
</DIV>
\cgalHeading{3D intersections}
The return type can be obtained through `cpp11::result_of<Kernel::Intersect_3(A, B)>::%type`.
It is equivalent to `boost::optional< boost::variant< T... > >`, the last column in the table providing the template parameter pack.
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1">
<TR> <TH> Type1 </TH>
<TH> Type2 </TH>
<TH> Return Type: `T...` </TH>
</TR>
<TR>
<TD VALIGN="CENTER" > Line_3 </TD>
<TD VALIGN="CENTER" > Line_3 </TD>
<TD>Point_3, or Line_3</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Line_3 </TD>
<TD VALIGN="CENTER" > Plane_3 </TD>
<TD>Point_3, or Line_3</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Line_3 </TD>
<TD VALIGN="CENTER" > Ray_3 </TD>
<TD>Point_3, or Ray_3</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Line_3 </TD>
<TD VALIGN="CENTER" > Segment_3 </TD>
<TD>Point_3, or Segment_3</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Line_3 </TD>
<TD VALIGN="CENTER" > Triangle_3 </TD>
<TD>Point_3, or Segment_3</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Plane_3 </TD>
<TD VALIGN="CENTER" > Plane_3 </TD>
<TD>Line_3, or Plane_3</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Plane_3 </TD>
<TD VALIGN="CENTER" > Ray_3 </TD>
<TD>Point_3, or Ray_3</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Plane_3 </TD>
<TD VALIGN="CENTER" > Segment_3 </TD>
<TD>Point_3, or Segment_3</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Plane_3 </TD>
<TD VALIGN="CENTER" > Sphere_3 </TD>
<TD>Point_3, or Circle_3</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Plane_3 </TD>
<TD VALIGN="CENTER" > Triangle_3 </TD>
<TD>Point_3, or Segment_3, or Triangle_3</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Ray_3 </TD>
<TD VALIGN="CENTER" > Ray_3 </TD>
<TD>Point_3, or Ray_3, or Segment_3</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Ray_3 </TD>
<TD VALIGN="CENTER" > Segment_3 </TD>
<TD>Point_3, or Segment_3</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Ray_3 </TD>
<TD VALIGN="CENTER" > Triangle_3 </TD>
p <TD>Point_3, or Segment_3</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Segment_3 </TD>
<TD VALIGN="CENTER" > Segment_3 </TD>
<TD>Point_3, or Segment_3</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Segment_3 </TD>
<TD VALIGN="CENTER" > Triangle_3 </TD>
<TD>Point_3, or Segment_3</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Sphere_3 </TD>
<TD VALIGN="CENTER" > Sphere_3 </TD>
<TD>Point_3, or Circle_3, or Sphere_3</TD>
</TR>
<TR>
<TD VALIGN="CENTER" > Triangle_3 </TD>
<TD VALIGN="CENTER" > Triangle_3 </TD>
<TD>Point_3, or Segment_3, or Triangle_3, or std::vector < Point_3 ></TD>
</TR>
</TABLE>
</DIV>
\cgalHeading{Example}
The following example demonstrates the most common use of
`intersection` routines with the 2D and 3D Linear %Kernel.
\code
#include <CGAL/intersections.h>
template <typename R>
struct Intersection_visitor {
typedef void result_type;
void operator()(const Point_2<R>& p) const
{
// handle point
}
void operator()(const Segment_2<R>& s) const
{
// handle segment
}
};
template <typename R>
void foo (const Segment_2<R>& seg, const Line_2<R>& lin)
{
// with C++11 support
// auto result = intersection(seg, lin);
// without C++11
cpp11::result_of<R::Intersect_2(Segment_2<R>, Line_2<R>)>::type
result = intersection(seg, lin);
if (result) { boost::apply_visitor(Intersection_visitor(), *result); }
else {
// no intersection
}
// alternatively:
if (result) {
if (const Segment_2<R>* s = boost::get<Segment_2>(&*result)) {
// handle segment
} else {
const Point_2<R>* p = boost::get<Point_2<R> >(&*result);
// handle point
}
}
}
\endcode
Another example showing the use of the intersection function as a
plain function call and with `Dispatch_output_iterator` combined with
a standard library algorithm.
\cgalExample{Kernel_23/intersections.cpp}
*/
template <typename Kernel>
cpp11::result_of<Kernel::Intersect_23(Type1, Type2)>::type
intersection(Type1<Kernel> obj1, Type2<Kernel> obj2);
/*!
returns the intersection of 3 planes, which can be a
point, a line, a plane, or empty.
*/
template <typename Kernel>
boost::optional< boost::variant< Point_3, Line_3, Plane_3 > >
intersection(const Plane_3<Kernel>& pl1,
const Plane_3<Kernel>& pl2,
const Plane_3<Kernel>& pl3);
/// @}
}
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